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X-WR-CALNAME:IAS Mathematics
BEGIN:VEVENT
UID:d5440b52-6c21-4b84-8906-69a104d8cd51
DTSTAMP:20200808T213738Z
CREATED:20200124T160538Z
DESCRIPTION:Topic: Using discrepancy theory to improve the design of random
ized controlled trials\n\nSpeaker: Daniel Spielman\, Yale University\n\nVi
deo: https://video.ias.edu/csdm/2020/0511-DanielSpielman\n\nIn randomized
experiments\, such as a medical trials\, we randomly assign the treatment\
, such as a drug or a placebo\, that each experimental subject receives. R
andomization can help us accurately estimate the difference in treatment e
ffects with high probability. We also know that we want the two groups to
be similar: ideally the two groups would be similar in every statistic we
can measure beforehand. Recent advances in algorithmic discrepancy theory
allow us to divide subjects into groups with similar statistics.\n\nBy exp
loiting the Gram-Schmidt Walk algorithm of Bansal\, Dadush\, Garg\, and Lo
vett\, we can obtain random assignments of low discrepancy. These allow us
to obtain more accurate estimates of treatment effects when the informati
on we measure about the subjects is predictive\, while also bounding the w
orst-case behavior when it is not.\n\nIn this talk\, I will formally expla
in the problem of estimating treatment effects in randomized controlled tr
ials\, the dangers of using fancy inference techniques instead of fancy de
signs\, how we use the Gram-Schmidt Walk algorithm\, a tight analysis of t
his algorithm\, and how we use it to obtain confidence intervals. I hope t
o explain just how much we don't yet know.\n\nThis is joint work with Chri
stopher Harshaw\, Fredrik Sävje\, and Peng Zhang.
DTSTART:20200511T150000Z
DTEND:20200511T160000Z
LAST-MODIFIED:20200515T011654Z
LOCATION:https://theias.zoom.us/j/360043913
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/node/108111
END:VEVENT
BEGIN:VEVENT
UID:6e68da36-17d2-4343-9bd1-8b2ce5e98bd0
DTSTAMP:20200808T213738Z
CREATED:20200423T184346Z
DESCRIPTION:Topic: Convex Set Disjointness\, Distributed Learning of Halfsp
aces\, and Linear Programming\n\nSpeaker: Shay Moran\, Member\, School of
Mathematics\n\nVideo: https://video.ias.edu/csdm/2020/0512-ShayMoran\n\nDi
stributed learning protocols are designed to train on distributed data wit
hout gathering it all on a single centralized machine\, thus contributing
to the efficiency of the system and enhancing its privacy. We study a cent
ral problem in distributed learning\, called Distributed Learning of Halfs
paces: let U \subset R^d be a known domain of size n and let h:R^d —> R be
an unknown target affine function. A set of examples {(u\,b)} is distribu
ted between several parties\, where u \in U is a point and b = sign(h(u))
\in {-1\, +1} is its label. The parties' goal is to agree\, using minimum
communication\, on a classifier f: U—>{-1\,+1} such that f(u)=b for every
input example (u\,b). (In practice\, the finite domain U is defined implic
itly by the representation of d-dimensional vectors which is used in the p
rotocol.) We establish a (nearly) tight bound of ~$\Theta$ (d*log n) on th
e communication complexity of the problem of distributed learning of halfs
paces in the two-party setting. Since this problem is closely related to t
he Convex Set Disjointness problem in communication complexity and the pro
blem of Distributed Linear Programming in distributed optimization\, we ar
e able to derive upper and lower bounds of ~O(d^2\log n) and ~Ω(d\log n) f
or both of these basic problems as well. Our main technical contribution l
ies in the design and analysis of the protocols which imply the upper boun
ds. To this end\, we introduce a technique called Halfspace Containers\, a
llowing for a compressed approximate representation of every halfspace. Ha
lfspace containers may be of independent interest and are closely related
to bracketing numbers in statistics and to hyperplane cuttings in discrete
geometry. Joint paper with Mark Braverman\, Gillat Kol\, and Raghuvansh R
Saxena
DTSTART:20200512T143000Z
DTEND:20200512T163000Z
LAST-MODIFIED:20200515T011733Z
LOCATION:https://theias.zoom.us/j/360043913
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/node/110746
END:VEVENT
BEGIN:VEVENT
UID:72b1b5c8-8a9d-44c0-9a22-bc9821345a8b
DTSTAMP:20200808T213738Z
CREATED:20200413T175029Z
DESCRIPTION:Topic: Quantitative decompositions of Lipschitz mappings\n\nSpe
aker: Guy C. David\, Ball State University\n\nGiven a Lipschitz map\, it i
s often useful to chop the domain into pieces on which the map has simple
behavior. For example\, depending on the dimensions of source and target\,
one may ask for pieces on which the map behaves like a bi-Lipschitz embed
ding or like a linear projection. For many issues\, it is even more useful
if this decomposition is quantitative\, i.e.\, with bounds independent of
the particular map or spaces involved. After surveying the question of bi
-Lipschitz decomposition\, we will discuss the more complicated case in wh
ich dimension decreases\, e.g.\, for maps from $\mathbb{R}^3$ to $\mathbb{
R}^2$.\n\nThis is recent joint work with Raanan Schul\, improving a previo
us result of Azzam-Schul.
DTSTART:20200512T150000Z
DTEND:20200512T160000Z
LAST-MODIFIED:20200515T011813Z
LOCATION:https://theias.zoom.us/j/562592856
SUMMARY:Analysis Seminar
URL:https://www.ias.edu/node/110496
END:VEVENT
BEGIN:VEVENT
UID:5018a574-4890-45cb-8313-5cc4bbea0d6b
DTSTAMP:20200808T213738Z
CREATED:20200506T110655Z
DESCRIPTION:Topic: Generative Modeling by Estimating Gradients of the Data
Distribution\n\nSpeaker: Stefano Ermon\, Stanford University\n\nVideo: htt
ps://video.ias.edu/machinelearning/2020/0512-StefanoErmon\n\nExisting gene
rative models are typically based on explicit representations of probabili
ty distributions (e.g.\, autoregressive or VAEs) or implicit sampling proc
edures (e.g.\, GANs). We propose an alternative approach based on modeling
directly the vector field of gradients of the data distribution (scores).
Our framework allows flexible energy-based model architectures\, requires
no sampling during training or the use of adversarial training methods. U
sing annealed Langevin dynamics\, we produces samples comparable to GANs o
n MNIST\, CelebA and CIFAR-10 datasets\, achieving a new state-of-the-art
inception score of 8.91 on CIFAR-10. Finally\, I will discuss challenges i
n evaluating bias and generalization in generative models.
DTSTART:20200512T160000Z
DTEND:20200512T173000Z
LAST-MODIFIED:20200515T011850Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/110876
END:VEVENT
BEGIN:VEVENT
UID:10ed4945-e31c-43b4-b2c4-e3586e18016e
DTSTAMP:20200808T213738Z
CREATED:20200506T112306Z
DESCRIPTION:Topic: The Simplicity Conjecture\n\nSpeaker: Daniel Cristofaro-
Gardiner\, University of California\, Santa Cruz\; von Neumann Fellow\, Sc
hool of Mathematics\n\nIn the 60s and 70s\, there was a flurry of activity
concerning the question of whether or not various subgroups of homeomorph
ism groups of manifolds are simple\, with beautiful contributions by Fathi
\, Kirby\, Mather\, Thurston\, and many others. A funnily stubborn case th
at remained open was the case of area-preserving homeomorphisms of surface
s. For example\, for balls of dimension at least 3\, the relevant group wa
s shown to be simple by work of Fathi in 1980\; but\, the answer in the tw
o-dimensional case\, asked by Mather in the 70s\, was not known. We recent
ly answered Mather's question by showing that the group of compactly suppo
rted area-preserving homeomorphisms of the two-disc is in fact not simple.
After surveying the history described above\, I will give a very gentle i
ntroduction to some of the key ideas in our proof\; what is crucial is the
fact that the 2-ball with its volume form is a symplectic manifold. Our w
ork underscores that it is natural to study continuous symplectic geometry
\, and I will briefly explain what this means.
DTSTART:20200513T213000Z
DTEND:20200513T230000Z
LAST-MODIFIED:20200509T185444Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/110881
END:VEVENT
BEGIN:VEVENT
UID:6bc4f603-3541-435a-89b5-ae43b42ec175
DTSTAMP:20200808T213738Z
CREATED:20200420T122707Z
DESCRIPTION:Topic: A geometric view on Iwasawa theory\n\nSpeaker: Mladen D
imitrov\, Université de Lille\n\nVideo: https://video.ias.edu/puias/2020/0
514-MladenDimitrov\n\nWe will investigate the geometry of the p-adic eigen
curve at classical points where the Galois representation is locally trivi
al at p\, and will give applications to Iwasawa and Hida theories.
DTSTART:20200514T183000Z
DTEND:20200514T193000Z
LAST-MODIFIED:20200515T011934Z
LOCATION:https://theias.zoom.us/j/959183254
SUMMARY:Joint IAS/Princeton University Number Theory Seminar
URL:https://www.ias.edu/node/110596
END:VEVENT
BEGIN:VEVENT
UID:cbce2448-9368-4e1b-8f11-9c5ce44f43c3
DTSTAMP:20200808T213738Z
CREATED:20191025T211502Z
DESCRIPTION:Topic: MathZero\, The Classification Problem\, and Set-Theoreti
c Type Theory\n\nSpeaker: David McAllester\, Toyota Technological Institut
e at Chicago \n\nVideo: https://video.ias.edu/machinelearning/2020/0514-Da
vidMcAllester\n\nAlphaZero learns to play go\, chess and shogi at a superh
uman level through self play given only the rules of the game. This raises
the question of whether a similar thing could be done for mathematics ---
a MathZero. MathZero would require a formal foundation and an objective.
We propose the foundation of set-theoretic dependent type theory and an ob
jective defined in terms of the classification problem --- the problem of
classifying concept instances up to isomorphism. Isomorphism is central to
the structure of mathematics. Mathematics is organized around concepts su
ch as graphs\, groups\, topological spaces and manifolds each of which is
associated with a notion of isomorphism. Each concept is associated with a
classification problem --- the problem of enumerating the instances of a
given concept up to isomorphism. The natural numbers arise as the solution
to the classification problem for finite sets. In this talk we attempt to
set the stage for MathZero by giving what we believe to be the first isom
orphism inference rules for set-theoretic dependent type theory with propo
sitional set-theoretic equality. The presentation is intended to be access
ible to mathematicians with no prior exposure to type theory.
DTSTART:20200514T190000Z
DTEND:20200514T203000Z
LAST-MODIFIED:20200515T012016Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/106041
END:VEVENT
BEGIN:VEVENT
UID:43540bbe-697d-4cdd-8a36-9151831f239b
DTSTAMP:20200808T213738Z
CREATED:20200420T142606Z
DESCRIPTION:Topic: Reflections on Cylindrical Contact Homology\n\nSpeaker:
Jo Nelson\, Rice University\n\nVideo: https://video.ias.edu/puias/2020/051
5-JoNelson\n\nThis talk beings with a light introduction\, including some
historical anecdotes to motivate the development of this Floer theoretic m
achinery for contact manifolds some 25 years ago. I will discuss joint wor
k with Hutchings which constructs nonequivariant and a family Floer equiva
riant version of contact homology. Both theories are generated by two copi
es of each Reeb orbit over Z and capture interesting torsion information.
I will explain the need for an obstruction bundle gluing correction term i
n the expression of the differential in the presence of contractible Reeb
orbits\, which is essential even in the simple example of an ellipsoid. I
will then explain how one can recover the original cylindrical theory prop
osed by Eliashberg-Givental-Hofer via our constructions.
DTSTART:20200515T130000Z
DTEND:20200515T143000Z
LAST-MODIFIED:20200518T001716Z
LOCATION:https://princeton.zoom.us/j/745635914
SUMMARY:IAS/PU-Montreal-Tel-Aviv Symplectic Geometry Seminar
URL:https://www.ias.edu/node/110621
END:VEVENT
BEGIN:VEVENT
UID:9b329e0c-6c7a-4f97-a869-c725f80e72d2
DTSTAMP:20200808T213738Z
CREATED:20200506T112735Z
DESCRIPTION:Topic: Square function estimate for the cone in R^3\n\nSpeaker:
Hong Wang\, Member\, School of Mathematics\n\nVideo: https://video.ias.ed
u/analysis/2020/05/18-HongWang\n\nWe prove a sharp square function estimat
e for the cone in R^3 and consequently the local smoothing conjecture for
the wave equation in 2+1 dimensions. The proof uses induction on scales an
d an incidence estimate for points and tubes.\n\nThis is joint work with L
arry Guth and Ruixiang Zhang.
DTSTART:20200518T150000Z
DTEND:20200518T160000Z
LAST-MODIFIED:20200518T180249Z
LOCATION:Remote Access via Zoom videoconferencing (link below)
SUMMARY:Analysis Seminar
URL:https://www.ias.edu/node/110886
END:VEVENT
BEGIN:VEVENT
UID:44cb234b-d667-4ff2-b6ba-82cbab8a8105
DTSTAMP:20200808T213738Z
CREATED:20200423T185014Z
DESCRIPTION:Topic: The Non-Stochastic Control Problem\n\nSpeaker: Elad Haza
n\, Princeton University\n\nVideo: https://video.ias.edu/csdm/2020/0518-El
adHazan\n\nLinear dynamical systems are a continuous subclass of reinforce
ment learning models that are widely used in robotics\, finance\, engineer
ing\, and meteorology. Classical control\, since the work of Kalman\, has
focused on dynamics with Gaussian i.i.d. noise\, quadratic loss functions
and\, in terms of provably efficient algorithms\, known systems and observ
ed state. We'll discuss how to apply new machine learning methods which re
lax all of the above: efficient control with adversarial noise\, general l
oss functions\, unknown systems\, and partial observation.\n\nBased on a s
eries of works with Naman Agarwal\, Nataly Brukhim\, Karan Singh\, Sham Ka
kade\, Max Simchowitz\, Cyril Zhang\, Paula Gradu\, John Hallman
DTSTART:20200518T150000Z
DTEND:20200518T160000Z
LAST-MODIFIED:20200518T180314Z
LOCATION:https://theias.zoom.us/j/360043913
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/node/110751
END:VEVENT
BEGIN:VEVENT
UID:c811b5b4-32dd-48f5-b70b-e69275f8ede7
DTSTAMP:20200808T213738Z
CREATED:20200515T121054Z
DESCRIPTION:Topic: Neural SDEs: Deep Generative Models in the Diffusion Lim
it\n\nSpeaker: Maxim Raginsky\, University of Illinois Urbana-Champaign\n
\nVideo: https://video.ias.edu/tml/2020/0519-MaximRaginsky\n\nIn deep gene
rative models\, the latent variable is generated by a time-inhomogeneous M
arkov chain\, where at each time step we pass the current state through a
parametric nonlinear map\, such as a feedforward neural net\, and add a sm
all independent Gaussian perturbation. In this talk\, based on joint work
with Belinda Tzen\, I will discuss the diffusion limit of such models\, wh
ere we increase the number of layers while sending the step size and the n
oise variance to zero. I will first provide a unified viewpoint on both sa
mpling and variational inference in such generative models through the len
s of stochastic control. Then I will show how we can quantify the expressi
veness of diffusion-based generative models. Specifically\, I will prove t
hat one can efficiently sample from a wide class of terminal target distri
butions by choosing the drift of the latent diffusion from the class of mu
ltilayer feedforward neural nets\, with the accuracy of sampling measured
by the Kullback-Leibler divergence to the target distribution. Finally\, I
will briefly discuss a scheme for unbiased\, finite-variance simulation i
n such models. This scheme can be implemented as a deep generative model w
ith a random number of layers.
DTSTART:20200519T160000Z
DTEND:20200519T173000Z
LAST-MODIFIED:20200519T183213Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/110971
END:VEVENT
BEGIN:VEVENT
UID:ec93ed9e-8443-4fc8-b643-bcf5628898fa
DTSTAMP:20200808T213738Z
CREATED:20200511T183237Z
DESCRIPTION:Topic: Conley's fundamental theorem of dynamical systems\n\nSpe
aker: Amie Wilkinson\, University of Chicago\n\nIn 1978\, Charles Conley c
lassified all continuous dynamical systems. His theorem\, dubbed the 'fund
amental theorem of dynamical systems' states that the orbits of any contin
uous map on a compact metric space fall into two classes: gradient-like an
d recurrent. When the recurrent part is factored out\, the dynamics appear
to be gradient-like. While one might wonder how a theorem that applies to
every continuous map could be of any use\, it plays a foundational role i
n many deep results.
DTSTART:20200520T213000Z
DTEND:20200520T230000Z
LAST-MODIFIED:20200518T134724Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/110951
END:VEVENT
BEGIN:VEVENT
UID:2271c93b-d390-418a-849c-96b9a44a44fa
DTSTAMP:20200808T213738Z
CREATED:20200507T143913Z
DESCRIPTION:Topic: Iwasawa theory and Bloch-Kato conjecture for unitary gro
ups\n\nSpeaker: Xin Wan\, Morningside Center of Mathematics\, Chinese Acad
emy of Sciences\n\nVideo: https://video.ias.edu/jointnumbertheory/2020/052
1-XinWan\n\nWe describe a new method to study Eisenstein family and Iwasaw
a theory on unitary groups over totally real fields of general signatures.
As a consequence we prove that if the central L-value of a cuspidal eigen
form on the unitary group twisted by a CM character is 0\, then the corres
ponding Selmer group has positive rank. The method also has a byproduct th
e p-adic functional equations for p-adic L-functions and p-adic families o
f Eisenstein series on unitary groups.
DTSTART:20200521T130000Z
DTEND:20200521T140000Z
LAST-MODIFIED:20200521T162146Z
LOCATION:https://theias.zoom.us/j/959183254
SUMMARY:Joint IAS/Princeton University Number Theory Seminar
URL:https://www.ias.edu/node/110896
END:VEVENT
BEGIN:VEVENT
UID:8083e5a3-d780-4116-ae18-6de3bd8b0b85
DTSTAMP:20200808T213738Z
CREATED:20200506T110159Z
DESCRIPTION:Topic: Forecasting Epidemics and Pandemics\n\nSpeaker: Roni Ros
enfeld\, Carnegie Mellon University\n\nVideo: https://video.ias.edu/tml/20
20/0521-RoniRosenfeld\n\nEpidemiological forecasting is critically needed
for decision making by national and local governments\, public health offi
cials\, healthcare institutions and the general public. The Delphi group a
t Carnegie Mellon University was founded in 2012 to advance the theory and
technological capability of epidemiological forecasting\, and to promote
its role in decision making\, both public and private. Our long term visio
n is to make epidemiological forecasting as useful and universally accepte
d as weather forecasting is today. I will describe some of the methods we
developed over the past eight year for forecasting flu\, dengue and other
epidemics\, and the challenges we faced in adapting these method to the CO
VID pandemic in the past few months.
DTSTART:20200521T190000Z
DTEND:20200521T200000Z
LAST-MODIFIED:20200521T221956Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/110871
END:VEVENT
BEGIN:VEVENT
UID:5ab1959e-1555-4709-95ec-320ab872ff2f
DTSTAMP:20200808T213738Z
CREATED:20200420T142731Z
DESCRIPTION:Topic: Mirrors of curves and their Fukaya categories\n\nSpeaker
: Denis Auroux\, Harvard University\n\nHomological mirror symmetry predict
s that the derived category of coherent sheaves on a curve has a symplecti
c counterpart as the Fukaya category of a mirror space. However\, with the
exception of elliptic curves\, this mirror is usually a symplectic Landau
-Ginzburg model\, i.e. a non-compact manifold equipped with the extra data
of a 'stop' in its boundary at infinity. Most of the talk will focus on a
family of Landau-Ginzburg models which provide mirrors to curves in (C*)^
2 or in toric surfaces (or more generally to hypersurfaces in toric variet
ies)\, and their fiberwise wrapped Fukaya categories (joint work with Moha
mmed Abouzaid). I will then discuss more a speculative way of constructing
mirrors of curves without Landau-Ginzburg models\, involving a new flavor
of Lagrangian Floer theory in trivalent configurations of Riemann surface
s (joint work with Alexander Efimov and Ludmil Katzarkov).
DTSTART:20200522T130000Z
DTEND:20200522T143000Z
LAST-MODIFIED:20200526T182702Z
LOCATION:https://princeton.zoom.us/j/745635914
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/110626
END:VEVENT
BEGIN:VEVENT
UID:da93f3c8-c983-4c21-9b8b-f78bf1d0b440
DTSTAMP:20200808T213738Z
CREATED:20200513T150837Z
DESCRIPTION:Topic: An application of integers of the 12th cyclotomic field
in the theory of phase transitions\n\nSpeaker: Alik Mazel\, AMC Health\n\n
The construction of pure phases from ground states is performed for $ u >
u_*(d)$ for all values of $d$ except for 39 special ones. For values $d$ w
ith a single equivalence class all periodic ground states generate the cor
responding pure phase which provides a complete description of extreme Gib
bs measures (complete phase diagram). For a general $d$ we prove that at l
east one class of ground states generates pure phases and propose an algor
ithm that decides\, after finitely many iterations\, which classes of grou
nd states generate pure phases. We cojecture that in case of several class
es only one of them generates pure phases which is confirmed by (numerical
) application of our algorithm to several (relatively small) values of $d$
.
DTSTART:20200525T150000Z
DTEND:20200525T160000Z
LAST-MODIFIED:20200518T133844Z
LOCATION:Remote Access via Zoom videoconferencing (link below)
SUMMARY:Analysis Seminar
URL:https://www.ias.edu/node/110961
END:VEVENT
BEGIN:VEVENT
UID:da74fdf0-6e43-4fc7-a81b-252af952cda5
DTSTAMP:20200808T213738Z
CREATED:20200518T135028Z
DESCRIPTION:Topic: Emerging symmetries in statistical physics systems\n\nSp
eaker: Hugo Duminil-Copin\, Université de Genève/IHES\n\nA great achieveme
nt of physics in the second half of the twentieth century has been the pre
diction of conformal symmetry of the scaling limit of critical statistical
physics systems. Around the turn of the millenium\, the mathematical unde
rstanding of this fact has progressed tremendously in two dimensions with
the introduction of the Schramm-Loewner Evolution and the proofs of confor
mal invariance of the Ising model and dimers. Nevertheless\, the understan
ding is still restricted to very specific models. In this talk\, we will g
ently introduce the notion of conformal invariance of lattice systems by t
aking the example of percolation models. We will also explain some recent
and partial progress in the direction of proving conformal invariance for
a large class of such models.
DTSTART:20200527T213000Z
DTEND:20200527T230000Z
LAST-MODIFIED:20200526T121254Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111001
END:VEVENT
BEGIN:VEVENT
UID:99e3ec04-7c61-4e8d-8611-bc13dd3f6853
DTSTAMP:20200808T213738Z
CREATED:20200507T144300Z
DESCRIPTION:Topic: Joint equidistribution of adelic torus orbits and famili
es of twisted L-functions\n\nSpeaker: Farrell Brumley\, Université Sorbonn
e Paris Nord\n\nVideo: https://video.ias.edu/puias/2020/0518-FarrellBrumle
y\n\nThe classical Linnik problems are concerned with the equidistribution
of adelic torus orbits on the homogeneous spaces attached to inner forms
of GL2\, as the discriminant of the torus gets large. When specialized\, t
hese problems admit beautiful classical interpretations\, such as the equi
distribution of integer points on spheres\, of Heegner points or packets o
f closed geodesics on the modular surface\, or of supersingular reductions
of CM elliptic curves. In the mid 20th century\, Linnik and his school es
tablished the equidistribution of many of these classical variants through
his ergodic method\, under a congruence condition on the discriminants mo
dulo a fixed auxiliary prime. More recently\, the Waldspurger formula and
subconvex estimates on L-functions were used to remove these congruence co
nditions\, and provide effective power-savings rates.\n\nIn their 2006 ICM
address\, Michel and Venkatesh proposed a variant of this problem in whic
h one considers the product of two distinct inner forms of GL2\, along wit
h a diagonally embedded torus. One can again specialize the setting to obt
ain interesting classical reformulations\, such as the joint equidistribut
ion of integer points on the sphere\, together with the shape of the ortho
gonal lattice. This hybrid context has received a great deal of attention
recently in the dynamics community\, where\, for instance\, the latter pro
blem was solved by Aka\, Einsiedler\, and Shapira\, under supplementary co
ngruence conditions modulo two fixed primes\, using as critical input the
joinings theorem of Einsiedler and Lindenstrauss.\n\nIn joint (ongoing) wo
rk with Valentin Blomer\, we remove the supplementary congruence condition
s in the joint equidistribution problem\, conditionally on the Riemann Hyp
othesis\, while obtaining a logarithmic rate of convergence. The proof use
s Waldsurger’s theorem and estimates of fractional moments of L-functions
in the family of class group twists.
DTSTART:20200528T140000Z
DTEND:20200528T150000Z
LAST-MODIFIED:20200528T183157Z
LOCATION:https://theias.zoom.us/j/959183254
SUMMARY:Joint IAS/Princeton University Number Theory Seminar
URL:https://www.ias.edu/node/110901
END:VEVENT
BEGIN:VEVENT
UID:b51e971f-93ba-4647-8ef5-c35350b28944
DTSTAMP:20200808T213738Z
CREATED:20200420T142839Z
DESCRIPTION:Topic: Duality for Rabinowitz-Floer homology\n\nSpeaker: Alex O
ancea\, Institut de Mathématiques de Jussieu-Paris Rive Gauche\n\nI will e
xplain a duality theorem with products in Rabinowitz-Floer homology. This
has a bearing on string topology and explains a number of dualities that h
ave been observed in that setting. Joint work in progress with Kai Cielieb
ak and Nancy Hingston.
DTSTART:20200529T130000Z
DTEND:20200529T143000Z
LAST-MODIFIED:20200526T121546Z
LOCATION:https://princeton.zoom.us/j/745635914
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/110631
END:VEVENT
BEGIN:VEVENT
UID:a54a7fbe-7b94-4948-aa56-90247018a497
DTSTAMP:20200808T213738Z
CREATED:20200420T132103Z
DESCRIPTION:Topic: Winding for Wave Maps\n\nSpeaker: Max Engelstein\, Unive
rsity of Minnesota\n\nVideo: https://video.ias.edu/analysis/2020/0601-MaxE
ngelstein\n\nWave maps are harmonic maps from a Lorentzian domain to a Rie
mannian target. Like solutions to many energy critical PDE\, wave maps can
develop singularities where the energy concentrates on arbitrary small sc
ales but the norm stays bounded. Zooming in on these singularities yields
a harmonic map (called a soliton or bubble) in the weak limit. One fundame
ntal question is whether this weak limit is unique\, that is to say\, whet
her different bubbles may appear as the limit of different sequences of re
scalings. We show by example that uniqueness may not hold if the target ma
nifold is not analytic. Our construction is heavily inspired by Peter Topp
ing's analogous example of a ``winding' bubble in harmonic map heat flow.
However\, the Hamiltonian nature of the wave maps will occasionally necess
itate different arguments.\n\nThis is joint work with Dana Mendelson (U Ch
icago).
DTSTART:20200601T150000Z
DTEND:20200601T160000Z
LAST-MODIFIED:20200602T150012Z
LOCATION:Remote Access via Zoom videoconferencing (link below)
SUMMARY:Analysis Seminar
URL:https://www.ias.edu/node/110606
END:VEVENT
BEGIN:VEVENT
UID:4bcb663a-86b4-4e8f-811d-30f14055c9e3
DTSTAMP:20200808T213738Z
CREATED:20200522T165815Z
DESCRIPTION:Topic: Mathematics formalization for mathematicians\n\nSpeaker:
Patrick Massot\, Université Paris-Sud\n\nA growing number of mathematicia
ns are having fun explaining mathematics to computers using proof assistan
t softwares. This process is called formalization. For instance\, together
with Kevin Buzzard and Johan Commelin\, I recently formalized enough topo
logy and algebra to define Scholze's perfectoid spaces to a computer. In t
his talk I'll describe what formalization looks like\, what kind of things
it teaches us\, and how it could even turn out to be useful (in our usual
sense of 'useful'). This will not be a talk about foundations of mathemat
ics\, and I will stick to elementary examples.
DTSTART:20200603T213000Z
DTEND:20200603T230000Z
LAST-MODIFIED:20200601T125349Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111041
END:VEVENT
BEGIN:VEVENT
UID:22570138-6945-4189-b694-840a287f828f
DTSTAMP:20200808T213738Z
CREATED:20200508T180330Z
DESCRIPTION:Topic: Dynamical generalizations of the Prime Number Theorem an
d disjointness of additive and multiplicative actions\n\nSpeaker: Florian
Richter\, Northwestern University\n\nOne of the fundamental challenges in
number theory is to understand the intricate way in which the additive and
multiplicative structures in the integers intertwine. We will explore a d
ynamical approach to this topic. After introducing a new dynamical framewo
rk for treating questions in multiplicative number theory\, we will presen
t an ergodic theorem which contains various classical number-theoretic res
ults\, such as the Prime Number Theorem\, as special cases. This naturally
leads to a formulation of an extended form of Sarnak's conjecture\, which
deals with the disjointness of actions of (N\,+) and (N\,*).\n\nThis talk
is based on joint work with Vitaly Bergelson.
DTSTART:20200604T190000Z
DTEND:20200604T200000Z
LAST-MODIFIED:20200519T123508Z
LOCATION:https://theias.zoom.us/j/959183254
SUMMARY:Joint IAS/Princeton University Number Theory Seminar
URL:https://www.ias.edu/node/110931
END:VEVENT
BEGIN:VEVENT
UID:d0b8e6af-aa77-403a-812a-8470daa5926b
DTSTAMP:20200808T213738Z
CREATED:20200504T152739Z
DESCRIPTION:Topic: Three Short Research Talks\n\nSpeaker: Morgan Weiler\, J
oé Brendel\, Abror Pirnapasov\n\nMorgan Weiler\, Rice University: Infinite
staircases of symplectic embeddings of ellipsoids into Hirzebruch surface
s\n\nGromov nonsqueezing tells us that symplectic embeddings are governed
by more complex obstructions than volume. In particular\, in 2012\, McDuff
-Schlenk computed the embedding capacity function of the ball\, whose valu
e at a is the size of the smallest four-dimensional ball into which the el
lipsoid E(1\,a) symplectically embeds. They found that it contains an “inf
inite staircase” of piecewise-linear sections accumulating from below to t
he golden ratio to the fourth power. However\, infinite staircases seem to
be rare for more general targets. Work of Cristofaro-Gardiner-Holm-Mandin
i-Pires suggests that\, up to scaling\, there are only finitely many ratio
nal symplectic toric manifolds whose embedding capacity functions contain
infinite staircases\, while Usher has found infinitely many irrational pol
ydisks with infinite staircases. Using ECH capacities in conjunction with
the methods of McDuff-Schlenk\, we will explain how we have found several
infinite families of Hirzebruch surfaces whose embedding capacity function
s we expect to contain an infinite staircase. Many of these staircases are
“descending” rather than “ascending.' This is joint work with Maria Berto
zzi\, Tara Holm\, Emily Maw\, Dusa McDuff\, Grace Mwakyoma\, and Ana Rita
Pires.\n\nJoé Brendel\, University of Neuchâtel: Real Lagrangian Tori in t
oric symplectic manifolds\n\nIn this talk we will be addressing the questi
on whether a given Lagrangian torus in a toric monotone symplectic manifol
d can be realized as the fixed point set of an anti-symplectic involution
(in which case it is called 'real'). In the case of toric fibres\, the ans
wer depends on the geometry of the moment polytope of the ambient manifold
. In the case of the Chekanov torus\, the answer is always no. This can be
proved using displacement energy and versal deformations.\n\nAbror Pirnap
asov\, Ruhr-Universität Bochum: Reeb orbits that force topological entropy
\n\nA transverse link in a contact 3-manifold forces topological entropy i
f every Reeb flow possessing this link as a set of periodic orbits has pos
itive topological entropy. We will explain how cylindrical contact homolog
y on the complement of transverse links can be used to show that certain t
ransverse links force topological entropy. As an application\, we show tha
t on every closed contact 3-manifold exists transverse knots that force to
pological entropy. We also generalize to the category of Reeb flows a beau
tiful result due to Denvir and Mackay\, which says that if a Riemannian me
tric on the two-dimensional torus has a contractible closed geodesic then
its geodesic flow has positive topological entropy. All this is joint work
s with Marcelo R.R. Alves\, Umberto L. Hryniewicz and Pedro A.S. Salomão
DTSTART:20200605T130000Z
DTEND:20200605T143000Z
LAST-MODIFIED:20200622T154723Z
LOCATION:https://princeton.zoom.us/j/745635914
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/110831
END:VEVENT
BEGIN:VEVENT
UID:fafb9a29-b35a-4686-8a99-d2e4ee8ea956
DTSTAMP:20200808T213738Z
CREATED:20200601T110927Z
DESCRIPTION:Topic: What Do Our Models Learn?\n\nSpeaker: Aleksander Mądry\,
Massachusetts Institute of Technology\n\nVideo: https://video.ias.edu/tml
/2020/0609-AleksanderMadry\n\nLarge-scale vision benchmarks have driven---
and often even defined---progress in machine learning. However\, these ben
chmarks are merely proxies for the real-world tasks we actually care about
. How well do our benchmarks capture such tasks?\n\nIn this talk\, I will
discuss the alignment between our benchmark-driven ML paradigm and the rea
l-world uses cases that motivate it. First\, we will explore examples of b
iases in the ImageNet dataset\, and how state-of-the-art models exploit th
em. We will then demonstrate how these biases arise as a result of design
choices in the data collection and curation processes.\n\nBased on joint w
orks with Logan Engstrom\, Andrew Ilyas\, Shibani Santurkar\, Jacob Steinh
ardt\, Dimitris Tsipras and Kai Xiao.
DTSTART:20200609T163000Z
DTEND:20200609T174500Z
LAST-MODIFIED:20200610T164105Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111116
END:VEVENT
BEGIN:VEVENT
UID:4aae92df-062b-4293-8a5f-e7950f6eb6f6
DTSTAMP:20200808T213738Z
CREATED:20200604T175725Z
DESCRIPTION:Topic: New constraints on the Galois configurations of algebrai
c integers in the complex plane \n\nSpeaker: Vesselin Dimitrov\, Universit
y of Toronto\n\nVideo: https://video.ias.edu/puias/2020/0611-VesselinDimit
rov\n\nFekete (1923) discovered the notion of transfinite diameter while s
tudying the possible configurations of Galois orbits of algebraic integers
in the complex plane. Based purely on the fact that the discriminants of
monic integer irreducible polynomials $P(X) \in \mathbb{Z}[X]$ are at leas
t $1$ in magnitude (since they are non-zero integers)\, he found that the
incidences $(\mathcal{K}\, P)$ between these polynomials $P(X)$ and compac
ts $\mathcal{K} \subset \mathbb{C}$ of transfinite diameter $d(\mathcal{K}
)\n\nBreusch (1951) solved the non-reciprocal case of the Lehmer problem b
y taking up a lossless arithmetic input from resultants rather than discri
minants. In this talk\, I will present some further lossless constraints t
hat derive from certain whole infinite sequences of Hankel determinants at
tached to the polynomial $P(X)$ by algebraic operations. This will allow u
s to update on Fekete's theorem on the incidences $(\mathcal{K}\,P)$\, by
focusing this time on the fibers over the argument $P$ for compacts $\math
cal{K}$ that are made of finite unions of Jordan arcs continua covering th
e roots of $P$ with certain congruence conditions on $P$ and on the connec
ted components of $\mathcal{K}$. The ensuing taming on Galois orbits turn
out to be sufficiently severe to resolve the conjecture of Schinzel and Za
ssenhaus (I will explain this case in detail)\, amidst certain other cases
of the Lehmer problem that are far off from Salem's extreme. In a geometr
ic formulation for $\mathcal{A}_g$ with its Kobayashi metric\, the root sp
acing constraints are likewise sufficiently severe to furthermore yield th
e exact $\mathcal{A}_g$ analogs of the well-known polynomial counting theo
rems of Penner and Leininger-Margalit on the '$L$-short' geodesics of modu
li space $\mathcal{M}_g$.
DTSTART:20200611T190000Z
DTEND:20200611T200000Z
LAST-MODIFIED:20200612T162646Z
LOCATION:https://theias.zoom.us/j/959183254
SUMMARY:Joint IAS/Princeton University Number Theory Seminar
URL:https://www.ias.edu/node/111151
END:VEVENT
BEGIN:VEVENT
UID:895b8bbc-fc88-4b46-937f-caf46f60d288
DTSTAMP:20200808T213738Z
CREATED:20200506T113428Z
DESCRIPTION:Topic: On Langevin Dynamics in Machine Learning\n\nSpeaker: Mic
hael I. Jordan\, University of California\, Berkeley\n\nVideo: https://vid
eo.ias.edu/machinelearning/2020/0611-MichaelI.Jordan\n\nLangevin diffusion
s are continuous-time stochastic processes that are based on the gradient
of a potential function. As such they have many connections---some known a
nd many still to be explored---to gradient-based machine learning. I'll di
scuss several recent results in this vein: (1) the use of Langevin-based a
lgorithms in bandit problems\; (2) the acceleration of Langevin diffusions
\; (3) how to use Langevin Monte Carlo without making smoothness assumptio
ns. I'll present these results in the context of a general argument about
the virtues of continuous-time perspectives in the analyis of discrete-tim
e optimization and Monte Carlo algorithms.
DTSTART:20200611T190000Z
DTEND:20200611T203000Z
LAST-MODIFIED:20200612T162713Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/110891
END:VEVENT
BEGIN:VEVENT
UID:8aca2dd3-52cb-414b-8f1b-637a04e0758a
DTSTAMP:20200808T213738Z
CREATED:20200504T152913Z
DESCRIPTION:Topic: Floer Cohomology and Arc Spaces\n\nSpeaker: Mark McLean\
, Stony Brook University\n\nVideo: https://video.ias.edu/puias/2020/0612-M
arkMcLean\n\nLet f be a polynomial over the complex numbers with an isolat
ed singular point at the origin and let d be a positive integer. To such a
polynomial we can assign a variety called the dth contact locus of f. Mor
ally\, this corresponds to the space of d-jets of holomorphic disks in com
plex affine space whose boundary `wraps' around the singularity d times. W
e show that Floer cohomology of the dth power of the Milnor monodromy map
is isomorphic to compactly supported cohomology of the dth contact locus.
This answers a question of Paul Seidel and it also proves a conjecture of
Nero Budur\, Javier Fernández de Bobadilla\, Quy Thuong Lê and Hong Duc Ng
uyen. The key idea of the proof is to use a jet space version of the PSS m
ap together with a filtration argument.
DTSTART:20200612T131500Z
DTEND:20200612T143000Z
LAST-MODIFIED:20200612T162741Z
LOCATION:Remote Access - see Zoom link below
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/110836
END:VEVENT
BEGIN:VEVENT
UID:fc2b27f0-8b2e-4505-8e5e-97e86e3e6193
DTSTAMP:20200808T213738Z
CREATED:20200519T123912Z
DESCRIPTION:Topic: On learning in the presence of biased data and strategic
behavior\n\nSpeaker: Avrim Blum\, Toyota Technological Institute at Chica
go\n\nVideo: https://video.ias.edu/tml/2020/0616-AvrimBlum\n\nIn this talk
I will discuss two lines of work involving learning in the presence of bi
ased data and strategic behavior. In the first\, we ask whether fairness c
onstraints on learning algorithms can actually improve the accuracy of the
classifier produced\, when training data is unrepresentative or corrupted
due to bias. Typically\, fairness constraints are analyzed as a tradeoff
with classical objectives such as accuracy. Our results here show there ar
e natural scenarios where they can be a win-win\, helping to improve overa
ll accuracy. In the second line of work we consider strategic classificati
on: settings where the entities being measured and classified wish to be c
lassified as positive (e.g.\, college admissions) and will try to modify t
heir observable features if possible to make that happen. We consider this
in the online setting where a particular challenge is that updates made b
y the learning algorithm will change how the inputs behave as well.
DTSTART:20200616T190000Z
DTEND:20200616T203000Z
LAST-MODIFIED:20200622T154417Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111006
END:VEVENT
BEGIN:VEVENT
UID:3532b747-3a0d-499a-b416-9c25f0ed9381
DTSTAMP:20200808T213738Z
CREATED:20200522T170057Z
DESCRIPTION:Topic: Infinite dimensional Hamiltonian systems: when hard prob
lems become harder\n\nSpeaker: Gigliola Staffilani\, Massachusetts Institu
te of Technology\n\nIn this talk I will first recall three classical theor
ems in the theory of finite dimensional Hamiltonian systems\, then I will
use the periodic nonlinear Schrodinger equation as an example of an infini
te dimensional Hamiltonian system and I will report on the extension of th
ose three theorems in this more difficult set up.
DTSTART:20200617T213000Z
DTEND:20200617T230000Z
LAST-MODIFIED:20200615T114136Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111051
END:VEVENT
BEGIN:VEVENT
UID:6fe336d7-e2ff-4dbd-9d82-e0ca02abe254
DTSTAMP:20200808T213738Z
CREATED:20200603T154520Z
DESCRIPTION:Topic: Independence of ℓ for Frobenius conjugacy classes attach
ed to abelian varieties\n\nSpeaker: Rong Zhou\, Imperial College London\n
\nVideo: https://video.ias.edu/jnt/2020/0618-RongZhou\n\nLet $A$ be an abe
lian variety over a number field $E\subset \mathbb{C}$ and let $v$ be a pl
ace of good reduction lying over a prime $p$. For a prime $\ell\neq p$\, a
result of Deligne implies that upon replacing $E$ by a finite extension\,
the Galois representation on the $\ell$-adic Tate module of $A$ factors a
s $\rho_\ell:\mathrm{Gal}(\overline{E}/E)\rightarrow G_A$\, where $G_A$ is
the Mumford--Tate group of $A_{\mathbb{C}}$. For $p>2$\, we prove that th
e conjugacy class of $\rho_\ell(\mathrm{Frob}_v)$ is defined over $\mathbb
{Q}$ and independent of $\ell$. This is joint work with Mark Kisin.
DTSTART:20200618T190000Z
DTEND:20200618T200000Z
LAST-MODIFIED:20200619T142259Z
LOCATION:https://theias.zoom.us/j/959183254
SUMMARY:Joint IAS/Princeton University Number Theory Seminar
URL:https://www.ias.edu/node/111136
END:VEVENT
BEGIN:VEVENT
UID:9008f18d-c6a6-4ba9-9047-40b89608d013
DTSTAMP:20200808T213738Z
CREATED:20200521T145613Z
DESCRIPTION:Topic: The challenges of model-based reinforcement learning and
how to overcome them\n\nSpeaker: Csaba Szepesvári\, University of Alberta
\n\nVideo: https://video.ias.edu/tml/2020/0618-CsabaSzepesvari\n\nSome bel
ieve that truly effective and efficient reinforcement learning algorithms
must explicitly construct and explicitly reason with models that capture t
he causal structure of the world. In short\, model-based reinforcement lea
rning is not optional. As this is not a new belief\, it may be surprising
that empirically\, at least as far as the current state of art is concerne
d\, the majority of the top performing algorithms are model-free. In this
talk\, I will define three major challenges that need to be overcome for m
odel-based methods to take their place above\, or before the model-free on
es: (1) planning with large models\; (2) models are never well-specified\;
(3) models need to focus on task relevant aspects and ignore others. For
each of the challenges\, I will describe recent results that address them
and I will also take a tally of the most interesting (and challenging) rem
aining open problems.
DTSTART:20200618T190000Z
DTEND:20200618T203000Z
LAST-MODIFIED:20200619T165459Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111031
END:VEVENT
BEGIN:VEVENT
UID:717d157c-be63-45be-bb64-1dea5bea5071
DTSTAMP:20200808T213738Z
CREATED:20200504T153003Z
DESCRIPTION:Topic: Exotic symplectomorphisms and contact circle action\n\nS
peaker: Igor Uljarevic\, University of Belgrade\n\nAn exotic symplectomorp
hism is a symplectomorphism that is not isotopic to the identity through c
ompactly supported symplectomorphisms.Using Floer-theoretic methods\, we p
rove that the non-existence of an exotic symplectomorphism on the standard
symplectic ball\, $\mathbb{B}^{2n}\,$ implies a rather strict topological
condition on the free contact circle actions on the standard contact sphe
re\, $\mathbb{S}^{2n-1}.$ We also prove an analogue for a Liouville domain
and contact circle actions on its boundary. Applications include results
on the symplectic mapping class group\, the fundamental group of the group
of contactomorphisms\, and exotic contact structures on $\mathbb{S}^3.$ T
he talk is based on joint work with Dusan Drobnjak.
DTSTART:20200619T131500Z
DTEND:20200619T143000Z
LAST-MODIFIED:20200609T181104Z
LOCATION:Remote Access - see Zoom link below
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/110841
END:VEVENT
BEGIN:VEVENT
UID:568155db-3af8-43c4-941f-f80edfc46a13
DTSTAMP:20200808T213738Z
CREATED:20200619T121836Z
DESCRIPTION:Topic: Generalizable Adversarial Robustness to Unforeseen Attac
ks\n\nSpeaker: Soheil Feizi\, University of Maryland\n\nIn the last couple
of years\, a lot of progress has been made to enhance robustness of model
s against adversarial attacks. However\, two major shortcomings still rema
in: (i) practical defenses are often vulnerable against strong “adaptive”
attack algorithms\, and (ii) current defenses have poor generalization to
“unforeseen” attack threat models (the ones not used in training).\n\nIn t
his talk\, I will present our recent results to tackle these issues. I wil
l first discuss generalizability of a class of provable defenses based on
randomized smoothing to various Lp and non-Lp attack models. Then\, I will
present adversarial attacks and defenses for a novel “perceptual” adversa
rial threat model. Remarkably\, the defense against perceptual threat mode
l generalizes well against many types of unforeseen Lp and non-Lp adversar
ial attacks.\n\nThis talk is based on joint works with Alex Levine\, Sahil
Singla\, Cassidy Laidlaw\, Aounon Kumar and Tom Goldstein.
DTSTART:20200623T163000Z
DTEND:20200623T174500Z
LAST-MODIFIED:20200619T121836Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111271
END:VEVENT
BEGIN:VEVENT
UID:e894c82c-cfd0-4cb1-b042-afcf5c0ba318
DTSTAMP:20200808T213738Z
CREATED:20200522T170347Z
DESCRIPTION:Topic: Knot concordance and 4-manifolds\n\nSpeaker: Lisa Piccir
illo\, Brandeis University/Massachusetts Institute of Technology\n\nThere
is a rich interplay between the fields of knot theory and 3- and 4-manifol
d topology. In this talk\, I will describe a weak notion of equivalence fo
r knots called concordance\, and highlight some historical and recent conn
ections between knot concordance and the study of 4-manifolds\, with a par
ticular emphasis on applications of knot concordance to the construction a
nd detection of small 4-manifolds which admit multiple smooth structures.
DTSTART:20200624T213000Z
DTEND:20200624T230000Z
LAST-MODIFIED:20200619T175732Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111056
END:VEVENT
BEGIN:VEVENT
UID:0383d93e-5541-443b-8405-cd38adbd1cb6
DTSTAMP:20200808T213738Z
CREATED:20200619T122716Z
DESCRIPTION:Topic: Instance-Hiding Schemes for Private Distributed Learning
\n\nSpeaker: Sanjeev Arora\, Princeton University\; Distinguishing Visitin
g Professor\, School of Mathematics\n\nAn important problem today is how t
o allow multiple distributed entities to train a shared neural network on
their private data while protecting data privacy. Federated learning is a
standard framework for distributed deep learning Federated Learning\, and
one would like to assure full privacy in that framework . The proposed met
hods\, such as homomorphic encryption and differential privacy\, come with
drawbacks such as large computational overhead or large drop in accuracy.
This work introduces a new and simple encryption of training data\, which
hides the information in it and allows its use in the usual deep learning
pipeline. The encryption is inspired by classic notion of instance-hiding
in cryptography. Experiments show that it allows training with fairly sma
ll effect on final accuracy.\n\nWe also give some theoretical analysis of
privacy guarantees for this encryption\, showing that violating privacy re
quires attackers to solve a difficult computational problem.\n\nJoint work
with Yangsibo Huang\, Zhao Song\, and Kai Li. To appear at ICML 2020.
DTSTART:20200625T190000Z
DTEND:20200625T203000Z
LAST-MODIFIED:20200619T190336Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111276
END:VEVENT
BEGIN:VEVENT
UID:81303cb4-6873-4348-a50a-9d23880dff1a
DTSTAMP:20200808T213738Z
CREATED:20200504T153057Z
DESCRIPTION:Topic: Distinguishing monotone Lagrangians via holomorphic annu
li\n\nSpeaker: Ailsa Keating\, University of Cambridge\n\nWe present techn
iques for constructing families of compact\, monotone (including exact) La
grangians in certain affine varieties\, starting with Brieskorn-Pham hyper
surfaces. We will focus on dimensions 2 and 3. In particular\, we'll expla
in how to set up well-defined counts of holomorphic annuli for a range of
these families. Time allowing\, we will give a number of applications.
DTSTART:20200626T131500Z
DTEND:20200626T143000Z
LAST-MODIFIED:20200622T153044Z
LOCATION:Remote Access - see Zoom link below
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/110846
END:VEVENT
BEGIN:VEVENT
UID:93ffe5b5-620c-4bcd-b315-cc1c440656dd
DTSTAMP:20200808T213738Z
CREATED:20200610T122747Z
DESCRIPTION:Topic: The reversibility paradox: 130 years after Loschmidt an
d Zermelo\n\nSpeaker: Laure Saint-Reymond\, École normale supérieure de Ly
on\n\nThe reversibility paradox is the objection that it should not be pos
sible to deduce an irreversible process from time-symmetric dynamics. A fi
rst result reconciling the fundamental microscopic physical processes (wit
h time reversal symmetry) and macroscopic models (satisfying the second la
w of thermodynamics) has been proved 50 years ago by Lanford. Our recent w
ork with T. Bodineau\, I. Gallagher\, and S. Simonella brings a new light
on this asymptotic derivation\, recovering some reversibility in the limit
.
DTSTART:20200701T213000Z
DTEND:20200701T230000Z
LAST-MODIFIED:20200626T120754Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111211
END:VEVENT
BEGIN:VEVENT
UID:ee93c582-f9ff-40f8-ada3-ccf395273381
DTSTAMP:20200808T213738Z
CREATED:20200622T153746Z
DESCRIPTION:Topic: Infinite staircases and reflexive polygons\n\nSpeaker: A
na Rita Pires\, University of Edinburgh\n\nVideo: https://video.ias.edu/p
uias/2020/0703-AnaRitaPires\n\nA classic result\, due to McDuff and Schlen
k\, asserts that the function that encodes when a four-dimensional symplec
tic ellipsoid can be embedded into a four-dimensional ball has a remarkabl
e structure: the function has infinitely many corners\, determined by the
odd-index Fibonacci numbers\, that fit together to form an infinite stairc
ase. The work of McDuff and Schlenk has recently led to considerable inter
est in understanding when the ellipsoid embedding function for other sympl
ectic 4-manifolds is partly described by an infinite staircase. In this ta
lk we will discuss a general framework for analyzing this question for a l
arge family of targets\, and in particular give an obstruction to the exis
tence of an infinite staircase that experimentally seems strong.\n\nWe wil
l then look at the special case of rational convex toric domains / closed
symplectic toric manifolds\, for which we prove the existence of six famil
ies of targets with infinite staircases that are distinguished by the fact
that their moment polygon is reflexive. The proof uses\, among other tool
s\, almost toric fibrations -- see also the second of the ellipsoid day ta
lks.\n\nFinally\, we conjecture that these six families constitute a compl
ete answer to the question of existence of infinite staircase. This conjec
ture has been verified in the case when the target is an ellipsoid -- see
the third of the ellipsoid day talks.\n\nThis is based on joint work of Da
n Cristofaro-Gardiner\, Tara Holm\, Alessia Mandini\, and Ana Rita Pires.
DTSTART:20200703T131500Z
DTEND:20200703T143000Z
LAST-MODIFIED:20200708T182528Z
LOCATION:Remote Access - see Zoom link below
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/111291
END:VEVENT
BEGIN:VEVENT
UID:47adc82a-5fa0-4ff4-8498-af9137929b54
DTSTAMP:20200808T213738Z
CREATED:20200630T125136Z
DESCRIPTION:Topic: Machine learning-based design (of proteins\, small molec
ules and beyond)\n\nSpeaker: Jennifer Listgarten\, University of Californi
a\, Berkeley\n\nVideo: https://video.ias.edu/machinelearning/2020/0707-Jen
niferListgarten\n\nData-driven design is making headway into a number of a
pplication areas\, including protein\, small-molecule\, and materials engi
neering. The design goal is to construct an object with desired properties
\, such as a protein that binds to a target more tightly than previously o
bserved. To that end\, costly experimental measurements are being replaced
with calls to a high-capacity regression model trained on labeled data\,
which can be leveraged in an in silico search for promising design candida
tes. The aim then is to discover designs that are better than the best des
ign in the observed data. This goal puts machine-learning based design in
a much more difficult spot than traditional applications of predictive mod
elling\, since successful design requires\, by definition\, some degree of
extrapolation---a pushing of the predictive models to its unknown limits\
, in parts of the design space that are a priori unknown. In this talk\, I
will anchor this overall problem in protein engineering\, and discuss our
emerging approaches to tackle it.
DTSTART:20200707T163000Z
DTEND:20200707T174500Z
LAST-MODIFIED:20200710T130411Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111386
END:VEVENT
BEGIN:VEVENT
UID:a5d7d291-0c22-4362-a9d3-de7637705799
DTSTAMP:20200808T213738Z
CREATED:20200522T165936Z
DESCRIPTION:Topic: Weyl laws and dense periodic orbits\n\nSpeaker: Michael
Hutchings\, University of California\, Berkeley\n\nWe review a 'Weyl law'
in embedded contact homology\, relating periods of orbits of the Reeb vect
or field on a contact three-manifold to volume. (This was also mentioned i
n the talk by Dan Cristofaro-Gardiner.) We explain a clever argument by Ke
i Irie which deduces from this that a generic contact form has dense perio
dic orbits. There is also a parallel story for minimal surfaces.
DTSTART:20200708T213000Z
DTEND:20200708T230000Z
LAST-MODIFIED:20200702T181000Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111046
END:VEVENT
BEGIN:VEVENT
UID:c876b030-6c25-4738-9f64-ab3b85c0c360
DTSTAMP:20200808T213738Z
CREATED:20200630T130242Z
DESCRIPTION:Topic: Role of Interaction in Competitive Optimization\n\nSpeak
er: Anima Anandkumar\, California Institute of Technology\n\nVideo: https:
//video.ias.edu/machinelearning/2020/0709-AnimaAnandkumar\n\nCompetitive o
ptimization is needed for many ML problems such as training GANs\, robust
reinforcement learning\, and adversarial learning. Standard approaches to
competitive optimization involve each agent independently optimizing their
objective functions using SGD or other gradient-based approaches. However
\, they suffer from oscillations and instability\, since the optimization
does not account for interaction among the players. We introduce competiti
ve gradient descent (CGD) that explicitly incorporates interaction by solv
ing for Nash equilibrium of a local game. We extend CGD to competitive mir
ror descent (CMD) for solving conically constrained competitive problems b
y using the dual geometry induced by a Bregman divergence.\n\nWe demonstra
te the effectiveness of our approach for training GANs and solving constra
ined reinforcement learning (RL) problems. We also derive a competitive po
licy optimization method to train RL agents in competitive games. Finally\
, we provide a novel perspective on training GANs by pointing out the 'GAN
-dilemma' a fundamental flaw of the divergence-minimization perspective on
GANs. Instead\, we argue that an implicit competitive regularization due
to simultaneous training methods\, such as CGD\, is a crucial mechanism be
hind GAN performance.
DTSTART:20200709T190000Z
DTEND:20200709T203000Z
LAST-MODIFIED:20200710T130442Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111396
END:VEVENT
BEGIN:VEVENT
UID:b5e2b768-f08f-48a6-971e-b7828bb1d261
DTSTAMP:20200808T213738Z
CREATED:20200630T130959Z
DESCRIPTION:Topic: Knot Floer homology and bordered algebras\n\nSpeaker: Pe
ter Ozsváth\, Princeton University\n\nVideo: https://video.ias.edu/puias/2
020/0710-PeterOzsvath\n\nKnot Floer homology is an invariant for knots in
three-space\, defined as a Lagrangian Floer homology in a symmetric produc
t. It has the form of a bigraded vector space\, encoding topological infor
mation about the knot. I will discuss an algebraic approach to computing k
not Floer homology\, and a corresponding version for links\, based on deco
mposing knot diagrams.\n\nThis is joint work with Zoltan Szabo\, building
on earlier joint work (bordered Heegaard Floer homology) with Robert Lipsh
itz and Dylan Thurston.
DTSTART:20200710T131500Z
DTEND:20200710T143000Z
LAST-MODIFIED:20200710T235922Z
LOCATION:Remote Access - see Zoom link below
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/111406
END:VEVENT
BEGIN:VEVENT
UID:a1d00f11-0bac-4c7c-b1a2-6c52493f485a
DTSTAMP:20200808T213738Z
CREATED:20200705T213719Z
DESCRIPTION:Topic: Relaxing the I.I.D. Assumption: Adaptive Minimax Optimal
Sequential Prediction with Expert Advice\n\nSpeaker: Jeffrey Negrea\, Uni
versity of Toronto\n\nWe consider sequential prediction with expert advice
when the data are generated stochastically\, but the distributions genera
ting the data may vary arbitrarily among some constraint set. We quantify
relaxations of the classical I.I.D. assumption in terms of possible constr
aint sets\, with I.I.D. at one extreme\, and an adversarial mechanism at t
he other. The Hedge algorithm\, long known to be minimax optimal for in th
e adversarial regime\, has recently been shown to also be minimax optimal
in the I.I.D. setting. We show that Hedge is sub-optimal between these ext
remes\, and present a new algorithm that is adaptively minimax optimal wit
h respect to our relaxations of the I.I.D. assumption\, without knowledge
of which setting prevails.
DTSTART:20200714T163000Z
DTEND:20200714T174500Z
LAST-MODIFIED:20200705T213719Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111456
END:VEVENT
BEGIN:VEVENT
UID:fc397d66-2357-4a82-a611-e727087e15ec
DTSTAMP:20200808T213738Z
CREATED:20200608T185649Z
DESCRIPTION:Topic: On the cap-set problem and the slice rank polynomial met
hod\n\nSpeaker: Lisa Sauermann\, Stanford University\n\nIn 2016\, Ellenber
g and Gijswijt made a breakthrough on the famous cap-set problem\, which a
sks about the maximum size of a subset of \mathbb{F}_3^n not containing a
three-term arithmetic progression. Ellenberg and Gijswijt proved that any
such set has size at most 2.756^n. Their proof used a new polynomial metho
d introduced by Croot\, Lev and Pach just a few weeks earlier. In this tal
k\, we will discuss the proof of the Ellenberg-Gijswijt bound\, following
a reformulation of their original proof by Tao. In this reformulation\, Ta
o introduced what is now called the slice rank polynomial method. At the e
nd of the talk\, we will also discuss further applications as well as limi
tations of the slice rank polynomial method.
DTSTART:20200715T213000Z
DTEND:20200715T230000Z
LAST-MODIFIED:20200713T144250Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111206
END:VEVENT
BEGIN:VEVENT
UID:a8c3181a-dd5e-4c15-9b9a-11e0e78b699a
DTSTAMP:20200808T213738Z
CREATED:20200630T131208Z
DESCRIPTION:Speaker: Yusuke Kawamoto\, Shira Tanny\, Javier Martínez-Aguina
ga \, École Normale Supérieure\, Tel Aviv University\, Complutensian Unive
rsity of Madrid\n\nVideo: https://video.ias.edu/sg/2022/0717-various\n\nYu
suke Kawamoto:Homogeneous quasimorphism\, C^0-topology and Lagrangian inte
rsection\n\nAbstract: We construct an example of a non-trivial homogeneous
quasimorphism on the group of Hamiltonian diffeomorphisms of the $2$- and
$4$-dimensional quadric which is continuous with respect to both $C^0$-to
pology and the Hofer metric. This answers a variant of a question of Entov
-Polterovich-Py which is one of the open problems listed in the monograph
of McDuff-Salamon. A comparison of spectral invariants for quantum cohomol
ogy rings with different coefficient fields plays a crucial role in the pr
oof which might be of independent interest.\n\nShira Tanny: Floer theory o
f disjointly supported Hamiltonians\n\nAbstract. We discuss the Floer-theo
retic interaction between disjointly supported Hamiltonians\, a problem co
nsidered earlier by Polterovich\, Seyfaddini\, Ishikawa and Humilière-Le R
oux-Seyfaddini. In aspherical symplectic manifolds\, we find new constrain
ts on Floer trajectories\, and derive applications to spectral invariants
and the boundary depth\, as well as to the action selector constructed by
Abbondandolo\, Haug\, and Schlenk. Furthermore\, we prove that the spectra
l invariants\, with respect to the fundamental and point classes\, of Hami
ltonians supported in certain domains\, are independent of the ambient man
ifold. This is a joint work in progress with Yaniv Ganor.\n\nJavier Martín
ez-Aguinaga: Formal Legendrian and horizontal embeddings\n\nAbstract. In t
his talk we will discuss some recent results about the space of Formal Leg
endrian embeddings in contact 3-manifolds and Formal Horizontal embeddings
in Engel manifolds. At the π0−level\, formal invariants of Legendrian emb
eddings correspond to the well understood classical invariants. We will in
troduce analogous invariants at the π1−level\, which can be described in a
geometrical way. As an application we can construct new examples of non-t
rivial loops of Legendrian embeddings which are trivial as loops of smooth
embeddings. Joint work with Eduardo Fernández (ICMAT-UCM) and Francisco P
resas (ICMAT).
DTSTART:20200717T131500Z
DTEND:20200717T143000Z
LAST-MODIFIED:20200719T191115Z
LOCATION:Remote Access - see Zoom link below
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/111411
END:VEVENT
BEGIN:VEVENT
UID:fab7c098-112c-4379-8a14-d23bce0fb256
DTSTAMP:20200808T213738Z
CREATED:20200630T125706Z
DESCRIPTION:Topic: Graph Nets: The Next Generation\n\nSpeaker: Max Welling\
, University of Amsterdam\n\nVideo: https://video.ias.edu/machinelearning/
2020/0721-MaxWelling\n\nIn this talk I will introduce our next generation
of graph neural networks. GNNs have the property that they are invariant t
o permutations of the nodes in the graph and to rotations of the graph as
a whole. We claim this is unnecessarily restrictive and in this talk we wi
ll explore extensions of these GNNs to more flexible equivariant construct
ions. In particular\, Natural Graph Networks for general graphs are global
ly equivariant under permutations of the nodes but can still be executed t
hrough local message passing protocols. Our mesh-CNNs on manifolds are equ
ivariant under SO(2) gauge transformations and as such\, unlike regular GN
Ns\, entertain non-isotropic kernels. And finally our SE(3)-transformers a
re local message passing GNNs\, invariant to permutations but equivariant
to global SE(3) transformations. These developments clearly emphasize the
importance of geometry and symmetries as design principles for graph (or o
ther) neural networks.\n\nJoint with: Pim de Haan and Taco Cohen (Natural
Graph Networks) Pim de Haan\, Maurice Weiler and Taco Cohen (Mesh-CNNs) Fa
bian Fuchs and Daniel Worrall (SE(3)-Transformers)
DTSTART:20200721T163000Z
DTEND:20200721T174500Z
LAST-MODIFIED:20200723T204528Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111391
END:VEVENT
BEGIN:VEVENT
UID:58585bf3-5b77-4400-850b-57b0e5c76a22
DTSTAMP:20200808T213738Z
CREATED:20200522T172515Z
DESCRIPTION:Topic: Singularities of solutions of the Hamilton-Jacobi equati
on. A toy model: distance to a closed subset.\n\nSpeaker: Albert Fathi\, G
eorgia Institute of Technology\n\nThis is a joint work with Piermarco Cann
arsa and Wei Cheng.\n\nMost of the lecture is about the distance function
to a closed subset in Euclidean subset\, at the level of a beginning gradu
ate student.\n\nIf $A$ is a closed subset of the Euclidean space $\mathbb
R^k$\, the Euclidean distance function $d_A: \mathbb R^k\to [0\,+\infty[$
is defined by $d_A(x)=\min_{a\in A}\Vert x-a\Vert$. This function is Lipsc
hitz\, therefore differentiable almost everywhere. We will give topologica
l properties of the set ${\rm Sing}(F)$ of points in $\mathbb R^k\setminus
M$ where $F$ is not differentiable. For example it is locally connected.
We will also discuss the homotopy type of ${\rm Sing}(F)$. We will sketch
a proof.\n\nAlthough\, we will concentrate on $d_A$\, if time permits: 1)
We will give applications in Riemannian geometry: Topology of the pairs of
points that can be joined by at least 2 minimizing geodesics. 2) We will
explain that it is a particular case of a more general result on the singu
larities of a viscosity solution $U:M\times ]0\,+\infty[\to \mathbb R$ of
the evolution Hamilton-Jacobi equation $$\partial_tU+H(x\,\partial_xU)=0\,
$$ where $H:TM\to \mathbb R\, (x\,p)\mapsto H(x\,p)$ is a C$^2$ Tonelli Ha
miltonian\, i.e. convex and superlinear in the momentum $p$\, on the smoot
h manifold $M$.
DTSTART:20200722T213000Z
DTEND:20200722T230000Z
LAST-MODIFIED:20200717T180149Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111061
END:VEVENT
BEGIN:VEVENT
UID:2be7e789-9180-4f34-b31c-a85c027de3e5
DTSTAMP:20200808T213738Z
CREATED:20200630T130534Z
DESCRIPTION:Topic: Priors for Semantic Variables\n\nSpeaker: Yoshua Bengio\
, Université de Montréal\n\nVideo: https://video.ias.edu/machinelearning/2
020/0723-YoshuaBengio\n\nSome of the aspects of the world around us are ca
ptured in natural language and refer to semantic high-level variables\, wh
ich often have a causal role (referring to agents\, objects\, and actions
or intentions). These high-level variables also seem to satisfy very pecul
iar characteristics which low-level data (like images or sounds) do not sh
are\, and it would be good to clarify these characteristics in the form of
priors which can guide the design of machine learning systems benefitting
from these assumptions. Since these priors are not just about the joint d
istribution between the semantic variables (e.g. it has a sparse factor gr
aph corresponding to a modular decomposition of knowledge) but also about
how the distribution changes (typically by causal interventions)\, this an
alysis may also help to build machine learning systems which can generaliz
e better out-of-distribution. Introducing such assumptions is necessary to
even start having a theory about generalizing out-of-distribution. There
are also fascinating connections between these priors and what is hypothes
ized about conscious processing in the brain\, with conscious processing a
llowing us to reason (i.e.\, perform chains of inferences about the past a
nd the future\, as well as credit assignment) at the level of these high-l
evel variables. This involves attention mechanisms and short-term memory t
o form a bottleneck of information being broadcast around the brain betwee
n different parts of it\, as we focus on different high-level variables an
d some of their interactions. The presentation summarizes a few recent res
ults using some of these ideas for discovering causal structure and modula
rizing recurrent neural networks with attention mechanisms in order to obt
ain better out-of-distribution generalization and move deep learning towar
ds capturing some of the functions associated with conscious processing ov
er high-level semantic variables.
DTSTART:20200723T190000Z
DTEND:20200723T203000Z
LAST-MODIFIED:20200723T204602Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111401
END:VEVENT
BEGIN:VEVENT
UID:56de0b60-b50f-43c5-851b-53f3a5d97acd
DTSTAMP:20200808T213738Z
CREATED:20200630T131444Z
DESCRIPTION:Topic: Pontryagin - Thom for orbifold bordism\n\nSpeaker: John
Pardon\, Princeton University\n\nVideo: https://video.ias.edu/puias/2020/0
724-JohnPardon\n\nThe classical Pontryagin–Thom isomorphism equates manifo
ld bordism groups with corresponding stable homotopy groups. This construc
tion moreover generalizes to the equivariant context. I will discuss work
which establishes a Pontryagin--Thom isomorphism for orbispaces (an orbisp
ace is a 'space' which is locally modelled on Y/G for Y a space and G a fi
nite group\; examples of orbispaces include orbifolds and moduli spaces of
pseudo-holomorphic curves). This involves defining a category of orbispec
tra and an involution of this category extending Spanier--Whitehead dualit
y. Global homotopy theory also plays a key role.
DTSTART:20200724T131500Z
DTEND:20200724T143000Z
LAST-MODIFIED:20200727T124359Z
LOCATION:Remote Access - see Zoom link below
SUMMARY:IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Zoominar
URL:https://www.ias.edu/node/111416
END:VEVENT
BEGIN:VEVENT
UID:e6f7fc29-557f-499c-875d-ecb8934dcfae
DTSTAMP:20200808T213738Z
CREATED:20200714T134621Z
DESCRIPTION:Topic: Generalized Energy-Based Models\n\nSpeaker: Arthur Grett
on\, University College London\n\nI will introduce Generalized Energy Base
d Models (GEBM) for generative modelling. These models combine two trained
components: a base distribution (generally an implicit model)\, which can
learn the support of data with low intrinsic dimension in a high dimensio
nal space\; and an energy function\, to refine the probability mass on the
learned support. Both the energy function and base jointly constitute the
final model\, unlike GANs\, which retain only the base distribution (the
'generator'). In particular\, while the energy function is analogous to th
e GAN critic function\, it is not discarded after training.\nGEBMs are tra
ined by alternating between learning the energy and the base. Both trainin
g stages are well-defined: the energy is learned by maximising a generaliz
ed likelihood\, and the resulting energy-based loss provides informative g
radients for learning the base. Samples from the posterior on the latent s
pace of the trained model can be obtained via MCMC\, thus finding regions
in this space that produce better quality samples. Empirically\, the GEBM
samples on image-generation tasks are of much better quality than those fr
om the learned generator alone\, indicating that all else being equal\, th
e GEBM will outperform a GAN of the same complexity. GEBMs also return sta
te-of-the-art performance on density modelling tasks\, and when using base
measures with an explicit form.
DTSTART:20200728T163000Z
DTEND:20200728T174500Z
LAST-MODIFIED:20200730T122159Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111646
END:VEVENT
BEGIN:VEVENT
UID:28f174a4-68c0-4eb9-a4ae-fb19aa3d6d96
DTSTAMP:20200808T213738Z
CREATED:20200714T134846Z
DESCRIPTION:Topic: Efficient Robot Skill Learning via Grounded Simulation L
earning\, Imitation Learning from Observation\, and Off-Policy Reinforceme
nt Learning\n\nSpeaker: Peter Stone\, The University of Texas at Austin\n
\nFor autonomous robots to operate in the open\, dynamically changing worl
d\, they will need to be able to learn a robust set of skills from relativ
ely little experience. This talk begins by introducing Grounded Simulation
Learning as a way to bridge the so-called reality gap between simulators
and the real world in order to enable transfer learning from simulation to
a real robot. It then introduces two new algorithms for imitation learnin
g from observation that enable a robot to mimic demonstrated skills from s
tate-only trajectories\, without any knowledge of the actions selected by
the demonstrator. Connections to theoretical advances in off-policy reinfo
rcement learning will be highlighted throughout.\n\nGrounded Simulation Le
arning has led to the fastest known stable walk on a widely used humanoid
robot\, and imitation learning from observation opens the possibility of r
obots learning from the vast trove of videos available online.
DTSTART:20200730T190000Z
DTEND:20200730T203000Z
LAST-MODIFIED:20200722T102602Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111651
END:VEVENT
BEGIN:VEVENT
UID:6736c09f-9219-4faf-9b90-bf12225d373e
DTSTAMP:20200808T213738Z
CREATED:20200724T122744Z
DESCRIPTION:Topic: Nonlinear Independent Component Analysis\n\nSpeaker: Aap
o Hyvärinen\, University of Helsinki\n\nUnsupervised learning\, in particu
lar learning general nonlinear representations\, is one of the deepest pro
blems in machine learning. Estimating latent quantities in a generative mo
del provides a principled framework\, and has been successfully used in th
e linear case\, e.g. with independent component analysis (ICA) and sparse
coding. However\, extending ICA to the nonlinear case has proven to be ext
remely difficult: A straight-forward extension is unidentifiable\, i.e. it
is not possible to recover those latent components that actually generate
d the data. Here\, we show that this problem can be solved by using additi
onal information either in the form of temporal structure or an additional
observed variable. We start by formulating two generative models in which
the data is an arbitrary but invertible nonlinear transformation of time
series (components) which are statistically independent of each other. Dra
wing from the theory of linear ICA\, we formulate two distinct classes of
temporal structure of the components which enable identification\, i.e. re
covery of the original independent components. We further generalize the f
ramework to the case where instead of temporal structure\, an additional '
auxiliary' variable is observed and used by means of conditioning (e.g. au
dio in addition to video). Our methods are closely related to 'self-superv
ised' methods heuristically proposed in computer vision\, and also provide
a theoretical foundation for such methods in terms of estimating a latent
-variable model. Likewise\, we show how variants of deep latent-variable m
odels such as VAE's can be seen as nonlinear ICA\, and made identifiable b
y suitable conditioning.
DTSTART:20200804T163000Z
DTEND:20200804T174500Z
LAST-MODIFIED:20200729T114814Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111801
END:VEVENT
BEGIN:VEVENT
UID:496e63b7-7479-42da-a167-63c5baa98389
DTSTAMP:20200808T213738Z
CREATED:20200724T123058Z
DESCRIPTION:Topic: A Blueprint of Standardized and Composable Machine Learn
ing\n\nSpeaker: Eric Xing\, Carnegie Mellon University\n\nIn handling wide
range of experiences ranging from data instances\, knowledge\, constraint
s\, to rewards\, adversaries\, and lifelong interplay in an ever-growing s
pectrum of tasks\, contemporary ML/AI research has resulted in thousands o
f models\, learning paradigms\, optimization algorithms\, not mentioning c
ountless approximation heuristics\, tuning tricks\, and black-box oracles\
, plus combinations of all above. While pushing the field forward rapidly\
, these results also make a comprehensive grasp of existing ML techniques
more and more difficult\, and make standardized\, reusable\, repeatable\,
reliable\, and explainable practice and further development of ML/AI produ
cts quite costly\, if possible\, at all. In this talk\, we present a simpl
e and systematic blueprint of ML\, from the aspects of losses\, optimizati
on solvers\, and model architectures\, that provides a unified mathematica
l formulation for learning with all experiences and tasks. The blueprint o
ffers a holistic understanding of the diverse ML algorithms\, guidance of
operationalizing ML for creating problem solutions in a composable and mec
hanic manner\, and unified framework for theoretical analysis.
DTSTART:20200806T190000Z
DTEND:20200806T203000Z
LAST-MODIFIED:20200731T111325Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111806
END:VEVENT
BEGIN:VEVENT
UID:3e387236-e277-4af8-951e-4aea4580e8f6
DTSTAMP:20200808T213738Z
CREATED:20200803T202139Z
DESCRIPTION:Topic: Statistical Learning Theory for Modern Machine Learning
\n\nSpeaker: John Shawe-Taylor\, University College London\n\nProbably App
roximately Correct (PAC) learning has attempted to analyse the generalisat
ion of learning systems within the statistical learning framework. It has
been referred to as a ‘worst case’ analysis\, but the tools have been exte
nded to analyse cases where benign distributions mean we can still general
ise even if worst case bounds suggest we cannot. The talk will cover the P
AC-Bayes approach to analysing generalisation that is inspired by Bayesian
inference\, but leads to a different role for the prior and posterior dis
tributions. We will discuss its application to Support Vector Machines and
Deep Neural Networks\, including the use of distribution defined priors.
DTSTART:20200811T163000Z
DTEND:20200811T174500Z
LAST-MODIFIED:20200807T153019Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111866
END:VEVENT
BEGIN:VEVENT
UID:61c5f4ae-f04f-4de1-af15-0fad703b001f
DTSTAMP:20200808T213738Z
CREATED:20200803T202729Z
DESCRIPTION:Topic: Latent State Discovery in Reinforcement Learning\n\nSpea
ker: John Langford\, Microsoft Research\n\nThere are three core orthogonal
problems in reinforcement learning: (1) Crediting actions (2) generalizin
g across rich observations (3) Exploring to discover the information neces
sary for learning. Good solutions to pairs of these problems are fairly we
ll known at this point\, but solutions for all three are just now being di
scovered. I’ll discuss several such results and dive into details on a few
of them.
DTSTART:20200813T190000Z
DTEND:20200813T203000Z
LAST-MODIFIED:20200805T201939Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111881
END:VEVENT
BEGIN:VEVENT
UID:61683ab9-437d-4879-8d75-f44e6e625aee
DTSTAMP:20200808T213738Z
CREATED:20200803T202352Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: Li Deng\, Citadel\n\n
DTSTART:20200818T163000Z
DTEND:20200818T174500Z
LAST-MODIFIED:20200803T202352Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111871
END:VEVENT
BEGIN:VEVENT
UID:6b9c0bbf-0d16-4276-8743-4e33e5202a37
DTSTAMP:20200808T213738Z
CREATED:20200803T202936Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: Jason Eisner\, Johns Hopkins
University\n\n
DTSTART:20200820T190000Z
DTEND:20200820T203000Z
LAST-MODIFIED:20200803T202936Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111886
END:VEVENT
BEGIN:VEVENT
UID:054b855f-b368-47e3-afcf-f9c0bf7451b6
DTSTAMP:20200808T213738Z
CREATED:20200803T202512Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: Piotr Indyk\, Massachusetts
Institute of Technology\n\n
DTSTART:20200825T163000Z
DTEND:20200825T174500Z
LAST-MODIFIED:20200803T202512Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111876
END:VEVENT
BEGIN:VEVENT
UID:ebc8c183-654e-4b16-8a5b-476e52f18543
DTSTAMP:20200808T213738Z
CREATED:20200803T203049Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: Inderjit Dhillon\, Universit
y of Texas\, Austin\n\n
DTSTART:20200827T190000Z
DTEND:20200827T203000Z
LAST-MODIFIED:20200803T203049Z
LOCATION:Remote Access Only - see link below
SUMMARY:Seminar on Theoretical Machine Learning
URL:https://www.ias.edu/node/111891
END:VEVENT
BEGIN:VEVENT
UID:8d2e8611-647b-4c4f-981a-aa67bd2e9294
DTSTAMP:20200808T213738Z
CREATED:20200713T175121Z
DESCRIPTION:Topic: Statistical modeling and missing data\n\nSpeaker: Rod Li
ttle\, University of Michigan\n\nAbstract: There is a very extensive liter
ature of statistical methods for the analysis of data with missing values.
I'll provide a historical overview\, including ad-hoc approaches\, statis
tical models and conditions for ignoring the missingness mechanism\, maxim
um likelihood methods\, factored likelihood methods\, the EM algorithm\, B
ayesian approaches\, multiple imputation\, and methods based on estimating
equations. I'll discuss some recent developments in robust modeling and m
issing not at random models. I'll comment briefly on the differing perspec
tives of full probability modeling and more algorithmic machine learning a
pproaches.
DTSTART:20200908T131500Z
DTEND:20200908T141500Z
LAST-MODIFIED:20200713T175429Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111626
END:VEVENT
BEGIN:VEVENT
UID:099e0f19-8107-48e5-a8d3-ec3858e960a9
DTSTAMP:20200808T213738Z
CREATED:20200713T175941Z
DESCRIPTION:Topic: Supervised learning with missing values\n\nSpeaker: Juli
e Josse\, Polytechnique\n\nAbstract: An abundant literature addresses miss
ing data in an inferential framework: estimating parameters and their vari
ance from incomplete tables. Here\, we consider supervised-learning settin
gs: predicting a target when missing values appear in both training and te
sting data. We study the seemingly-simple case where the target to predic
t is a\nlinear function of the fully-observed data and we show that\, in t
he presence of missing values\, the optimal predictor is not linear in gen
eral. In the particular Gaussian case\, it can be written as a linear func
tion of multiway interactions between the observed data and the various mi
ssing-value indicators. Due to its intrinsic complexity\, we study a simpl
e approximation and prove generalization bounds with finite samples\, high
lighting regimes for which each method performs best. We then show that mu
ltilayer perceptrons with ReLU activation functions can be consistent\, an
d can explore good trade-offs between the true model and approximations.
DTSTART:20200908T144000Z
DTEND:20200908T150000Z
LAST-MODIFIED:20200730T130117Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111631
END:VEVENT
BEGIN:VEVENT
UID:d14b301d-fa24-423a-b4bb-83747d8b2d2f
DTSTAMP:20200808T213738Z
CREATED:20200713T180208Z
DESCRIPTION:Topic: Missing data in single cell studies: augmentation\, inte
gration\, and discovery\n\nSpeaker: Barbara Englehardt\, Princeton Univers
ity\n\n
DTSTART:20200908T150500Z
DTEND:20200908T152500Z
LAST-MODIFIED:20200730T130224Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111636
END:VEVENT
BEGIN:VEVENT
UID:64c6fa1c-4f9d-4630-b662-f0e7913f8c99
DTSTAMP:20200808T213738Z
CREATED:20200715T144143Z
DESCRIPTION:Topic: Experimental Evaluation of Computer-Assisted Human Decis
ion Making: A Missing Data Approach\n\nSpeaker: Kosuke Imai\, Harvard Univ
ersity\n\nAbstract: In today’s data-driven society\, human beings still ma
ke most critical decisions and yet they are increasingly utilizing recomme
ndations produced by statistical and machine learning methods. Given the p
revalence of this approach in many areas of the society including business
\, healthcare\, and public policy\, there exists an urgent need to evaluat
e the impact of such computer-assisted human decision making. Using the po
tential outcomes framework of causal inference\, we develop a statistical
methodology for assessing how human decisions are influenced by computer-g
enerated inputs. We apply the proposed methodology to the randomized evalu
ation of a pretrial risk assessment instrument (PRAI) in the criminal just
ice system. The PRAI is used by judges in many states when making pretrial
decisions about whether an arrested individual should be released and und
er what conditions. A key methodological challenge is to infer whether an
arrestee would commit a new crime if released. Hence\, this can be formula
ted as a missing data problem. We analyze how this instrument influences j
udges’ decisions and derive an optimal PRAI to help judges satisfy a range
of possible fairness criteria.
DTSTART:20200908T155500Z
DTEND:20200908T161500Z
LAST-MODIFIED:20200730T130313Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111686
END:VEVENT
BEGIN:VEVENT
UID:5dbc788e-b18f-4d27-82a6-f1af5f37afd0
DTSTAMP:20200808T213738Z
CREATED:20200715T144506Z
DESCRIPTION:Topic: Model-based clustering of high-dimensional data: Pitfall
s & solutions\n\nSpeaker: David Dunson\, Duke University\n\nAbstract: In m
any applications\, it is of interest to cluster subjects based on very hig
h-dimensional data\, often in the presence of missing data. Although discr
ete mixture models are routinely used\, we demonstrate pitfalls in high-di
mensional settings. As we are interested in characterizing uncertainty in
clustering\, we focus on Bayesian methods. As the dimension p increases\,
we find that (1) MCMC mixing gets worse and worse\; and (2) the true poste
rior often has aberrant limiting behavior\, assigning all observations to
the same cluster or to different clusters. We propose LAtent Mixtures for
Bayesian (Lamb) clustering to solve (1)-(2) by clustering based on a low-d
imensional latent variable. We provide theoretical support showing that th
e posterior over partitions approximates the posterior obtained by an orac
le having knowledge of a lower-dimensional representation of the data. Sub
stantial gains relative to competitors are shown in simulations and the me
thods are applied to clustering of single cell RNAseq data. The methods ca
n trivially handle missing data under MAR assumptions.\n\nJoint work with
Noirrit Kiran Chandra & Tony Canale
DTSTART:20200909T160000Z
DTEND:20200909T170000Z
LAST-MODIFIED:20200715T144506Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111691
END:VEVENT
BEGIN:VEVENT
UID:95f43034-6f3b-426a-95dd-b42785002650
DTSTAMP:20200808T213738Z
CREATED:20200715T144859Z
DESCRIPTION:Topic: Causal inference with binary outcomes subject to both mi
ssingness and misclassification\n\nSpeaker: Grace Yi\, University of Wisco
nsin\, Oshkosh\n\nAbstract: Causal inference has been widely conducted in
various fields and many methods have been proposed for different settings.
However\, for noisy data with both mismeasurements and missing observatio
ns\, those methods often break down. In this talk\, I will discuss a probl
em concerning estimation of the average treatment effects (ATE) when binar
y outcomes are subject to both missingness and misclassification.\n\nThe a
symptotic biases caused by ignoring missingness and/or misclassification w
ill be examined. Methods of simultaneously correcting for missingness and
misclassification effects will be discussed. Simulation studies are conduc
ted to assess the performance of the proposed methods. An application to s
moking cessation data is reported to illustrate the use of the proposed me
thods.
DTSTART:20200909T173000Z
DTEND:20200909T175000Z
LAST-MODIFIED:20200730T130403Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111696
END:VEVENT
BEGIN:VEVENT
UID:3248adc9-5b10-4f57-b953-f82ebb97ce1d
DTSTAMP:20200808T213738Z
CREATED:20200715T145200Z
DESCRIPTION:Topic: Co-manifold learning with missing data\n\nSpeaker: Eric
Chi\, North Carolina State University\n\nAbstract: Representation learning
is typically applied to only one mode of a data matrix\, either its rows
or columns. Yet in many applications\, there is an underlying geometry to
both the rows and the columns. We propose utilizing this coupled structure
to perform co-manifold learning: uncovering the underlying geometry of bo
th the rows and the columns of a given matrix\, where we focus on a missin
g data setting. Our unsupervised approach consists of three components. We
first solve a family of optimization problems to estimate a complete matr
ix at multiple scales of smoothness. We then use this collection of smooth
matrix estimates to compute pairwise distances on the rows and columns ba
sed on a new multi-scale metric that implicitly introduces a coupling betw
een the rows and the columns. Finally\, we construct row and column repres
entations from these multi-scale metrics. We demonstrate that our approach
outperforms competing methods in both data visualization and clustering.
DTSTART:20200909T175500Z
DTEND:20200909T181500Z
LAST-MODIFIED:20200730T130459Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111706
END:VEVENT
BEGIN:VEVENT
UID:18e3561f-0864-40cc-8464-ea1f80a6eff4
DTSTAMP:20200808T213738Z
CREATED:20200715T145533Z
DESCRIPTION:Topic: Regularization and spurious correlations in sparse singl
e-cell transcriptomes\n\nSpeaker: Mickey Atwal\, Cold Spring Harbor Labora
tory\n\nAbstract: Recent advances in biotechnology and genomics have gener
ated dizzying amounts of large\, noisy\, and sparse datasets that require
concomitant development of machine learning methods. The analyses of singl
e-cell RNA-seq data have driven the development of data processing methods
\, such as transcript abundance normalization and imputation\, to address
the numerous sources of technical variability and missing data. While thes
e regularization methods have been demonstrated to be effective in imputin
g individual gene expression\, the suitability of these methods to the inf
erence of gene-gene interactions and gene networks have not been systemati
cally investigated. We report that the leading published methods all induc
e widespread and significant inflation of gene expression correlations acr
oss the genome\, resulting in erroneous inferences of molecular pathways a
nd networks. A model-agnostic correction approach is proposed that can eff
ectively eliminate correlation artifacts whilst still accurately inferring
gene expression levels.
DTSTART:20200909T184500Z
DTEND:20200909T190500Z
LAST-MODIFIED:20200730T130601Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111711
END:VEVENT
BEGIN:VEVENT
UID:7aef7200-3322-41fe-8188-6ee110120c0e
DTSTAMP:20200808T213738Z
CREATED:20200715T145806Z
DESCRIPTION:Topic: Statistical challenges with single cell RNA-Seq technolo
gies\n\nSpeaker: Rafael Irizarry\, Harvard University\n\nAbstract: I will
give a brief introduction to the technology followed by some exploratory d
ata analysis demonstrating the statistical challenges and how some of thes
e can be considered missing data problems.
DTSTART:20200910T160000Z
DTEND:20200910T170000Z
LAST-MODIFIED:20200715T145817Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111716
END:VEVENT
BEGIN:VEVENT
UID:c0833548-5375-4c5b-8c85-df8d5565247e
DTSTAMP:20200808T213738Z
CREATED:20200715T150138Z
DESCRIPTION:Topic: Gene expression recovery in single cell transcriptomic d
ata\n\nSpeaker: Nancy Zhang\, University of Pennsylvania\n\nAbstract: Cell
s are the basic biological units of multicellular organisms. The developme
nt of single-cell technologies such as single cell RNA sequencing (scRNA-s
eq) have enabled us to study the diversity of cell types in tissue and to
elucidate the roles of individual cell types in disease. Single cell RNA-s
eq data are noisy and sparse. The efficiency\, that is\, the proportion of
transcripts in the cell that are eventually counted\, can vary between 2-
60%\, and can be especially low in highly parallelized technologies. This
leads to a severe case of not-at-random missing data\, which hinders and c
onfounds analysis\, especially for low to moderately expressed genes. In t
his talk\, I will describe\, SAVER\, a noise reduction and missing-data im
putation framework for single cell RNA sequencing. We illustrate how this
critical recovery step allows improves cell-type classification\, increase
d power in the identification of cell type markers\, and more accurate ass
essment of gene-gene relationships at the single cell level. I will also d
escribe a transfer learning framework based on deep neural nets to borrow
information across related single cell data sets for de-noising. Our goal
is to leverage the expanding resources of publicly available scRNA-seq dat
a\, for example\, the Human Cell Atlas which aims to be a comprehensive ma
p of cell types in the human body. Through this framework\, we explore the
limits of data sharing: How much can be learned across cell types\, tissu
es\, and species? How useful are data from other technologies and labs in
improving the estimates from your own study? If time allows\, I will also
discuss the implications of such data denoising to downstream statistical
inference.
DTSTART:20200910T173000Z
DTEND:20200910T175000Z
LAST-MODIFIED:20200730T130650Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111721
END:VEVENT
BEGIN:VEVENT
UID:0355f16d-9b04-4836-bd88-cb9a1e0a5849
DTSTAMP:20200808T213738Z
CREATED:20200715T150353Z
DESCRIPTION:Topic: Synthesizing medical images using generative adversarial
networks\; applications\, promises\, and pitfalls\n\nSpeaker: Sanmi Koyej
o\, University of Illinois\n\n
DTSTART:20200910T175500Z
DTEND:20200910T181500Z
LAST-MODIFIED:20200730T130758Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111726
END:VEVENT
BEGIN:VEVENT
UID:228c5ecc-9ca2-4d06-a394-edd420b61bf5
DTSTAMP:20200808T213738Z
CREATED:20200715T150713Z
DESCRIPTION:Topic: High-dimensional omics data analysis with missing values
\n\nSpeaker: Anru Zhang\, University of Wisconsin\n\nAbstract: We have see
n the rise of high-dimensional omics data\, e.g.\, genome\, transcriptome\
, microbiome\, and proteome in recent decades. The different types of miss
ingness in modern omics data bring up significant biological and statistic
al challenges. In this talk\, we focus on two problems in modern omics dat
a analysis with missing values.\n\nFirst\, motivated by applications in ge
nomic data integration\, we propose a new framework of structured matrix c
ompletion (SMC) that treats structured missingness by design. Specifically
\, our proposed method aims at efficient matrix recovery when a subset of
the rows and columns of an approximately low-rank matrix are observed. We
provide theoretical justification for the proposed method and derive lower
bound for the estimation errors\, which together establish the optimal ra
te of recovery over certain classes of approximately low-rank matrices. Th
e method is applied to integrate several ovarian cancer genomic studies wi
th different extent of genomic measurements\, which enables us to construc
t more accurate prediction rules for ovarian cancer survival.\n\nThen\, we
address the common issues of missing counts and the high variability in t
he sequencing reads in the microbiome data. We introduce a surprisingly si
mple\, interpretable\, and efficient method for the estimation of composit
ional data regression through the lens of a novel high-dimensional log-err
or-in-variable regression model. The proposed method provides both correct
ions on sequencing data with possible overdispersion and simultaneously av
oids any subjective imputation of missing read counts. We provide theoreti
cal justification with matching upper and lower bounds for the estimation
error. The merit of the procedure is illustrated through real microbiome d
ata analysis and simulation studies.
DTSTART:20200910T184500Z
DTEND:20200910T190500Z
LAST-MODIFIED:20200730T130849Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111731
END:VEVENT
BEGIN:VEVENT
UID:a47934d8-53c2-4e9a-b2e6-f05fa16223b7
DTSTAMP:20200808T213738Z
CREATED:20200715T150957Z
DESCRIPTION:Topic: Metric and manifold repair for missing data\n\nSpeaker:
Anna Gilbert\, Yale University\n\nAbstract: For many machine learning task
s\, the input data lie on a low-dimensional manifold embedded in a high-di
mensional space and\, because of this high-dimensional structure\, most al
gorithms inefficient. The typical solution is to reduce the dimension of t
he input data using a standard dimension reduction algorithms such as {\sc
Isomap\, Laplacian Eigenmaps} or {\sc LLEs}. This approach\, however\, do
es not always work in practice as these algorithms require that we have so
mewhat ideal data. Unfortunately\, most data sets either have missing entr
ies or unacceptably noisy values. That is\, real data are far from ideal a
nd we cannot use these algorithms directly.\n\nIn this talk\, we focus on
the case when we have missing data. Some techniques\, such as matrix compl
etion\, can be used to fill in missing data but these methods do not captu
re the non-linear structure of the manifold. Here\, we present a new algor
ithm {\sc MR-Missing} that extends these previous algorithms and can be us
ed to compute low dimensional representation on data sets with missing ent
ries. We demonstrate the effectiveness of our algorithm by running three d
ifferent experiments.
DTSTART:20200911T160000Z
DTEND:20200911T170000Z
LAST-MODIFIED:20200715T150957Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111736
END:VEVENT
BEGIN:VEVENT
UID:f4738793-c152-49d4-8c7d-aaac7a153caf
DTSTAMP:20200808T213738Z
CREATED:20200715T151224Z
DESCRIPTION:Topic: Low-rank matrix recovery from quantized or count observa
tions\n\nSpeaker: Mark Davenport\, Georgia Tech\n\nAbstract: Low-rank matr
ices play a fundamental role in modeling and computational methods for sig
nal processing and machine learning. In many applications where low-rank m
atrices arise\, these matrices cannot be fully sampled or directly observe
d\, and one encounters the problem of recovering the matrix given only inc
omplete and indirect observations. The last decade has seen tremendous adv
ances in both the theory and algorithms for this setting. In this talk I w
ill discuss challenging versions of the low-rank matrix recovery problem i
n settings where our observations are highly quantized or consist of event
counts\, describing both existing results as well as open problems in thi
s space.
DTSTART:20200911T173000Z
DTEND:20200911T175000Z
LAST-MODIFIED:20200730T130932Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111741
END:VEVENT
BEGIN:VEVENT
UID:e9c81f17-8e5f-496d-a5ef-22e1b52fb342
DTSTAMP:20200808T213738Z
CREATED:20200715T151457Z
DESCRIPTION:Topic: Low Algebraic Dimension Matrix Completion\n\nSpeaker: La
ura Balzano\, Member\, School of Mathematics\n\nLow rank matrix completion
(LRMC) has received tremendous attention in recent years. The low rank as
sumption means that the columns (or rows) of the matrix to be completed ar
e points on a low-dimensional linear variety. This work extends this think
ing to cases where the columns are points on low-dimensional nonlinear alg
ebraic varieties\, a problem which we call Low Algebraic-Dimension Matrix
Completion (LADMC). We discuss two optimization approaches to this problem
\, one kernelized algorithm and one that leverages existing LRMC technique
s on a tensorized representation of the data. We also provide a formal mat
hematical justification for the success of our method and experimental res
ults showing that the new approach outperforms existing state-of-the-art m
ethods for matrix completion in many situations.
DTSTART:20200911T180000Z
DTEND:20200911T182000Z
LAST-MODIFIED:20200730T131012Z
LOCATION:Virtual
SUMMARY:Virtual Workshop on Missing Data Challenges in Computation\, Statis
tics and Applications
URL:https://www.ias.edu/node/111746
END:VEVENT
BEGIN:VEVENT
UID:f2d79439-e428-483c-bae0-3e20600e7f84
DTSTAMP:20200808T213738Z
CREATED:20200110T165145Z
DESCRIPTION:
DTSTART:20200921T130000Z
DTEND:20200921T130000Z
LAST-MODIFIED:20200110T165145Z
LOCATION:
SUMMARY:IAS School of Mathematics Term I Begins
URL:https://www.ias.edu/node/107721
END:VEVENT
BEGIN:VEVENT
UID:d676abf8-8beb-4986-8210-7b7c46331be7
DTSTAMP:20200808T213738Z
CREATED:20200806T225120Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201007T213000Z
DTEND:20201007T230000Z
LAST-MODIFIED:20200806T225219Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111906
END:VEVENT
BEGIN:VEVENT
UID:59f04d9b-dd46-47df-9fa7-9b8e0d0f6903
DTSTAMP:20200808T213738Z
CREATED:20200806T225404Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201014T213000Z
DTEND:20201014T230000Z
LAST-MODIFIED:20200806T225404Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111911
END:VEVENT
BEGIN:VEVENT
UID:825d0f2e-79e3-4979-934b-e6ee118acd0b
DTSTAMP:20200808T213738Z
CREATED:20200806T225427Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201021T213000Z
DTEND:20201021T230000Z
LAST-MODIFIED:20200806T225427Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111916
END:VEVENT
BEGIN:VEVENT
UID:b791a067-4512-4d32-9ef2-774449477840
DTSTAMP:20200808T213738Z
CREATED:20200806T225453Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201028T213000Z
DTEND:20201028T230000Z
LAST-MODIFIED:20200806T225453Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111921
END:VEVENT
BEGIN:VEVENT
UID:09d2e368-bf1d-466a-ae53-90ae7fe4401e
DTSTAMP:20200808T213738Z
CREATED:20200806T231920Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201104T223000Z
DTEND:20201105T000000Z
LAST-MODIFIED:20200806T231920Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111926
END:VEVENT
BEGIN:VEVENT
UID:b8235581-a75a-4a28-a2ed-f8bf97cb647f
DTSTAMP:20200808T213738Z
CREATED:20200806T231946Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201111T223000Z
DTEND:20201112T000000Z
LAST-MODIFIED:20200806T231946Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111931
END:VEVENT
BEGIN:VEVENT
UID:8c36df9d-4558-4a1b-a5bb-c3ede27db25f
DTSTAMP:20200808T213738Z
CREATED:20200806T232026Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201118T223000Z
DTEND:20201119T000000Z
LAST-MODIFIED:20200806T232026Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111936
END:VEVENT
BEGIN:VEVENT
UID:eb45fc96-2305-4500-9873-39c57f6d7e16
DTSTAMP:20200808T213738Z
CREATED:20200806T232058Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201125T223000Z
DTEND:20201126T000000Z
LAST-MODIFIED:20200806T232058Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111941
END:VEVENT
BEGIN:VEVENT
UID:c37694bd-a3ee-422d-914b-802a9d5509a6
DTSTAMP:20200808T213738Z
CREATED:20200806T232132Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201202T223000Z
DTEND:20201203T000000Z
LAST-MODIFIED:20200806T232132Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111946
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DTSTAMP:20200808T213738Z
CREATED:20200806T232156Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201209T223000Z
DTEND:20201210T000000Z
LAST-MODIFIED:20200806T232156Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111951
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UID:757c827c-8e1b-423f-9f5d-3fd76e441023
DTSTAMP:20200808T213738Z
CREATED:20200806T232220Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201216T223000Z
DTEND:20201217T000000Z
LAST-MODIFIED:20200806T232220Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111956
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UID:2b81e5d0-2322-42a6-b5f9-81eef2fb29d8
DTSTAMP:20200808T213738Z
CREATED:20200110T165522Z
DESCRIPTION:
DTSTART:20201218T230000Z
DTEND:20201218T230000Z
LAST-MODIFIED:20200110T165522Z
LOCATION:
SUMMARY:IAS School of Mathematics Term I Ends
URL:https://www.ias.edu/node/107731
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BEGIN:VEVENT
UID:af44a1b5-1364-46a7-af10-70158612befb
DTSTAMP:20200808T213738Z
CREATED:20200806T232258Z
DESCRIPTION:Topic: To Be Announced\n\nSpeaker: To Be Announced\n\n
DTSTART:20201223T223000Z
DTEND:20201224T000000Z
LAST-MODIFIED:20200806T232258Z
LOCATION:Remote Access Only
SUMMARY:Mathematical Conversations
URL:https://www.ias.edu/node/111961
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UID:c60e06ec-2698-44d1-8127-7aaa4c19fab3
DTSTAMP:20200808T213738Z
CREATED:20200110T165737Z
DESCRIPTION:
DTSTART:20210111T140000Z
DTEND:20210111T140000Z
LAST-MODIFIED:20200110T165737Z
LOCATION:
SUMMARY:IAS School of Mathematics Term II Begins
URL:https://www.ias.edu/node/107736
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UID:f3496c52-a9d9-4209-946e-dfd82cb6de6a
DTSTAMP:20200808T213738Z
CREATED:20200110T165817Z
DESCRIPTION:
DTSTART:20210409T220000Z
DTEND:20210409T220000Z
LAST-MODIFIED:20200110T165817Z
LOCATION:
SUMMARY:IAS School of Mathematics Term II Ends
URL:https://www.ias.edu/node/107741
END:VEVENT
END:VCALENDAR