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UID:37353961-3632-4533-b464-346432363432
X-WR-TIMEZONE:UTC
X-WR-CALNAME:IAS CSDM Seminars
BEGIN:VEVENT
UID:37356437-3430-4566-b939-663135316330
DTSTAMP:20240418T113225Z
CREATED:20231207T152209Z
DESCRIPTION:Topic: Marton's Conjecture\, aka the Polynomial Freiman--Ruzsa
Conjecture\n\nSpeakers: Frederick Manners\n\nA function $f : \mathbb{F}_2^
n \to \mathbb{F}_2^n$ is linear if\n$f(x+y)=f(x)+f(y)$ for all pairs $(x\,
y)$.\n\nSuppose $f$ is 'a bit linear' -- say\, $f(x+y)=f(x)+f(y)$ for 1% o
f\npairs $(x\,y)$. Must $f$ agree with a truly linear function a\npositiv
e proportion of the time? How large a proportion?\n\nThis question turns
out to be equivalent to asking for good\nquantitative bounds in the Freima
n--Ruzsa theorem\, a foundational\nresult in additive combinatorics. Mart
on gave a formulation\,\nequivalent to the statement above\, which she con
jectured should have\npolynomial bounds. I will outline a recent proof of
this\nconjecture.\n\nJoint work with Timothy Gowers\, Ben Green and Teren
ce Tao.
DTSTART:20240122T160000Z
DTEND:20240122T170000Z
LAST-MODIFIED:20240403T153245Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-558
END:VEVENT
BEGIN:VEVENT
UID:65623530-6362-4039-b037-366236386662
DTSTAMP:20240418T113225Z
CREATED:20231212T163308Z
DESCRIPTION:Topic: Online Discrepancy Minimization\n\nSpeakers: Victor Reis
\n\nThe online discrepancy minimization problem asks\, given unit vectors
\nv_1\, ...\, v_t arriving one at a time\, for online signs x_1 ...\, x_t4
\nin {-1\, 1} so that the signed sum x_1 v_1 + ... + x_t v_t has small\nco
ordinates in absolute value. \n\nIn the first half of the talk\, we survey
previous work in the adaptive\nand oblivious settings. In the second half
\, we present an online\nalgorithm for the oblivious setting which keeps s
igned sums\n10-subgaussian.\n\nBased on joint work with Janardhan Kulkarni
and Thomas Rothvoss.\n\n
DTSTART:20240123T153000Z
DTEND:20240123T173000Z
LAST-MODIFIED:20240123T124539Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-552
END:VEVENT
BEGIN:VEVENT
UID:66386365-3639-4565-b364-643836363839
DTSTAMP:20240418T113225Z
CREATED:20231212T161845Z
DESCRIPTION:Topic: The Tree Evaluation Problem: Context and Recent Results
\n\nSpeakers: Ian Mertz\n\nThe Tree Evaluation Problem has emerged in the
past decade as a\nleading candidate for separating logspace from polynomia
l time. In\nthis talk we will introduce the problem\, as well as the conte
xt behind\nits introduction and conjectured hardness. We then review recen
t lines\nof work challenging this conjecture\, leading up to a recent resu
lt\ntogether with James Cook showing near-logspace algorithms for Tree\nEv
aluation.
DTSTART:20240129T160000Z
DTEND:20240129T170000Z
LAST-MODIFIED:20240129T125957Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-559
END:VEVENT
BEGIN:VEVENT
UID:39636563-3961-4166-a138-636131646134
DTSTAMP:20240418T113225Z
CREATED:20231212T163412Z
DESCRIPTION:Topic: Omniprediction and Multigroup Fairness\n\nSpeakers: Pari
kshit Gopalan\n\nConsider a scenario where we are learning a predictor\, w
hose\npredictions will be evaluated by their expected loss. What if we do
\nnot know the precise loss at the time of learning\, beyond some\ngeneric
properties (like convexity)? What if the same predictor will\nbe used in
several applications in the future\, each with their own\nloss function? C
an we still learn predictors that have strong\nguarantees? \n\nThis motiva
tes the notion of omnipredictors: predictors with strong\nloss minimizatio
n guarantees across a broad family of loss\nfunctions\, relative to a benc
hmark hypothesis class. Omniprediction\nturns out to be intimately connect
ed to multigroup fairness notions\nsuch as multicalibration\, and also to
other topics like boosting\, swap\nregret minimization\, and the approxima
te rank of matrices. This talk\nwill present some recent work in this area
\, emphasizing these\nconnections.
DTSTART:20240130T153000Z
DTEND:20240130T173000Z
LAST-MODIFIED:20240130T134400Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-553
END:VEVENT
BEGIN:VEVENT
UID:65373466-6266-4662-b131-303665643636
DTSTAMP:20240418T113225Z
CREATED:20231212T162042Z
DESCRIPTION:Topic: Expanding the Reach of P Not Equal to NP: the Minimum Ci
rcuit Size Problem with a Random Oracle is NP-hard\n\nSpeakers: Rahul Ilan
go\n\nIn this talk\, I will discuss progress on showing hardness of the\nM
inimum Circuit Size Problem (MCSP). The computational complexity of\nMCSP
is a longstanding mystery\, dating back as far as Levin's seminal\nwork on
NP-completeness in 1973. Over the past several years\,\nresearchers have
utilized MCSP's seemingly special properties\n(properties not known for\,
say\, SAT) to prove intriguing connections\nbetween MCSP and other areas o
f theoretical computer science\,\nincluding learning theory\, cryptography
\, average-case complexity\, and\nproof complexity. \n\nWe give\, in our v
iew\, the strongest evidence yet that MCSP is in fact\nNP-complete (and th
us that SAT does indeed have these special\nproperties) by giving a reduct
ion in the presence of a 'random\noracle.' In particular our results yield
the first candidate reduction\nfrom SAT to MCSP and show that the existen
ce of sufficiently\n'unstructured' functions implies a problem with a know
n\n(non-black-box) worst-case to average-case reduction is NP-complete.\nC
uriously\, a key part of our reduction involves computing a\ncryptographic
proof of work.\n\nNo background knowledge on MCSP or other areas of compl
exity is\nrequired!
DTSTART:20240205T160000Z
DTEND:20240205T170000Z
LAST-MODIFIED:20240403T153442Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-560
END:VEVENT
BEGIN:VEVENT
UID:64363634-3666-4532-b934-366432363439
DTSTAMP:20240418T113225Z
CREATED:20231212T163613Z
DESCRIPTION:Topic: An Exponential Lower Bound on Three Query\, Linear Local
ly Correctable Codes\n\nSpeakers: Pravesh Kothari\n\nI will prove that the
block length of every linear 3-query Locally\nCorrectable Code (LCC) with
a constant distance over any small field\ngrows _exponentially_ with k\,
the dimension of the code. This result\ngives the first separation between
LCCs and LDCs where it is known\nthat 3-query codes of subexponential len
gth exist. (A q-query LCC is a\ncode where every coordinate of a codeword
can be recovered whp from q\nqueries into a corrupted codeword provided th
e fraction of errors is a\nsmall (but positive) constant. In contrast\, an
LDC only allows for\nrecovery of some linearly independent set $k$ of the
$n$ coordinates.)\n\nMy goal is to explain the following conceptual idea
in the talk: You\ncan often take an arbitrary combinatorial object (such a
s a local code\nwith some rate) and associate it with a family of satisfia
ble XOR\nformulas (e.g.\, encoding that the local checks 'work'). Proving
the\nunsatisfiability of a randomly chosen member of this family yields th
e\nimpossibility of the existence of this combinatorial object (in our\nca
se a code with the given rate.) We might naturally turn to the\nlarge body
of tools for analyzing random XOR formulas. Unfortunately\,\nin our setti
ng\, the transformation from codes produces formulas on $n$\nvariables usi
ng roughly only polylog n bits of randomness so one\ncannot hope for a pro
of of the unsatisfiability of the formulas via\nnaive probabilistic analys
is. \n\nThe new 'ace up our sleeve' is a class of spectral methods that ca
n\nprove even such 'randomness-starved' formulas unsatisfiable. These\nspe
ctral methods are based on variants of 'Kikuchi matrices' for\nwhich\, the
re is now an emerging set of tools for analyzing the\nspectral properties
via tight connections to the 'local' combinatorial\nstructure of the targe
t XOR formula. \n\nBased on joint work with Peter Manohar (CMU).
DTSTART:20240206T153000Z
DTEND:20240206T173000Z
LAST-MODIFIED:20240403T153549Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-554
END:VEVENT
BEGIN:VEVENT
UID:31346134-3430-4937-b765-356539343839
DTSTAMP:20240418T113225Z
CREATED:20231212T162206Z
DESCRIPTION:Topic: Advances in Parallel and Private Stochastic Optimization
from Ball Acceleration\n\nSpeakers: Kevin Tian\n\nConsider an oracle whic
h takes a point $x$ and returns the minimizer\nof a convex function $f$ in
an $\ell_2$ ball of radius $r$ around $x$.\nWhile it is straightforward t
o show that $\approx r^{-1}$ queries to\nthis oracle suffice to minimize $
f$ to high accuracy in a unit ball\,\nperhaps surprisingly\, we establishe
d recently that $r^{-2/3}$ queries\nis the tight rate up to logarithmic fa
ctors. The resulting framework\,\nalso known as ball acceleration\, has ad
vanced the state-of-the-art for\na host of fundamental optimization proble
ms exhibiting local\nstability. I will provide an overview of the ball acc
eleration\nframework\, its approximation-tolerant implementation\, and its
\napplications\, with an emphasis on parallel and private variants of\nsto
chastic convex optimization and outstanding open directions.
DTSTART:20240212T160000Z
DTEND:20240212T170000Z
LAST-MODIFIED:20240212T151243Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-561
END:VEVENT
BEGIN:VEVENT
UID:33316336-3763-4133-a138-366539306533
DTSTAMP:20240418T113225Z
CREATED:20231212T163652Z
DESCRIPTION:Topic: Reconstruction on Trees and Hypertrees\n\nSpeakers: Yuzh
ou Gu\n\nConsider the process where a signal propagates downward an infini
te\nrooted tree. On every edge some independent noise is applied to the\ns
ignal. The reconstruction problem asks whether it is possible to\nreconstr
uct the original signal given observations of signals received\nat vertice
s deep in the tree. This problem was first studied in the\n1970s in statis
tical physics\, and has found applications in noisy\ncomputation\, communi
ty detection\, genetics\, and so on. The hypertree\nversion of the reconst
ruction problem has relationships with problems\nsuch as random constraint
satisfaction problems and hypergraph\ncommunity detection.\n\nIn this tal
k I will discuss some recent progress on reconstruction\nproblems on trees
and hypertrees. In particular\, for a class of\nreconstruction on hypertr
ees problems\, we determine the exact\nreconstruction threshold for a wide
range of parameters. Two different\nmethods are used\, each with its adva
ntages and drawbacks. One method\nis based on strong data processing inequ
alities (SDPIs) and their\nmulti-terminal variants\, yielding non-asymptot
ic impossibility results\nthat are strong and sometimes tight. The other m
ethod is based on\nlarge degree asymptotics and robust reconstruction\, wh
ich gives tight\nimpossibility results in the large degree regime. An info
rmation\ntheoretic perspective plays an important role in these methods.\n
\nBased on joint works with Aaradhya Pandey and Yury Polyanskiy.\n\n
DTSTART:20240213T153000Z
DTEND:20240213T173000Z
LAST-MODIFIED:20240213T143814Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-555
END:VEVENT
BEGIN:VEVENT
UID:34663430-3036-4466-a131-356264626435
DTSTAMP:20240418T113225Z
CREATED:20231212T163732Z
DESCRIPTION:Topic: Analyzing the Max Entropy Algorithm for TSP\n\nSpeakers:
Nathan Klein\n\nI will discuss recent progress on approximating the metri
c traveling\nsalesperson problem\, focusing on a line of work beginning in
2011 that\nstudies the behavior of the max entropy algorithm. This algori
thm is a\nrandomized variant of the beautiful Christofides-Serdyukov algor
ithm\nfrom the 1970s which adds a minimum cost matching to the odd vertice
s\nof a minimum cost spanning tree. \n\nAfter giving a survey of importan
t concepts and results\, I will sketch\na proof that the max entropy algor
ithm is a better-than-3/2\napproximation for metric TSP. This sketch will
particularly emphasize\nthe utility of viewing the max entropy distributio
n over spanning\ntrees as a polynomial with a zero-free region. I will als
o discuss\nrecent work on lower bounds and derandomization\, as well as hi
ghlight\nopen directions. We are still far from understanding the worst ca
se\nperformance of this algorithm.\n\nBased on joint works with Anna Karli
n\, Shayan Oveis Gharan\, Leonid\nGurvits\, Jonathan Leake\, Billy Jin\, a
nd David Williamson.
DTSTART:20240220T153000Z
DTEND:20240220T173000Z
LAST-MODIFIED:20240208T151305Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-556
END:VEVENT
BEGIN:VEVENT
UID:64643332-6331-4463-b039-656537646164
DTSTAMP:20240418T113225Z
CREATED:20231212T162510Z
DESCRIPTION:Topic: Stability and Learning in Strategic Games\n\nSpeakers: É
va Tardos\n\nOver the last two decades we have developed good understandin
g how to\nquantify the impact of strategic user behavior on outcomes in ma
ny\ngames (including traffic routing and online auctions) and showed that
\nthe resulting bounds extend to repeated games assuming players use a\nfo
rm of learning (no-regret learning) to adapt to the environment. We\nwill
review how this area evolved since its early days\, and also\ndiscuss some
of the new frontiers\, including when repeated\ninteractions have carry-o
ver effects between rounds: when outcomes in\none round effect the game in
the future\, as is the case in many\napplications. \n\nIn this talk\, we
study this phenomenon in the context of a game\nmodeling queuing systems:
routers compete for servers\, where packets\nthat do not get served need t
o be resent\, resulting in a system where\nthe number of packets at each r
ound depends on the success of the\nrouters in the previous rounds. In joi
nt work with Jason Gaitonde\, we\nanalyze the resulting highly dependent r
andom processes\, and show\nbounds on the resulting budgeted welfare for a
uctions and the excess\nserver capacity needed to guarantee that all packe
ts get served in the\nqueuing system despite the selfish (myopic) behavior
of the\nparticipants. We will briefly mention work with Giannis Fikioris
in a\ndifferent game\, repeated auction with budgets\, where the same issu
e\narises also.
DTSTART:20240226T160000Z
DTEND:20240226T170000Z
LAST-MODIFIED:20240226T123722Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-563
END:VEVENT
BEGIN:VEVENT
UID:32393463-3265-4732-a635-336362653737
DTSTAMP:20240418T113225Z
CREATED:20240209T144226Z
DESCRIPTION:Topic: Computing Greatest Common Divisors of Polynomials in Par
allel\n\nSpeakers: Robert Andrews\n\nGiven two univariate polynomials\, ho
w does one compute their greatest\ncommon divisor (GCD)? This problem can
be solved in polynomial time\nusing the Euclidean algorithm\, and even in
quasi-linear time using a\nfast variant of the Euclidean algorithm. The GC
D can also be expressed\nin a linear-algebraic form. Basic tasks in linear
algebra like\ncomputing determinants and solving linear systems can be pe
rformed in\n$O(\log^2 n)$ parallel time\, and this can be used to compute
the GCD\nin $O(\log^2 n)$ parallel time. This algorithm does not take adva
ntage\nof any structure present in the resulting linear systems\, so in\np
rinciple one could compute the GCD even faster.\n\nIn this talk\, I will d
escribe a new algorithm that computes the GCD in\n$O(\log n)$ parallel tim
e by using a combination of polynomial\ninterpolation and Newton's identit
ies for symmetric polynomials.\nSimilar ideas yield $O(\log n)$ parallel t
ime algorithms to compute\nthe resultant\, Bézout coefficients\, and squar
efree decomposition.\n\nBased on joint work with Avi Wigderson.
DTSTART:20240227T153000Z
DTEND:20240227T173000Z
LAST-MODIFIED:20240227T190206Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-562
END:VEVENT
BEGIN:VEVENT
UID:63306666-3031-4664-b436-353430626266
DTSTAMP:20240418T113225Z
CREATED:20231212T162619Z
DESCRIPTION:Topic: Explicit SoS Lower Bounds from High Dimensional Expander
s\n\nSpeakers: Max Hopkins\n\nWhere are the hard problems? In the absence
of a proof of P ≠ NP\,\nresearchers have spent years proving unconditional
lower bounds for\nconstrained models of computation. In time\, a distinct
theme\narose: _random _problems (in particular random combinatorial\nopti
mization problems) are typically hard—fooling even our most\npowerful algo
rithmic frameworks like the Sum-of-Squares\nHierarchy._ _Despite this\, fi
nding such a hard\nproblem _explicitly_ has remained a major challenge: fo
r over 20\nyears\, no better method was known than brute force search. In
this\ntalk\, I will describe recent joint work with Ting-Chun Lin resolvin
g\nthis problem: a construction of explicit and near-optimally hard\n`cons
traint satisfaction problems’ for Sum-of-Squares based on\ntopological hig
h dimensional expanders.\n\nIn more detail\, in the first part of this tal
k I will give a brief\n`motivational’ introduction to Sum-of-Squares\, rev
iew Grigoriev’s\n1999 result proving hardness of random_ _XOR-instances fo
r\nSoS/refutation\, and discuss its close connection with the ubiquitous\n
notion of _graph expansion. _In the second part of the talk\,\nbuilding on
work of Dinur\, Filmus\, Harsha\, and Tulsiani (ITCS 2021) I\nwill show h
ow high dimensional expansion arises as a natural method of\nde-randomizin
g Grigoriev’s proof. Finally\, I’ll discuss the\nexistence of explicit con
structions of high dimensional expanders\,\ncompleting the proof. \n\nNo b
ackground in Sum-of-Squares or high dimensional expansion\nrequired!
DTSTART:20240304T160000Z
DTEND:20240304T170000Z
LAST-MODIFIED:20240304T152912Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-564
END:VEVENT
BEGIN:VEVENT
UID:62366136-3230-4534-b531-343630396436
DTSTAMP:20240418T113225Z
CREATED:20231218T154916Z
DESCRIPTION:Topic: Locally Consistent Decomposition of Strings with Applica
tions to Edit Distance Sketching\n\nSpeakers: Michal Koucký\n\nEdit distan
ce is a similarity measure for strings that counts how many\ncharacters ha
ve to be deleted\, inserted or substituted in one string\nto get another o
ne. It has many applications from comparing DNA\nsequences to text process
ing. We are still in search for its most\nefficient algorithms and its exa
ct computational complexity is still\nunknown. In this talk I will focus o
n sketching edit distance which\ncould provide an ultimate algorithm for e
dit distance in the context\nof large databases of strings. \n\nThe goal i
s to compute for each string a short sketch such that from\nsketches of tw
o strings we can estimate their edit distance. This has\nconnection to emb
edding of metric spaces.\n\nIn this talk I will provide an overview of wha
t is known about\nsketching edit distance\, and I will present a new local
ly consistent\ndecomposition of strings which has applications for sketchi
ng of edit\ndistance and approximate pattern matching.\n\nThis is based on
recent results with Sudatta Bhattacharya and Mike\nSaks.
DTSTART:20240305T153000Z
DTEND:20240305T173000Z
LAST-MODIFIED:20240305T123316Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-557
END:VEVENT
BEGIN:VEVENT
UID:66653036-6630-4964-b239-633732323561
DTSTAMP:20240418T113225Z
CREATED:20231212T162730Z
DESCRIPTION:Topic: Sparsification of Gaussian Processes\n\nSpeakers: Anindy
a De\n\nIn this talk\, we will show that the supremum of any centered Gaus
sian\nprocess can be approximated to any arbitrary accuracy by a finite\nd
imensional Gaussian process where the dimension of the approximator\nis ju
st dependent on the target error. As a corollary\, we show that\nfor any n
orm \Phi defined over R^n and target error \eps\, there is a\nnorm \Psi su
ch that (i) \Psi is only dependent on t(\eps) = \exp \exp\n(poly(1/\eps))
dimensions and (ii) \Psi(x)/\Phi(x) \in [1-\eps\, 1+\n\eps] with probabili
ty 1-\eps (when x is sampled from the Gaussian\nspace). Our proof relies o
n Talagrand's majorizing measures theorem. \n\nJoint work with Shivam Nadi
mpalli\, Ryan O'Donnell and Rocco\nServedio.
DTSTART:20240311T150000Z
DTEND:20240311T160000Z
LAST-MODIFIED:20240312T120426Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-565
END:VEVENT
BEGIN:VEVENT
UID:31363336-3339-4438-b963-366131316337
DTSTAMP:20240418T113225Z
CREATED:20240129T161945Z
DESCRIPTION:Topic: The Structure of Translational Tilings in Z^d\n\nSpeaker
s: Rachel Greenfeld\n\nA finite set $F$ in $\mathbb{Z}^d$ is a translation
al tile of \n$\mathbb{Z}^d$ if one can cover $\mathbb{Z}^d$ by translated
copies\nof $F$ without any overlaps\, i.e.\, there exists a translational
\ntiling of $\mathbb{Z}^d$ by $F$. Suppose that $F$ is a translational\nt
ile\; what can we say about the structure of tilings by $F$? In the\ntalk
we will discuss this question and introduce techniques\,\nconjectures\, r
esults\, and open problems in the area.
DTSTART:20240312T143000Z
DTEND:20240312T163000Z
LAST-MODIFIED:20240313T114510Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-558
END:VEVENT
BEGIN:VEVENT
UID:32643236-6465-4735-a163-636462666531
DTSTAMP:20240418T113225Z
CREATED:20231212T162901Z
DESCRIPTION:Topic: Computationally Sound Proofs of Network Properties\n\nSp
eakers: Rotem Oshman\n\nIn distributed certification\, our goal is to cert
ify that a network\nhas a certain desired property\, e.g.\, the network is
connected\, or the\ninternal states of its nodes encode a valid spanning
tree of the\nnetwork. To this end\, a prover generates certificates that a
re stored\nat each network node\, and the nodes can then interact with one
another\nin order to check their certificates and verify that the propert
y\nholds. This can be viewed as a distributed analog of NP. However\, like
\nmost theoretical models of distributed computing\, the traditional\nmode
l for distributed certification is information-theoretic: the\nprover and
the network nodes are computationally unbounded\, and the\nonly efficiency
measures we consider are the length of the\ncertificates and the communic
ation required to verify them. The\ninformation-theoretic nature of the mo
del sets the area of distributed\ncertification apart from classical compl
exity theory\, and also makes\nit subject to strong lower bounds from the
world of nondeterministic\ncommunication complexity.\n\nIn this talk\, I w
ill describe a computationally sound version of\ndistributed certification
\, where the prover and the network nodes are\nrequired to run in polynomi
al time in the size of the network.\nIntroducing computational restriction
s allows us to leverage\ncryptography\, and we show that any network prope
rty in P can be\ncertified using certificates of polylogarithmic length by
a global\nprover that sees the entire network. Ideally\, however\, we wou
ld like\nthe prover to also be distributed\, and we show that this can be
done\nas well: any polynomial distributed algorithm can efficiently certif
y\nits own execution with low overhead in terms of communication and\nroun
ds. The main challenge in the distributed setting is that no\nsingle netwo
rk node can see the entire execution of the algorithm.\n\nThis is joint wo
rk with Eden Aldema Tshuva\, Elette Boyle\, Ran Cohen\nand Tal Moran. No b
ackground in cryptography is assumed for the talk.
DTSTART:20240318T150000Z
DTEND:20240318T160000Z
LAST-MODIFIED:20240318T113843Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-566
END:VEVENT
BEGIN:VEVENT
UID:61396336-3763-4231-b533-376334663562
DTSTAMP:20240418T113225Z
CREATED:20240202T152130Z
DESCRIPTION:Topic: Geodesics and Minimal Surfaces in a Random Environment\n
\nSpeakers: Ron Peled\n\nEndow the edges of the $Z^D$ lattice with positiv
e weights\, sampled\nindependently from a suitable distribution (e.g.\, un
iformly\ndistributed on [a\,b] for some b>a>0). We wish to study the geome
tric\nproperties of the resulting network\, focusing on the following\ncha
llenges:\n\n * Geodesics (first-passage percolation): Given two vertices in
$Z^D$\,\nconsider the path with minimal sum of edge weights that connects
them.\nHow close is this path to a straight line?\n * Minimal surfaces: Co
nsider the cube {$-L\,...\, L$}$^D$ and the\nminimal cut separating the 'u
pper' and 'lower' halves of the boundary\nof the cube. How flat is this cu
t?\n\nI will give a gentle introduction to these challenges\, with emphasi
s\non the many open problems and some of the recently obtained results. \n
\nBased on joint works with Michal Bassan and Shoni Gilboa and with\nBarba
ra Dembin\, Dor Elboim and Daniel Hadas.
DTSTART:20240319T143000Z
DTEND:20240319T163000Z
LAST-MODIFIED:20240319T131020Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-559
END:VEVENT
BEGIN:VEVENT
UID:63336135-6339-4465-a664-663836613031
DTSTAMP:20240418T113225Z
CREATED:20240109T185048Z
DESCRIPTION:Topic: Tight Cell-Probe Lower Bounds for Dynamic Succinct Dicti
onaries\n\nSpeakers: Huacheng Yu\n\nA dictionary data structure maintains
a set of at most $n$ keys from\nthe universe $[U]$ under key insertions an
d deletions\, such that given\na query $x\in[U]$\, it returns if $x$ is in
the set. Some variants also\nstore values associated to the keys such tha
t given a query $x$\, the\nvalue associated to $x$ is returned when $x$ is
in the set.\n\nThis fundamental data structure problem has been studied f
or six\ndecades since the introduction of hash tables in 1953. A hash tabl
e\noccupies $O(n\log U)$ bits of space with constant time per operation\ni
n expectation. There has been a vast literature on improving its time\nand
space usage. The state-of-the-art dictionary by Bender\,\nFarach-Colton\,
Kuszmaul\, Kuszmaul and Liu has space consumption close\nto the informati
on-theoretic optimum\, using a total of\n\[\log\binom{U}{n}+O(n\log^{(k)}
n)\]\nbits\, while supporting all operations in $O(k)$ time\, for any\npar
ameter $k\leq \log^* n$. The term $O(\log^{(k)}\nn)=O(\underbrace{\log\cdo
ts\log}_k n)$ is referred to as the _wasted\nbits per key_.\n\nIn this tal
k\, we show a matching cell-probe lower bound: For\n$U=n^{1+\Theta(1)}$\,
any dictionary with $O(\log^{(k)} n)$ wasted bits\nper key must have expec
ted operational time $\Omega(k)$\, in the\ncell-probe model with word-size
$w=\Theta(\log U)$. Furthermore\, if a\ndictionary stores values of $\The
ta(\log U)$ bits\, we show that\nregardless of the query time\, it must ha
ve $\Omega(k)$ expected update\ntime. It is worth noting that this is the
first cell-probe lower bound\non the trade-off between space and update ti
me for general data\nstructures.\n\nJoint work with Tianxiao Li\, Jingxun
Liang and Renfei Zhou.
DTSTART:20240401T150000Z
DTEND:20240401T160000Z
LAST-MODIFIED:20240401T131737Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-568
END:VEVENT
BEGIN:VEVENT
UID:30313135-3165-4765-a332-323839303136
DTSTAMP:20240418T113225Z
CREATED:20240207T162308Z
DESCRIPTION:Topic: New Derandomized Agreement Testers\n\nSpeakers: Yotam Di
kstein\n\nAgreement testing (aka direct product testing)\, checks if consi
stent\nlocal information reveals global structure. Beyond its theoretical
\nconnections to probabilistic checkable proofs (PCPs)\, constructing\nagr
eement testers is a fundamental combinatorial question that has\nexciting
applications in coding theory and hardness amplification.\n\nLet (V\,S) be
a hypergraph with vertices. The direct product encoding\nencodes a functi
on $g:V \to \{0\,1\}$ by its restrictions $F(g)=\{g|_s:\ns\in S\}$. Agreem
ent testing asks the inverse question: Given\n$F=\{f_s:s \to \{0\,1\}: s \
in S\}$\, can we test whether $F$ is\nnon-trivially close to an encoding o
f some $g:V \to \{0\,1\}$\, by\nquerying only two random functions? The te
st we consider samples two\nrandom $s\,s' \in S$ and accepts if $f_s = f_{
s'}$ on the shared\nintersection. In this talk we focus on the more challe
nging 1%-regime\,\nwhere the probability that $F$ passes the test is non-n
egligible\, but\nsmall (1%). Hypergraphs where passing the test with non-n
egligible\nprobabiliy implies correlation with some $F(g)$\, are called so
und\nagreement tests.\n\nConstructing sound agreement tests was studied in
the 90'\, and works\nin complexity inspired the goal of constructing agre
ement tests where\nthe size of $S$ grows as slowly as possible with respec
t to $V$. Such\nsparse tests are an important prerequisite for derandomizi
ng some\nfundamental PCP constructions.\n\nIn this work we construct novel
agreement tests for the 1%-regime\,\nwhere $|S|=O(|V|)$. Quite surprising
ly\, constructing such tests\nrequires the hypergraph to have no small con
nected topological covers\,\nalong with other more combinatorial propertie
s. We construct such\nhypergraphs using subgroups of the symplectic group
over the piadic\nnumbers\, along with a variety of other topological and c
ombinatorial\ntools from high dimensional expander theory.\n\nThis talk is
based on joint work with Irit Dinur and Alex Lubotzky.\n\n
DTSTART:20240402T143000Z
DTEND:20240402T163000Z
LAST-MODIFIED:20240402T144633Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-561
END:VEVENT
BEGIN:VEVENT
UID:66376162-3833-4363-a631-636634353035
DTSTAMP:20240418T113225Z
CREATED:20240304T193352Z
DESCRIPTION:Topic: Polynomial Capacity and its Applications: To TSP and Bey
ond \n\nSpeakers: Jonathan Leake\n\nAbout 20 years ago\, Gurvits developed
the notion of polynomial\ncapacity to give a simple proof of the famous v
an der Waerden lower\nbound on the permanent of a doubly stochastic matrix
. Since then\,\nsimilar techniques have led to various other applications\
; for\nexample: approximate counting of the lattice points of certain\npol
ytopes\, an efficient algorithm for the non-commutative version of\nthe po
lynomial identity testing problem\, and most recently\, an\nimproved appro
ximation factor for the traveling salesperson problem\n(TSP) via the max-e
ntropy algorithm.\n\nIn this talk\, we will discuss polynomial capacity\,
some of its\napplications\, and its connection to entropy optimization. In
\nparticular\, we will discuss how we (with Gurvits and Klein) recently\nu
sed polynomial capacity to further improve the TSP approximation\nfactor.
\n\nJoint work with Petter Brändén\, Leonid Gurvits\, Nathan Klein\, Igor
\nPak\, Nisheeth Vishnoi.
DTSTART:20240408T150000Z
DTEND:20240408T160000Z
LAST-MODIFIED:20240408T140657Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-571
END:VEVENT
BEGIN:VEVENT
UID:33393664-3136-4636-b334-666230656263
DTSTAMP:20240418T113225Z
CREATED:20240304T193924Z
DESCRIPTION:Topic: The Method of Hypergraph Containers\n\nSpeakers: Wojciec
h Samotij\n\nThe method of hypergraph containers is a widely-applicable te
chnique\nin probabilistic combinatorics. The method enables one to gain co
ntrol\nover the independent sets of many `interesting' hypergraphs by\nexp
loiting the fact that these sets exhibit a certain subtle\nclustering phen
omenon. Since many problems studied in extremal and\nprobabilistic combina
torics\, Ramsey theory\, and discrete geometry can\nbe (naturally) phrased
in terms of independent sets in auxiliary\nhypergraphs\, good control ove
r these sets has many `practical'\nconsequences.\n\nIn the first part of t
his talk\, I will provide a gentle introduction\nto the method\, guided an
d motivated by the following elementary\nproblem in Ramsey theory: Does th
ere exist a graph G without a\ncomplete subgraph on four vertices that can
not be partitioned into two\ntriangle-free graphs?\n\nThe heart of the met
hod is a hypergraph container lemma (HCL) – a\nformal statement that quant
ifies the aforementioned notion of\nclustering. In the second part of this
talk\, I will state and discuss\nseveral HCLs and\, if time permits\, ske
tch a (short) proof of one of\nthem (found recently in collaboration with
Marcelo Campos).
DTSTART:20240409T143000Z
DTEND:20240409T163000Z
LAST-MODIFIED:20240409T120918Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-563
END:VEVENT
BEGIN:VEVENT
UID:31656635-3130-4364-a364-376436653664
DTSTAMP:20240418T113225Z
CREATED:20240304T193550Z
DESCRIPTION:Topic: Graphs\, CSPs and Codes\n\nSpeakers: Madhu Sudan\n\nA sp
arsification of a structure\, with respect to a class of queries\,\nproduc
es a compressed representation of the structure while answering\nevery que
ry in the class approximately correctly. The seminal example\nof sparsific
ation is 'graph sparsification with respect to cut\nqueries'\, due to work
s of Karger and Benczur and Karger from the\n1990s\, showing that every gr
aph can be compressed to near-linear size\n(in the number of nodes in the
graph) while approximately capturing\nthe size of every cut in the graph.
In 2015 Kogan and Krauthgamer\ngeneralized the notion of sparsification to
all Constraint\nSatisfaction Problems (CSPs) --- here the structure to be
compressed\nis an instance of the CSP on n variables and a query is an as
signment\nto the n variables\, and the goal thus is to approximately deter
mine\nthe number of constraints satisfied by the queried assignment. Sever
al\nfollow up works gave some non-trivial CSPs that allow for near linear
\n(in n) sparsifications\, including classification of all binary CSPs\n(w
here each constraint applies to two variables) that allow such\nsparsifica
tion\, but the general picture seemed wide open.\n\nIn our works we introd
uce a new class of sparsification problems\,\nnamely code sparsification\,
where the structure to be preserved is a\nlinear error correcting code\;
the query is a message\, and the goal is\nto compute the approximate weigh
t of the encoding of the message. We\nshow that this class of problems giv
es the right language to abstract\nthe techniques of Karger and Benczur an
d Karger --- and indeed all\ncodes can be sparsified to length nearly line
ar in the number of\nmessage bits. This generalization already resolves so
me basic\nquestions in CSP sparsification. A further generalization to add
itive\ncodes over finite abelian groups gives even powerful results and in
\nparticular completely classifies the class of symmetric Boolean CSPs\nth
at allow nearly linear sized sparsification. (Prior to our work even\nthe
case of sparsification of 3-XOR constraints was open.) \n\nBased on joint
works with Sanjeev Khanna (U. Penn.) and Aaron (Louie)\nPutterman (Harvard
).
DTSTART:20240415T150000Z
DTEND:20240415T160000Z
LAST-MODIFIED:20240327T125200Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-572
END:VEVENT
BEGIN:VEVENT
UID:63326539-3736-4633-b866-663665326231
DTSTAMP:20240418T113225Z
CREATED:20240314T154752Z
DESCRIPTION:Topic: Parallel Repetition for 3-Player XOR Games\n\nSpeakers:
Yang Liu\n\nIn a $3$-$\mathsf{XOR}$ game $\mathcal{G}$\, the verifier samp
les a\nchallenge $(x\,y\,z)\sim \mu$ where $\mu$ is a probability distribu
tion\nover $\Sigma\times\Gamma\times\Phi$\, and a map $t\colon\n\Sigma\ti
mes\Gamma\times\Phi\to\mathcal{A}$ for a finite Abelian group\n$\mathcal{A
}$ defining a constraint. The verifier sends the\nquestions $x$\, $y$ and
$z$ to the players Alice\, Bob and Charlie\nrespectively\, receives answ
ers $f(x)$\, $g(y)$ and $h(z)$ that are\nelements in $\mathcal{A}$ and acc
epts if $f(x)+g(y)+h(z) = t(x\,y\,z)$.\nThe value\, $\mathsf{val}(\mathcal
{G})$\, of the game is defined to be\nthe maximum probability the verifier
accepts over all players'\nstrategies.\n\nWe show that if $\mathcal{G}$ i
s a $3$-$\mathsf{XOR}$ game with value\nstrictly less than $1$\, whose und
erlying distribution over questions\n$\mu$ does not admit Abelian embeddin
gs into $(\mathbb{Z}\,+)$\, then\nthe value of the $n$-fold repetition of
$\mathcal{G}$ is exponentially\ndecaying. That is\, there exists $c=c(\mat
hcal{G})>0$ such that\n$\mathsf{val}(\mathcal{G}^{\otimes n})\leq 2^{-cn}$
. This extends a\nprevious result of [Braverman-Khot-Minzer\, FOCS 2023] s
howing\nexponential decay for the GHZ game. Our proof combines tools from
\nadditive combinatorics and tools from discrete Fourier analysis.\n\nBase
d on joint work with Amey Bhangale\, Mark Braverman\, Subhash Khot\,\nDor
Minzer.
DTSTART:20240416T143000Z
DTEND:20240416T163000Z
LAST-MODIFIED:20240416T124511Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-564
END:VEVENT
BEGIN:VEVENT
UID:39306164-3333-4162-a261-303931653364
DTSTAMP:20240418T113225Z
CREATED:20240205T201351Z
DESCRIPTION:Topic: Additive Combinatorics Without Groups\n\nSpeakers: Huy T
uan Pham\n\nSubsets $A$ of an abelian group with a small doubling $|A+A|/|
A|$ have\nbeen extensively studied\, and results of Freiman\, Ruzsa and Gr
een give\nfundamental structural descriptions of such sets. These have imp
ortant\napplications across combinatorics and computer science\, and have
\nmotivated the development of a number of influential techniques. \n\nIn
this talk\, I will discuss a new combinatorial approach to several\nproble
ms involving sets with small doubling. \n\nOver abelian groups where all e
lements have order at most $r$\, the\nFreiman-Ruzsa theorem says that a se
t $A$ with $|A+A| \le K|A|$ is\ncontained in a subgroup of size at most $O
_{r\,K}(|A|)$\, and Ruzsa\nconjectured a tight dependence on $K$. In the f
irst application\, I\nwill discuss a short complete resolution of Ruzsa’s
conjecture. \n\nIn the second application\, we show that random functions
give good\nsumset extractors in general (possibly nonabelian) groups. \n\n
Surprisingly\, our approach is crucially motivated by purely\ncombinatoria
l graph-theoretic insights\, where we find that the group\nstructure is su
perfluous and can be replaced by much more general\ncombinatorial structur
es. In particular\, I will describe a further\ncorollary\, which is a comb
inatorial generalization of the\nFreiman-Ruzsa theorem over $\mathbb{F}_2^
n$. \n\nBased on joint work with David Conlon\, Jacob Fox and Liana\nYepre
myan.
DTSTART:20240422T150000Z
DTEND:20240422T160000Z
LAST-MODIFIED:20240408T124636Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-569
END:VEVENT
BEGIN:VEVENT
UID:35383736-3235-4733-b463-393435656234
DTSTAMP:20240418T113225Z
CREATED:20240205T201531Z
DESCRIPTION:Topic: Random Cayley Graphs From a Combinatorial Perspective \n
\nSpeakers: Huy Tuan Pham\n\nCayley graphs provide interesting bridges bet
ween graph theory\,\nadditive combinatorics and group theory. Fixing an am
bient finite\ngroup\, random Cayley graphs are constructed by choosing a g
enerating\nset at random. These graphs reflect interesting symmetries and
\nproperties of the group\, at the cost of inducing complex\ndependencies.
\n\nI will discuss several results on clique and independence numbers of
\nrandom Cayley graphs in general groups\, progress towards a conjecture\n
of Alon on existence of Ramsey Cayley graphs\, and a proof of a\nconjectur
e of Alon and Orlitsky. These questions are naturally\nconnected with some
fundamental problems in additive combinatorics.\nSurprisingly\, our insig
hts suggest that in many of these problems\, the\ngroup structure is super
fluous and can be replaced by much more\ngeneral combinatorial structures.
\n\nI will discuss the main general combinatorial models and ideas behind
\nthese results. I will also discuss how they relate to the additive\ncomb
inatorial corollaries discussed in Monday’s talk. \n\nBased on joint work
with David Conlon\, Jacob Fox and Liana\nYepremyan.
DTSTART:20240423T143000Z
DTEND:20240423T163000Z
LAST-MODIFIED:20240408T124839Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-560
END:VEVENT
BEGIN:VEVENT
UID:37336433-3134-4139-a463-646332636433
DTSTAMP:20240418T113225Z
CREATED:20240212T154359Z
DESCRIPTION:Topic: Lower Bounds for Set-Multilinear Branching Programs\n\nS
peakers: Shubhangi Saraf\n\nIn this talk\, I will discuss lower bounds for
a certain\nset-multilinear restriction of algebraic branching programs. T
he\nsignificance of the lower bound and the model is underscored by the\nr
ecent work of Bhargav\, Dwivedi\, and Saxena (2023)\, which showed that\ns
uper-polynomial lower bounds for the model of sum of ordered set\nmultilin
ear ABPs -- when the underlying polynomial of sufficiently low\ndegree --
would imply super-polynomial lower bounds against general\nABPs\, thereby
resolving Valiant's longstanding conjecture that the\npermanent polynomial
cannot be computed efficiently by ABPs. We will\ndiscuss a recent result
which 'almost' meets this low-degree demand.\n\nThis is based on joint wor
k with Prerona Chatterjee\, Deepanshu Kush\nand Amir Shpilka.
DTSTART:20240429T150000Z
DTEND:20240429T160000Z
LAST-MODIFIED:20240408T124210Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-570
END:VEVENT
BEGIN:VEVENT
UID:31666363-6634-4831-b435-376136616163
DTSTAMP:20240418T113225Z
CREATED:20240314T154957Z
DESCRIPTION:Topic: Incidence Bounds via Extremal Graph Theory\n\nSpeakers:
Istvan Tomon\n\nA cornerstone result in geometry is the Szemerédi–Trotter
theorem\,\nwhich gives a sharp bound on the maximum number of incidences b
etween\n$m$ points and $n$ lines in the real plane. A natural generalizati
on\nof this is to consider point-hyperplane incidences in higher\ndimensio
ns. As proposed by Chazelle in the 90's\, we are interested in\nthe maximu
m number of incidences between $m$ points and $n$\nhyperplanes\, assuming
no $s$ points lie in the intersection of $s$\nhyperplanes. The latter cond
ition is needed to\navoid trivialities\, like all hyperplanes intersecting
in a\nline\, and all points contained in this line. Starting from dimensi
on\n3\, matching lower and upper bounds are no longer known for this\nprob
lem. I will talk about how to prove sharp bounds over arbitrary\nfields us
ing methods from extremal graph theory\, and discuss\nanalogues of this pr
oblem concerning point-variety incidences and\nunit distance graphs.\n\nBa
sed on a joint work with Aleksa Milojević and Benny Sudakov.
DTSTART:20240430T143000Z
DTEND:20240430T163000Z
LAST-MODIFIED:20240405T150807Z
LOCATION:Simonyi Hall 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar II
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-ii-565
END:VEVENT
BEGIN:VEVENT
UID:64663663-6631-4366-b235-343039613734
DTSTAMP:20240418T113225Z
CREATED:20240329T180207Z
DESCRIPTION:Speakers: Matthew Hastings
DTSTART:20240513T150000Z
DTEND:20240513T160000Z
LAST-MODIFIED:20240329T180410Z
LOCATION:Simonyi 101 and Remote Access
SUMMARY:Computer Science/Discrete Mathematics Seminar I
URL:https://www.ias.edu/math/events/computer-sciencediscrete-mathematics-se
minar-i-573
END:VEVENT
END:VCALENDAR