Seminars Sorted by Series

Special Mathematical Physics Seminar

Oct
22
2014

Special Mathematical Physics Seminar

Quasiperiodic operators with monotone potentials: sharp arithmetic spectral transitions and small coupling localization
Svetlana Jitomirskaya
4:00pm|S-101

It is well known that spectral properties of quasiperiodic operators depend rather delicately on the arithmetics of the parameters involved. Consequently, obtaining results for all parameters often requires considerably more difficult arguments than...

Oct
04
2016

Special Mathematical Physics Seminar

Derivation of the Vlasov equation
Peter Pickl
4:15pm|S-101

The rigorous derivation of the Vlasov equation from Newtonian mechanics of $N$ Coulomb-interacting particles is still an open problem. In the talk I will present recent results, where an $N$-dependent cutoff is used to make the derivation possible...

Jan
24
2017

Special Mathematical Physics Seminar

Reinforced random walks and statistical physics
Pierre Tarres
1:30pm

We explain how the Edge-reinforced random walk, introduced by Coppersmith and Diaconis in 1986, is related to several models in statistical physics, namely the supersymmetric hyperbolic sigma model studied by Disertori, Spencer and Zirnbauer (2010)...

Special Mathematics Physics Seminar

May
15
2018

Special Mathematics Physics Seminar

An Introduction to Liouville Theory
2:00pm|Simonyi Hall 101

Liouville Conformal Field Theory (LCFT) is an essential building block of Polyakov’s formulation of non critical string theory. Moreover, scaling limits of statistical mechanics models on random lattices (planar maps) are believed to be described by...

Special Members’ Seminar

Dec
13
2010

Special Members’ Seminar

Uniform Well-Posedness and Inviscid Limit for the Benjamin-Ono-Burgers Equation
4:15pm|S-101

We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation is uniformly globally well-posed in H^1 for all "\epsilon\in [0,1]". Moreover, we show that for any T>0 the solution converges in C([0,T]:H^1) to that of Benjamin-Ono equation as...

Special Members’ Seminar

Special Mini-Course in Geometric PDE

Mar
09
2009

Special Mini-Course in Geometric PDE

Dirichlet Duality and the Nonlinear Dirichlet Problem Part I: For domains in R^n; Part II: On Riemannian Manifolds
H. Blaine Lawson, Jr.
3:30pm|S-101

Manifolds with geometric structure carry large and useful families of non-standard “subharmonic” functions. For example, any almost complex manifold with hermitian metric carries plurisubharmonic functions. Moreover, it also carries “Lagrangian...

Special Number Theory Afternoon

Apr
21
2023

Special Number Theory Afternoon

Counting Irreducible Integral Polynomials with Roots Approximating Configuration of Points
2:30pm|Simonyi 101 and Remote Access

Suppose that $\Sigma \subset \mathbb{C}$ is compact and symmetric about the real axis and is a finite union of rectangles and real intervals with transfinite diameter $d_{\Sigma}>1$. Suppose that $\mu$ is a $H$ older arithmetic probability...

Apr
21
2023

Special Number Theory Afternoon

Murmurations of Arithmetic L-functions
Andrew Sutherland
4:00pm|Simonyi 101 and Remote Access

While conducting a series of number-theoretic machine learning experiments, He, Lee, Oliver, and Pozdnyakov noticed a curious oscillation in the averages of Frobenius traces of elliptic curves over Q.  If one computes the average value of a_p(E) for...

Special Number Theory Seminar

Mar
30
2012

Special Number Theory Seminar

Cup Products in Automorphic Cohomology
Matthew Kerr
4:00pm|S-101

In three very interesting and suggestive papers, H. Carayol introduced new aspects of complex geometry and Hodge theory into the study of non-classical automorphic representations -- in particular, those involving the totally degenerate limits of...

Apr
10
2013

Special Number Theory Seminar

Solvability in Polynomials of Pell Equations in a Pencil and a Conjecture of Pink
2:00pm|S-101

The classical Pell equation $X^2-DY^2=1$, to be solved in integers $X,Y\neq 0$, has a variant for function fields (studied already by Abel), where now $D=D(t)$ is a complex polynomial of even degree and we seek solutions in nonzero complex...

Mar
25
2014

Special Number Theory Seminar

Eisenstein series of weight 1
3:30pm|Fine 1201, Princeton University

Let \(N \geq 3\). In this talk, I will sketch a proof that the ring generated by Eisenstein series of weight \(1\) on the principal congruence subgroup \(\Gamma(N)\) contains all modular forms in weights \(2\) and above. This means that the only...

Apr
01
2014

Special Number Theory Seminar

Statistical behavior of eigenforms on quaternion algebras
Paul Nelson
3:30pm|Fine 1201, Princeton University

I will discuss an approach to studying the limiting behavior of automorphic forms on quaternion algebras that succeeds admirably when the levels involved are large squares, and describe some new technical problems that arise in trying to relax this...

Apr
08
2014

Special Number Theory Seminar

L-functions, sieves and the Tate Shafarevich group
3:30pm|Fine 1201, Princeton University

I will explain joint work with Kannan Soundararajan, where we find an "L-function analogue" of the Brun-Hooley sieve. Essentially, our method allows us to work analytically with long truncated Euler products inside the critical strip. As a...

Apr
06
2022

Special Number Theory Seminar

On the distribution of the Hodge locus
Emmanuel Ullmo
3:00pm|Simonyi Hall 101

The lecture will discuss a joint work with Gregorio Baldi and Bruno Klingler.  Given a polarized Z-VHS over a complex, smooth quasi-projective variety S, we describe some properties of the Hodge locus, a countable union of algebraic subvarieties of...

Special Probability Seminar

May
10
2018

Special Probability Seminar

Percolation of sign clusters for the Gaussian free field I
Pierre-Francois Rodriguez
2:00pm|Simonyi Hall 101

We consider level sets of the Gaussian free field on the $d$-dimensional lattice, for $d>2$, above a given real-valued height $h$. This defines a percolation model with strong, algebraically decaying correlations. We prove a conjecture of Lebowitz...

May
11
2018

Special Probability Seminar

Percolation of sign clusters for the Gaussian free field II
Pierre-Francois Rodriguez
2:00pm|Simonyi Hall 101

We consider level sets of the Gaussian free field on the d-dimensional lattice, for d>2, above a given real-valued height h. This defines a percolation model with strong, algebraically decaying correlations. We prove a conjecture of Lebowitz...

Special Program Learning Seminar

Sep
21
2022

Special Program Learning Seminar

Time Change for Unipotent Flows and Rigidity
11:00am|Simonyi Hall 101 and Remote Access

Two flows are said to be Kakutani equivalent if one is isomorphic to the other after time change, or equivalently if there are Poincare sections for the flows so that the respective induced maps are isomorphic to each other. Ratner showed that if $G...

Special Representation Theory Seminar

Mar
08
2017

Special Representation Theory Seminar

"Small" representations of finite classical groups
1:30pm

Suppose you have a finite group G and you want to study certain related structures (e.g., random walks, Cayley graphs, word maps, etc.). In many cases, this might be done using sums over the characters of G. A serious obstacle in applying these...

Mar
08
2017

Special Representation Theory Seminar

On the role of rank in representation theory of the classical groups
Roger Howe
2:35pm

Rank gives a natural filtration on representations of classical groups. The eta correspondence provides a clean description of a natural family of representations of a given rank, subject to certain bounds. There is evidence that this construction...

Special Seminar

Oct
01
2004

Special Seminar

Moduli of Connections with a Small Parameter on a Curve
D. Arinkin
11:00am|S-101
Oct
01
2004

Special Seminar

Divisibility of the Kappa Class
Ulrike Tilman
2:00pm|S-101
Feb
28
2005

Special Seminar

Undirected Graph Connectivity in Log-Space (SL=L)
4:00pm|S-101

We present a deterministic algorithm for graph connectivity that uses the minimal amount of memory possible, up to a constant factor. Specifically, the algorithm's memory is comparable to that needed to store only a single node of the graph (i.e...

Apr
08
2005

Special Seminar

Theory of Valuations of Manifolds
S. Alesker
2:00pm|Fine Hall 1201
Oct
07
2005

Special Seminar

Indefinite theta functions and mock theta functions
Don Zagier
2:00pm|S-101
Oct
25
2005

Special Seminar

Nonuniformly Hyperbolic Attractors; Invertible and Noninvertible
M. Benedicks
3:15pm|S-101
Feb
23
2006

Special Seminar

The Jones Polynomial and Quantum Computation
11:15am|S-101

I will explain a very intriguing connection between low dimensional topology, knot invariants, and quantum computation: It turns out that in some well defined sense, quantum computation is _equivalent_ to certain approximations of the Jones...

Apr
19
2006

Special Seminar

Huygens' Principle and Hyperplane Configurations
A. P. Veselov
2:15pm|Fine Hall 314, Princeton University

Huygens' principle (in the narrow Hadamard's sense) for a second-order hyperbolic equation means that its fundamental solution is located on the characteristic conoid. Physically this implies that a localised disturbance will have an effect...

Apr
04
2007

Special Seminar

Some Results in Differential Cohomology
Jim Simons, Renaissance Technologies
2:00pm|S-101
Oct
22
2007

Special Seminar

Quantum Cohomology of Real Varieities
Ozgur Ceyhan
3:00pm|S-101

Very recently, J.Y. Welschinger introduced a set of invariants for real varieties that give lower bounds on the number of real algebraic curves satisfying certain incidence relations. After J. Solomon's homological interpretation, these invariants...

Nov
14
2007

Special Seminar

Rigid Differential Equations
Dmitry Arinkin
3:00pm|S-101

We study systems of linear ordinary differential equations dy/dz=A(z)y, where A is a matrix-valued rational function of z. By definition, such equation is rigid if it is uniquely determined by the type of its singularities. Our goal is to provide a...

Dec
05
2007

Special Seminar

Baxter Operators and L-Functions
Sergei Oblezin
11:00am|S-101

The notion of Q-operator has been introduced by Baxter as a basic tool to solve quantum integrable systems. We develop Baxter Q-operator formalism for $\mathfrak{g}$-Toda chains for $\mathfrak{g}=\mathfrak{gl}(N,\mathbb{R})$. The constructed Q...

Feb
01
2008

Special Seminar

From Automorphic Sheaves to the Cohomology of the Moduli Spaces of F-Bundles
10:30am|S-101

Drinfeld has initiated two geometric approaches to global Langlands conjectures over function fields: one by constructing automorphic sheaves and another one by realizing representations in cohomology of the moduli spaces of F-sheaves (also known as...

Feb
08
2008

Special Seminar

Towards a Global Langlands Correspondence Over Function Fields
10:30am|S-101

In my talk I will describe our joint work with David Kazhdan on the global Langlands correspondence over function fields for arbitrary split reductive groups. Our main result asserts that for every pair $(\pi,\omega)$, where $\pi$ is a cuspidal...

Feb
12
2008

Special Seminar

Affine Tangles and Irreducible Exotic Sheaves
Rina Anno
2:00pm|S-101

We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories $D_n$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of $SL(2n)$ with two...

Feb
15
2008

Special Seminar

A Gentle Introduction to Derived Algebraic Geometry
10:30am|S-101

This will be a relaxed, very elementary introduction to the central ideas and applications of derived algebraic geometry. My objective is to describe the Artin-Lurie Representability Theorem, and to give a number of interesting examples.

Feb
22
2008

Special Seminar

Introduction to Non-Abelian p-Adic Hodge Theory
10:30am|S-101

This is the first in a series of (probably) three talks whose goal is to understand Faltings’ paper "A p-adic Simpson correspondence". Roughly speaking, this is a correspondence between Higgs bundles over a smooth proper curve X over the field of p...

Feb
27
2008

Special Seminar

Infinity Categories
10:30am|S-101

The aim of this talk is to introduce some of the technologies used in derived algebraic geometry. Beginning with an explanation of the notion of infinity-groupoid, I will develop the notion of infinity-categories. I will discuss the relationship...

Mar
11
2008

Special Seminar

Arithmetic Invariants of Discrete Langlands Parameters
B. Gross
1:00pm|S-101

Let G be a reductive algebraic group over a local field k . Hiraga, Ichino and Ikeda have recently proposed a general conjecture for the formal degree of a discrete series representation of G(k) , using special values of the adjoint L-function and...