Seminars Sorted by Series

Special Seminar

Mar
28
2008

Special Seminar

Joyce Invariants for K3 Surfaces and Mock Theta Functions
So Okada
2:00pm|S-101
Apr
02
2008

Special Seminar

Hypertoric Varieties and Koszul Duality
Ben Webster
10:30am|S-101
Apr
08
2008

Special Seminar

Quasi-Coxeter Algebras, Dynkin Diagram Cohomology and Quantum Weyl Groups
Valerio Toledano-Laredo
2:00pm|S-101
Apr
14
2008

Special Seminar

An Introduction to the Statistical Mechanics of Random Band Matrices
Tom Spencer
4:00pm|S-101

Spectral properties of random band matrices can be expressed in terms certain statistical mechanics models. Some of these models are generalizations of the Ising model except that the spins belong the the Poincare superdisc and there is...

Apr
16
2008

Special Seminar

An Introduction to the Statistical Mechanics of Random Band Matrices (continued)
Tom Spencer
4:00pm|S-101

Spectral properties of random band matrices can be expressed in terms certain statistical mechanics models. Some of these models are generalizations of the Ising model except that the spins belong the the Poincare superdisc and there is...

May
01
2008

Special Seminar

Equivariant Cohomology of Laumon's Quasiflags Spaces and the Quantum Calogero-Moser Hamiltonian
Andrei Negut
2:00pm|S-101

We will introduce certain operators A(m) on the equivariant cohomology ring of the Laumon quasiflags spaces M_d . The character of A(m) will be equal to the generating function Z(m) of the integrals of the Chern polynomial of the tangent bundle of...

Sep
10
2008

Special Seminar

The Formation of Black Holes in General Relativity
Demetrois Christodoulou
2:00pm|S-101
Oct
15
2008

Special Seminar

Higher Order Elliptic Problems in Non-Smooth Domains
1:30pm|S-101

We discuss sharp regularity results for the solutions of the polyharmonic equation in an arbitrary open set. Then we introduce an appropriate notion of capacity which allows to describe the precise correlation between the smoothness of the solution...

Nov
20
2009

Special Seminar

Spectral Edge Statistics of Random Band and Sparse Matrices
Alexander Sodin
2:00pm|S-101

We discuss the distribution of the extreme eigenvalues for several classes of large (N X N) Hermitian random matrices. For a class of sparse matrices, the distribution is approximately Tracy--Widom. For band matrices with band width W(N) , the...

Apr
07
2010

Special Seminar

Berkovich Spaces as Pro-Definable Spaces
Francois Loeser
10:30am|S-101
Apr
14
2010

Special Seminar

Cybersecurity, Mathematics, and Limits on Technology
4:00pm|S-101

Mathematics has contributed immensely to the development of secure cryptosystems and protocols. Yet our networks are terribly insecure, and we are constantly threatened with the prospect of imminent doom. Furthermore, even though such warnings have...

Oct
26
2010

Special Seminar

Nodal Lines of Random Waves
M. Sodin
3:15pm|S-101

In the talk, I will describe recent attempts to understand the mysterious and beautiful geometry of nodal lines of random spherical harmonics and of random plane waves. If time permits, I will also discuss asymptotic statistical topology of other...

Jan
20
2011

Special Seminar

Mechanizing the Odd Order Theorem: Local Analysis
Georges Gonthier
4:00pm|S-101

Abstract: In addition to formal definitions and theorems, mathematical theories also contain clever, context-sensitive notations, usage conventions, and proof methods. To mechanize advanced mathematical results it is essential to capture these more...

Mar
29
2011

Special Seminar

Uniqueness of Enhancements for Triangulated Categories
Dmitry Orlov
2:00pm|S-101

I am going to talk about triangulated categories in algebra, geometry and physics and about differential-graded (DG) enhancements of triangulated categories. I will discuss such properties of DG enhancements as uniqueness and existing. It can be...

Mar
29
2011

Special Seminar

Limit Theorems for the M\"{o}bius Function and Statistical Mechanics
4:00pm|S-101

I will present a recent joint work with Ya.G. Sinai. We investigate the ``randomness" of the classical Möbius function by means of a statistical mechanical model for square-free numbers and we prove some new results, including a non-standard limit...

Apr
06
2011

Special Seminar

Infinite Generaton of Non-Cocompact Lattices on Right-Angled Buildings
Anne Thomas
4:00pm|S-101

Let Gamma be a non-cocompact lattice on a right-angled building X. Examples of such X include products of trees, or Bourdon's building I_{p,q}, which has apartments hyperbolic planes tesselated by right-angled p-gons and all vertex links the...

Mar
16
2012

Special Seminar

Ramanujan Graphs and Siran Graphs, Applications to Classical and Quantum Coding Theory
Jean-Pierre Tillich
1:30pm|S-101

We explain in this talk how Ramanujan graphs can be used to devise optimal cycle codes and review how other graph families related to a construction proposed by Margulis yield interesting families of quantum codes with logarithmic minimum distance...

Dec
11
2012

Special Seminar

(1) Quantum Beauty; (2) Beauty in Mathematics
(1) Frank Wilczek; (2) Enrico Bombieri
2:45pm|S-101

(1) My lecture revolves around a question: Does the world embody beautiful ideas? That is a question that people have thought about for a long time. Pythagoras and Plato intuited that the world should embody beautiful ideas; Newton and Maxwell...

Dec
12
2012

Special Seminar

Universality in Mean Curvature Flow Neckpinches
Gang Zhou
3:30pm|S-101

This is from joint works with D. Knopf and I. M. Sigal. In this talk I will present a new strategy in studying neckpinching of mean curvature flow. Different from previous results, we do not use backward heat kernel, entropy estimates or subsequent...

Dec
19
2012

Special Seminar

Reflection Positivity and Infrared Bounds for Random Loop Models
Daniel Ueltschi
3:30pm|S-101

The random loop representations of Toth ('93) and Aizenman-Nachtergaele ('94) can be extended to describe certain SU(2)-invariant spin-1 Heisenberg models. Quantum spin correlations are given in terms of loop correlations. Existence of long-range...

Apr
25
2013

Special Seminar

Integrable Stochastic Particle Systems and Macdonald Processes
2:00pm|S-101

A large class of one dimensional stochastic particle systems are predicted to share the same universal long-time/large-scale behavior. By studying certain integrable models within this (Kardar-Parisi-Zhang) universality class we access what should...

Feb
21
2014

Special Seminar

Families of Lattice Polarized K3 Surfaces with Monodromy
Charles Doran
11:30am|S-101

We extend the notion of lattice polarization for K3 surfaces to families in a way that gives control over the action of monodromy on the algebraic cycles, and discuss the uses of this new theory in the study of families of K3 surfaces admitting...

Feb
19
2015

Special Seminar

Bordism, QFT, and a topological invariant of certain lattice systems
10:30am|Physics Library, Bloomberg Hall 201
Many features of Wick-rotated field theory are captured by an axiomatization using bordisms of smooth manifolds. There are many variations which have been extensively studied, particularly for conformal and topological field theories. I will give an...
Nov
30
2016

Special Seminar

Modulo $p$ representations of reductive $p$-adic groups: functorial properties
3:05pm|S-101

Let $F$ be a local field with finite residue characteristic $p$, let $C$ be an algebraically closed field of characteristic $p$, and let $\mathbf G$ be a connected reductive $F$-group. With Abe, Henniart, Herzig, we classified irreducible admissible...

Nov
03
2017

Special Seminar

Introduction to works of Takuro Mochizuki
2:00pm|S-101

I will give examples and motivations, about the local systems/Higgs bundles correspondence, the case of variations of Hodge structures and the case of irregular singularities. I hope this will help to enjoy the forthcoming lectures of T. Mochizuki...

Nov
15
2017

Special Seminar

Wild harmonic bundles and related topics I
2:00pm|S-101

Harmonic bundles are flat bundles equipped with a pluri-harmonic metric. They are very useful in the study of flat bundles on complex projective manifolds. Indeed, according to the fundamental theorem of Corlette, any semisimple flat bundle on a...

Nov
17
2017

Special Seminar

Wild harmonic bundles and related topics II
2:00pm|S-101

Harmonic bundles are flat bundles equipped with a pluri-harmonic metric. They are very useful in the study of flat bundles on complex projective manifolds. Indeed, according to the fundamental theorem of Corlette, any semisimple flat bundle on a...

Nov
20
2017

Special Seminar

How to modify the Langlands' dual group
3:15pm|S-101

Let $\mathcal G$ be a split reductive group over a $p$-adic field $F$, and $G$ the group of its $F$-points.The main insight of the local Langlands program is that to every irreducible smooth representation $(\rho, G, V )$ should correspond a...

Dec
08
2017

Special Seminar

Diophantine analysis in thin orbits
1:15pm|S-101

We will explain how the circle method can be used in the setting of thin orbits, by sketching the proof (joint with Bourgain) of the asymptotic local-global principle for Apollonian circle packings. We will mention extensions of this method due to...

Dec
08
2017

Special Seminar

Markoff surfaces and strong approximation
2:10pm|S-101

Markoff triples are integer solutions of the equation $x^2+y^2+z^2 = 3xyz$ which arose in Markoff's spectacular and fundamental work (1879) on diophantine approximation and has been henceforth ubiquitous in a tremendous variety of different fields...

Dec
08
2017

Special Seminar

Integral points on Markoff-type cubic surfaces
3:00pm|S-101

We report on some recent work with Peter Sarnak. For integers $k$, we consider the affine cubic surfaces $V_k$ given by $M(x) = x_1^2 + x_2 + x_3^2 − x_1 x_2 x_3 = k$. Then for almost all $k$, the Hasse Principle holds, namely that $V_k(Z)$ is non...

Dec
08
2017

Special Seminar

An asymptotic for the growth of Markoff-Hurwitz tuples
Ryan Ronan
4:15pm|S-101

For integer parameters $n \geq 3$, $a \geq 1$, and $k \geq 0$ the Markoff-Hurwitz equation is the diophantine equation \[ x_1^2 + x_2^2 + \cdots + x_n^2 = ax_1x_2 \cdots x_n + k.\] In this talk, we establish an asymptotic count for the number of...

Dec
08
2017

Special Seminar

Integral points and curves on moduli of local systems
Junho Peter Whang
5:05pm|S-101

The classical affine cubic surface of Markoff has a well-known interpretation as a moduli space for local systems on the once-punctured torus. We show that the analogous moduli spaces for general topological surfaces form a rich family of log Calabi...

May
07
2018

Special Seminar

Benjamini-Schramm convergence and eigenfunctions on Riemannian manifolds
Miklos Abert
3:15pm|Simonyi Hall 101

Let M be a compact manifold with negative curvature. The Quantum Unique Ergodicity conjecture of Rudnick and Sarnak says that eigenfunctions of the Laplacian on M get equidistributed as the eigenvalue tends to infinity. A weaker version, called...

May
23
2018

Special Seminar

Approximate spectral theory in heterogeneous media, asymptotic ballistic transport, and beyond?
Antoine Gloria
3:30pm|Dilworth Room

In this talk I’ll consider the Schrödinger in heterogeneous media and shall discuss long-time transport properties of localized initial conditions, and more precisely the regime of asymptotic ballistic transport. To this aim I’ll introduce an...

Nov
25
2019

Special Seminar

Topological quantum phases
5:00pm|Simonyi Hall 101

I will describe the problem of finding the homotopy type of the space of quantum Hamiltonians in dimension d under certain constraints. The common assumptions are that the interactions have finite range and that the ground state is separated from...

Oct
26
2021

Special Seminar

Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d > 2
Hugo Duminil-Copin
4:00pm|Simonyi Hall 101 and Remote Access

For the Bargmann--Fock field on $R^d$ with $d > 2$, we prove that the critical level $l_c(d)$ of the percolation model formed by the excursion sets $\{ f \ge l \}$ is strictly positive. This implies that for every l sufficiently close to 0 (in...

Nov
10
2021

Special Seminar

Random forests and hyperbolic symmetry
4:30pm|Simonyi Hall 101 and Remote Access

Given a finite graph, the arboreal gas is the measure on forests (subgraphs without cycles) in which each edge is weighted by a parameter $\beta>0$. Equivalently this model is bond percolation conditioned to be a forest, the independent sets of the...

Dec
07
2021

Special Seminar

Stable Vortex Sheets and Irreversibility of Turbulence
Alexander Migdal
4:00pm|Simonyi Hall 101 and Remote Access

New kinds of vortex sheets with vorticity confined to the boundary layer are proposed and investigated in detail. Exact solutions of the steady Navier-Stokes equations for a planar vortex sheet in arbitrary background strain are found in terms of...

Jul
18
2023

Special Seminar

Arthur Packets and Ramanujan Conjecture
Freydoon Shahidi
4:30pm|Simonyi Hall 101 and Remote Access

We start by relating a result on the reducibility of induced representations of a reductive group through local Langlands correspondence to Artin L-functions. Such a result is of interest in the study of the arithmetic theory of intertwining...

Special Seminar on Hilbert’s 13th Problem

Dec
05
2019

Special Seminar on Hilbert’s 13th Problem

The Geometry of Hilbert's 13th problem
Jesse Wolfson
1:00pm|Simonyi Hall 101

Given a polynomial in one variable, what is the simplest formula for the roots in terms of the coefficients? Hilbert conjectured that for polynomials of degree 6,7 and 8, any formula must involve functions of at least 2, 3 and 4 variables...