Seminars Sorted by Series
Special Seminar
Opers with Irregular Singularities and Spectra of the Quantum Shift of Argument Subalgebra
Hypertoric Varieties and Koszul Duality
Ben Webster
Quasi-Coxeter Algebras, Dynkin Diagram Cohomology and Quantum Weyl Groups
Valerio Toledano-Laredo
Unipotent Classes and Special Weyl Groups Representations
Crystal Structures on (Some) Global Nilpotent Cones
An Introduction to the Statistical Mechanics of Random Band Matrices
Tom Spencer
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...
Hall Algebras and Quantum Frobenius
An Introduction to the Statistical Mechanics of Random Band Matrices (continued)
Tom Spencer
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...
Strange Duality on Moduli of Sheaves on Curves and Surfaces
Equivariant Cohomology of Laumon's Quasiflags Spaces and the Quantum Calogero-Moser Hamiltonian
Andrei Negut
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...
The Formation of Black Holes in General Relativity
Demetrois Christodoulou
Higher Order Elliptic Problems in Non-Smooth Domains
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...
Spectral Edge Statistics of Random Band and Sparse Matrices
Alexander Sodin
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...
Berkovich Spaces as Pro-Definable Spaces
Francois Loeser
Cybersecurity, Mathematics, and Limits on Technology
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...
Nodal Lines of Random Waves
M. Sodin
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...
Mathematical Foundations of Population Genetics
THIS LECTURE IS BEING POSTPONED UNTIL NEXT TERM.
Mechanizing the Odd Order Theorem: Local Analysis
Georges Gonthier
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...
Uniqueness of Enhancements for Triangulated Categories
Dmitry Orlov
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...
Limit Theorems for the M\"{o}bius Function and Statistical Mechanics
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...
Infinite Generaton of Non-Cocompact Lattices on Right-Angled Buildings
Anne Thomas
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...
Ramanujan Graphs and Siran Graphs, Applications to Classical and Quantum Coding Theory
Jean-Pierre Tillich
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...
(1) Quantum Beauty; (2) Beauty in Mathematics
(1) Frank Wilczek; (2) Enrico Bombieri
(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...
Universality in Mean Curvature Flow Neckpinches
Gang Zhou
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...
Reflection Positivity and Infrared Bounds for Random Loop Models
Daniel Ueltschi
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...
The Hypoelliptic Laplacian: An Introduction
Integrable Stochastic Particle Systems and Macdonald Processes
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...
Families of Lattice Polarized K3 Surfaces with Monodromy
Charles Doran
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...
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...
Modulo $p$ representations of reductive $p$-adic groups: functorial properties
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...
Introduction to works of Takuro Mochizuki
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...
Wild harmonic bundles and related topics I
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...
Wild harmonic bundles and related topics II
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...
How to modify the Langlands' dual group
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...
Diophantine analysis in thin orbits
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...
Markoff surfaces and strong approximation
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...
Integral points on Markoff-type cubic surfaces
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...
An asymptotic for the growth of Markoff-Hurwitz tuples
Ryan Ronan
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...
Integral points and curves on moduli of local systems
Junho Peter Whang
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...
Benjamini-Schramm convergence and eigenfunctions on Riemannian manifolds
Miklos Abert
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...
Approximate spectral theory in heterogeneous media, asymptotic ballistic transport, and beyond?
Antoine Gloria
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...
Topological quantum phases
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...
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...
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...
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...
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
The Geometry of Hilbert's 13th problem
Jesse Wolfson
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...
Topology of resolvent problems
Benson Farb
In this talk I will describe a topological approach to some
problems about algebraic functions due to Klein and Hilbert. As a
sample application of these methods, I will explain the solution to
the following problem of Felix Klein: Let $\Phi_{g,n}$...
Special Seminar on Homological Stability and Number Theory
Stable Homology and the BKPLR Heuristics Over Function Fields
Jordan Ellenberg
A basic question in arithmetic statistics is: what does
the Selmer group of a random abelian variety look like? This
question is governed by the Poonen-Rains heuristics, later
generalized by Bhargava-Kane-Lenstra-Poonen-Rains, which predict,
for...
The Stable Homology of the Braid Group With Coefficients Arising From the Hyperelliptic Representation
Craig Westerland
3:00pm|Institute for Advanced Study, Simonyi Hall, Room 101
The braid group B_{2g+1} has a description in terms of the
hyperelliptic mapping class group of a curve X of genus g.
This equips it with an action on V = H_1(X), and we may
produce a wealth of new representations S^{\lambda}(V) by applying
Schur...