Seminars Sorted by Series
Members' Colloquium
Erd\H{o}s Unit Distance Problem and Graph Rigidity
1:00pm|Simonyi 101 and Remote Access
Erd\H{o}s unit distance problem asks the following: Let $P$ be a
set of $n$ distinct points in the plane, and let $U(P)$ denote the
number of pairs of points in $P$ that are at distance 1. How large
can $U(P)$ be? In 1946, Erd\H{o}s showed that for...
Buildings, Galleries and Beyond
Petra Schwer
1:00pm|Simonyi 101 and Remote Access
Originally introduced as analogs of symmetric spaces for
groups over non-archimedian fields buildings have proven
useful in various areas by now. In this talk I will introduce
(Bruhat-Tits) buildings, combinatorial toolkits to study them
and their...
The Mathematical Legacy of Hel Braun
1:00pm|Simonyi 101 and Remote Access
Hel Braun (IAS member 1947-1948) was a mathematician who
introduced approaches that continue to impact research today.
Braun's research contributions lie in three areas: classical number
theory problems about integers, modular and automorphic
forms...
Selmer Groups and Hilbert's Tenth Problem
1:00pm|Simonyi 101 and Remote Access
Selmer groups are a cohomological tool used to reduce the task
of finding solutions of certain diophantine equations to easier
field and modular arithmetic. I'll explain how this works in down
to earth terms and give some concrete applications...
Barcodes in Topology and Analysis
1:00pm|Simonyi 101 and Remote Access
Persistence modules and their associated barcodes were
intensively studied since the early 2000s with a view towards
applied mathematics. Recently they have also found numerous
applications in pure mathematics. We will discuss a few examples
from...
Unlikely Intersections and Connections to Geometry
1:30pm|Wolfensohn Hall and Remote Access
The field of unlikely Intersections
presents a robust paradigm for problems in which several
subjects intermingle: arithmetic, o-minimality, and hodge theory.
The goal of this talk will be to introduce some of those
connections. My aim is to...
1:30pm|Simonyi 101 and Remote Access
Consider a point mass traveling in a polygon. It travels in a
straight line, with constant speed, until it hits a side, at which
point it obeys the rules of elastic collision. What can we say
about this? When all the angles of the polygon are...
Random Perturbation of Toeplitz Matrices
1:30pm|Simonyi 101 and Remote Access
In 1947 John Von Neumann and Herman Goldstine, while developing
the IAS computing machines, wrote a seminal paper on numerical
errors in matrix computations. They suggested modeling the
"computing noise" (coming from rounding errors,
transcendental...
O-Minimality and Rational Numbers
1:30pm|Simonyi 101 and Remote Access
I'll give a brief introduction to o-minimality and how it can be
used to prove asymptotic estimates for the number of rational
points in definable sets. I'll then show how problems from various
areas of mathematics can be reformulated as questions...
A Dogged Pursuit for Satisfaction
1:30pm|Simonyi 101 and Remote Access
The SAT (Boolean Satisfiability) problem asks whether a given
logical formula on $n$ Boolean variables has an assignment of
true/false values to its variables that makes the formula
true. The P vs NP question is equivalent to asking whether
SAT has...
Categorical Local Langlands Correspondence and Applications
1:30pm|Simonyi 101 and Remote Access
Langlands, inspired by his work on classification of
representations of real groups, initiated a program of classifying
representations of certain topological groups associated to
reductive groups in terms of Langlands parameters. In the
recent...
Beyond Worst-Case Analysis in Online Learning
Tim Roughgarden
1:30pm|Simonyi 101 and Remote Access
One of the primary goals of the mathematical analysis of
algorithms is to provide guidance about which algorithm is the
“best” for solving a given computational problem. Worst-case
analysis summarizes the performance profile of an algorithm by
its...
1:30pm|Simonyi 101 and Remote Access
Riemannian metrics are the simplest generalizations of Euclidean
geometry to smooth manifolds. The Ricci curvature of a metric
measures, in an averaged sense, how the geometry deviates from
being flat. The tensor $-2\,\mathrm{Ric}$ can be viewed as...
Mathematical Exploration and Discovery at Scale
1:30pm|Simonyi 101 and Remote Access
Machine learning is transforming mathematical discovery,
enabling advances on longstanding open problems. In this talk, I
will discuss AlphaEvolve, a general-purpose evolutionary coding
agent that uses large language models to autonomously
discover...
New Methods in Resolution of Singularities
1:30pm|Simonyi 101 and Remote Access
Since Hironaka's famous resolution of singularities in
characteristics zero in 1964, it took about 40 years of intensive
work of many mathematicians to simplify the method, describe it
using conceptual tools and establish its functoriality.
However...
Fundamental Groups of Algebraic Varieties and the Shafarevich Conjecture
1:30pm|Simonyi 101 and Remote Access
The fundamental group $\pi_1(X)$ is an important invariant of a
complex algebraic variety X. Despite its topological nature,
it is closely connected to the geometry of many algebraic
structures on X. In this talk I want to discuss two
elementary...
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
1:30pm|Simonyi 101 and Remote Access
Members’ Seminar
Completing the Bernstein Program (A Geometric Conjecture within the Representation Theory of p-adic Groups)
Approximation algorithms and Grothendieck type inequalities
I will describe a connection between a classical inequality of
Grothendieck and approximation algorithms based on semi-definite
programming. The investigation of this connection suggests the
definition of a new graph parameter, called the...
Local Models of Shimura Varieties
George Pappas
Blow up in a 3-D "toy" model for the Euler equations
We present a 3-D vector dyadic model given in terms of an
infinite system of nonlinearly coupled ODE. This toy model is
inspired by approximations to the fluid equations studied by
Dinaburg and Sinai. The model has structural similarities with
the...
A New Characterization of Sobolev Spaces
This talk is motivated by some recent work of Bourgain-
rezis-Mironescu. A few years ago, they introduced an elementary way
of defining the Sobolev spaces $W^{1,p}$ without making any use of
derivatives. I will present their definition and some...
p-Adic Multiple Zeta Values
A Liouville Type Result for some Conformally Invariant Fully Nonlinear Equations
I will talk about some joint work with Yanyan Li which extended
the Liouville type theorem of Caffarelli-Gidas-Spruck's on the
Yamabe equation to the fully nonlinear case.
Polynomiality Properties of Type A Weight and Tensor Product Multiplicities
Kostka numbers and Littlewood-Richardson coefficients appear in
the representation theory of complex semisimple Lie algebras of
type A, respectively as the multiplicities of weights in
irreducible representations, and the multiplicities of...
Exotic Smooth Structures on Rational Surfaces
Most known smoothable simply connected 4--manifolds admit
infinitely many different smooth structures (distinguished, for
example, by Seiberg--Witten invariants). There are some
4--manifolds, though, for which the existence of such
'exotic'...
Iterated Integrals and Algebraic Cycles
It will be on some constructions in the candidate category of
mixed Tate Motives constructed by Bloch and Kriz.
Motivic Integration, Constructible Functions, and Stringy Chern Classes
In this talk I will discuss a joint work with Lupercio, Nevins
and Uribe, in which we use motivic integration to give a theory of
Chern classes for singular algebraic varieties that is birationally
well-behaved (i.e., with a "stringy" flavor). The...
On some Properties of the Nottingham Group
Let F be a finite field. The Nottingham group N(F) is the group
of formal power series \{ t(1+a_1 t + a_2 t^2 + ...): a_i \in F
\}or, equivalently, the group of wild automorohisms of the local
field F((t)). In spite of such a simple definition, the...
Generalized Teichmueller Spaces
Classical Teichmueller space parametrizes complex structures on
a Riemann surface of genus g>1. Recently several generalized
Teichmueller spaces have been defined and studied by very different
approaches. Nevertheless, some of the results are...
Quantitative Symplectic Geometry
Universality for Mathematical and Physical Systems
Percy Deift
All physical systems in equilibrium obey the laws of
thermodynamics. In other words, whatever the precise nature of the
interaction between the atoms and molecules at the microscopic
level, at the macroscopic level, physical systems exhibit...
Random Walks and Equidistribution on Lie Groups
I will discuss various issues related to the local problem on
Lie groups, the asymptotics of the return probablity, and the
equidistribution of dense subgroups.
The Deligne-Simpson Problem and Double Affine Hecke Algebras
Let us fix $m$ conjugacy classes $C_1,\dots,C_m$ inside $GL(n)$.
The variety of $m$-tuple of matrices such that: $$X_i\in C_i, \quad
i=1,\dots,m mbox{ and } X_1\dots X_m=1.$$ is a solution of the
Deligne-Simpson problem. Double affine Hecke algebras...
Deformation of Yang-Mills Theory Via Pure Spinors
Arithmetic Progressions and Nilmanifolds
Multivariable Mahler Measure and Regulators
The Mahler measure of an n-variable polynomial P is the integral
of log|P| over the n-dimensional unit torus T^n with the Haar
measure. For one-variable polynomials, this is a natural quantity
that appears in different problems such as Lehmer's...
