Previous Conferences & Workshops

Nov
11
2021

Joint IAS/Princeton University Number Theory Seminar

The unbounded denominators conjecture
Yunqing Tang
4:30pm|Simonyi Hall 101 and Remote Access

The unbounded denominators conjecture, first raised by Atkin and Swinnerton-Dyer, asserts that a modular form for a finite index subgroup of $SL_2(\mathbb Z)$ whose Fourier coefficients have bounded denominators must be a modular form for some...

Nov
11
2021

Discussions in Analysis and Geometry

Reading seminar on the papers of Tao on universality of the Euler equations
Cédric De Groote
2:00pm|Simonyi Hall 101 and Remote Access
We'll go through Tao's "On the universality of the incompressible Euler equation on compact manifolds".
Nov
10
2021

Mathematical Conversations

Stochastic Characteristics: ellipticity and hypoellipticity from finite to infinite dimensions
Jonathan Mattingly
6:00pm|Birch Garden, Simons Hall

I will give an elementary introduction to the connections between diffusions and stochastic characteristics in $\mathbb R^n$. I will then explain how one might think about what it means to be elliptic or hypoellipticity in an infinite dimensional...

Nov
10
2021

Special Seminar

Random forests and hyperbolic symmetry
Roland Bauerschmidt
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...

Nov
10
2021

Arithmetic Groups

The congruence subgroup property for SL(2,Z)
William Yun Chen
11:00am|Simonyi 101 and Remote Access

Somehow, despite the title, $SL(2,Z)$ is the poster child for arithmetic groups not satisfying the congruence subgroup property, which is to say that it has finite index subgroups which can not be defined by congruence conditions on their...

Nov
10
2021

Character Varieties, Dynamics and Arithmetic

Dynamics on character varieties
William Goldman
10:00am|Simonyi Hall 101 and Remote Access

In these two talks, I will describe how the classification of locally homogeneous geometric structures (closely related to flat connections) leads to interesting dynamical systems.

Many interesting dynamical systems arise from the classification of...

Nov
09
2021

Seminar in Analysis and Geometry

3D Navier-Stokes equations: the dynamics of a blow-up
Alexey P Cheskidov
2:00pm|Simonyi Hall 101 and Remote Access

I will present an elementary introduction to the regularity/uniqueness issues for the Navier-Stokes equations. Thanks to the convex integration technique, the h-principle is starting to take shape for the uniqueness problem. It might be possible...