Previous Conferences & Workshops

Dec
01
2021

Mathematical Conversations

A magnetic interpretation of the nodal count on graphs
Lior Alon
6:00pm|Birch Garden, Simons Hall

The study of nodal sets, i.e. zero sets of eigenfunctions, on geometric objects can be traced back to De Vinci, Galileo, Hook, and Chladni. Today it is a central subject of spectral geometry. Sturm (1836) showed that in 1D, the $n$-th eigenfunction...

Dec
01
2021

Joint IAS/Princeton University Number Theory Seminar

Abelian varieties not isogenous to Jacobians
Jacob Tsimerman
4:30pm|Simonyi Hall 101 and Remote Access

Katz and Oort raised the following question: Given an algebraically closed field $k$, and a positive integer $g > 3$, does there exist an abelian variety over k not isogenous to a Jacobian over $k$? There has been much progress on this question...

Dec
01
2021

Arithmetic Groups

Applications to modular forms and noncongruence arithmetic groups
Yunqing Tang and Frank Calegari
11:00am|Simonyi 101 and Remote Access

We explain our proof of the unbounded denominators conjecture. This talk will require the main theorem of the lecture on Nov. 17, 2021, as a “black box” but otherwise be logically independent of that talk.

Dec
01
2021

Character Varieties, Dynamics and Arithmetic

Integral points on character varieties
Junho Peter Whang
10:00am|Simonyi Hall 101 and Remote Access
In this talk, we discuss the Diophantine study of relative SL2-character varieties of surfaces. In particular, we prove that the integral points on these varieties are effectively finitely generated in a precise sense, and in particular their...
Nov
30
2021

Seminar in Analysis and Geometry

h-principle without pre-conditions for ridgy Lagrangians transverse to a distribution
Yakov Eliashberg
2:00pm|Simonyi Hall 101 and Remote Access

I will explain a proof of a joint with D. Alvarez-Gavela and D. Nadler theorem which allows to make a Lagrangian submanifold transverse to a given Lagrangian distribution in exchange for making them piecewise smooth with canonical singularities...

Nov
29
2021

Joint IAS/Princeton University Symplectic Geometry Seminar

Morse-Bott theory on singular analytic spaces and applications to the topology of symplectic four-manifolds
Paul Feehan
4:00pm|Simonyi Hall 101

We describe two extensions, called the virtual Morse-Bott index and circle-equivariant virtual Morse-Bott index, of the classical Morse-Bott index of a Morse-Bott function on a smooth manifold to the setting of (a) suitably defined analytic...

Nov
29
2021

Members' Colloquium

Fluid equations: regularity and Kolmogorov’s turbulence theory
Mimi Dai
2:00pm|Simonyi Hall 101 and Remote Access

The regularity theory for the Navier-Stokes equation will be reviewed. Motivations from Kolmogorov’s phenomenological theory of turbulence will be discussed. Rigorous mathematical results are obtained to confirm some of the phenomenologies.