Events and Activities

Explore current and upcoming events and activities happening at the Institute for Advanced Study.

May
12
2025

Computer Science/Discrete Mathematics Seminar I

The Sample Complexity of Smooth Boosting and the Tightness of the Hardcore Theorem
Guy Blanc
10:30am|Simonyi Hall 101 and Remote Access

This talk will be about two related results, one in complexity theory and one in learning.

On the learning side, we investigate the sample complexity of smooth boosters - These are boosting algorithms that do not place too much weight on any given...

May
12
2025

Joint IAS/PU Arithmetic Geometry

Higher singularities in positive characteristic
3:35pm|Simonyi 101 and Remote Access

I will start by reviewing various Hodge-theoretic invariants of complex singularities. After that, I will discuss how to study such singularities using methods of positive characteristic such as Cartier operators. This is based on joint work with...

May
13
2025

Analysis and Mathematical Physics

From Bourgain's Projection Theorem to Kakeya and Khintchine on Fractals: An Impressionistic Picture
Pablo Shmerkin
2:30pm|Simonyi Hall 101 and Remote Access

Several recent groundbreaking results in geometric measure theory, homogeneous dynamics and number theory ultimately rely on a key result of Bourgain known as Bourgain's Projection Theorem (of course, each of these results require many other tools...

May
13
2025

Joint IAS/PU Groups and Dynamics Seminar

Linear Flows on Translation Prisms
Jayadev Athreya
4:30pm|Simonyi 101

Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat 3-manifolds which we call translation prisms. Using ideas of Furstenberg, and Veech, we connect results about weak mixing properties of flows on...

May
14
2025

Special Year Seminar I

Modular Curves $X_1(n)$ as Moduli of Point Arrangements
Lev Borisov
2:00pm|Simonyi 101

For a complex elliptic curve $E$ and a point $p$ of order $n$ on it, the images of the points $p_k=kp$ under the Weierstrass embedding of $E$ into $CP^2$ are collinear if and only if the sum of indices is divisible by $n$. We prove that for $n$ at...

May
15
2025

Special Year Seminar II

On the Extremals of the Khovanskii-Teissier Inequality
10:00am|Simonyi 101

The Khovanskii-Teissier inequality provides the fundamental log-concavity property of intersection numbers of divisors of algebraic varieties, extending the Alexandrov-Fenchel inequality of convex geometry. In this talk I will explain, and attempt...

May
15
2025

What is...?

What is a p-adic zeta function?
1:00pm|Simonyi 101 and Remote Access

In the 1850s, Kummer discovered some striking congruences mod powers of a prime number p between values of the Riemann zeta function at negative odd integers.  This was part of his attempt to understand structural aspects of certain algebraic...

May
15
2025

Joint PU/IAS Number Theory

On the Arithmetic of Genus 4 Curves
Jiahui Gao
3:30pm|Simonyi 101 and Remote Access

We propose and study a new arithmetic invariant of non-hyperelliptic genus-4 curves: a canonical “quadratic” point on the Jacobian, defined by the two natural degree-2 maps to projective lines. Building on Xue’s result, that this point is...

May
16
2025

IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

Morse Theory of Loop Spaces and Hecke Algebras
Roman Krutowski
9:15am|Remote Access

One can associate an HDHF (symmetric) wrapped Fukaya category to a Liouville domain by counting higher genus curves, which are required to be branched covers. For the cotangent bundle of an orientable surface with genus at least one Honda, Tian, and...