Previous Conferences & Workshops

Dec
11
2024

Mathematical Conversations

Adding integers; when your fingers run out
6:00pm|Simons Hall Dilworth Room

In primary school, I never got beyond adding integers and the questions have only been piling up since! What do sets of integers $A$ look like if they generate only a few sums with the elements of another set $B$? Meester Jaap (my primary teacher)...

Dec
11
2024

Special Year Seminar I

Standard Monomials for Positroid Varieties
2:00pm|Simonyi 101

Influential work of Hodge from the 1940s led the way in using Gröbner bases to combinatorially study the Grassmannian. We follow Hodge's approach to investigate certain subvarieties of the Grassmannian, called positroid varieties. Positroid...

Dec
10
2024

Joint IAS/PU Groups and Dynamics Seminar

Corners with Polynomial Side Length
Noah Kravitz
4:30pm|Simonyi 101

 We prove ''reasonable'' quantitative bounds for sets in $\mathbb{Z}^2$ avoiding the ${polynomial}$ ${corner}$ ${configuration}$ $(x,y), (x+P(z),y), (x,y+P(z))$, where $P$ is any fixed integer-coefficient polynomial with an integer root of...

Dec
10
2024

Analysis and Mathematical Physics

Spectral Minimal Partitions: Local vs Global Minimality
2:30pm|Simonyi Hall 101 and Remote Access

In this overview talk we will explore a variational approach to the problem of Spectral Minimal Partitions (SMPs).  The problem is to partition a domain or a manifold into k subdomains so that the first Dirichlet eigenvalue on each subdomain is as...

Dec
10
2024

Symplectic Geometry Seminar

Open Gromov-Witten Invariants in Genus Zero
Amanda Hirschi
1:00pm|Simonyi 101 and Remote Access

Apart from the usual transversality problems in defining curve counting invariants, when defining the open Gromov-Witten invariants of a Lagrangian one has to deal with the fact that the moduli spaces have boundary. Thus a homological (virtual)...

Dec
09
2024

Joint IAS/PU Arithmetic Geometry

Inertia Stacks, Gerbes and Intersection Cohomology
Michael Groechenig
3:35pm|Simonyi 101 and Remote Access

I will discuss a theorem obtained in joint work with Wyss and Ziegler, which is devoted to describing the Frobenius traces for the IC sheaf on moduli space of objects in symmetric abelian categories linear over a finite field. The formula is...

Dec
09
2024

Special Year Seminar

Tits's Dream: Buildings Over F1 and Combinatorial Flag Varieties
2:30pm|Rubenstein Commons | Meeting Room 5

The theme of the lecture is the notion of points over F1, the field with one element. Several heuristic computations led to certain expectations on the set of F1-points: for example the Euler characteristic of a smooth projective complex variety X...

Dec
09
2024

Members' Colloquium

Poisson Boundary, Liouville Property and Asymptotic Geometry of Linear Groups
1:00pm|Simonyi 101 and Remote Access

The Poisson-Furstenberg boundary  is a measure space that describes asymptotics of infinite trajectories of random walks. The boundary is non-trivial if and only if the defining  measure admits non-constant bounded harmonic functions. 

The origin of...

Dec
09
2024

Computer Science/Discrete Mathematics Seminar I

Efficient Batch Verification: Recent Progress and Challenges
Ron Rothblum
10:30am|Simonyi 101 and Remote Access

Suppose Alice wants to convince Bob of the correctness of k NP statements. Alice could send the k witnesses to Bob, but as k grows the communication becomes prohibitive. Is it possible to convince Bob using smaller communication? This is the...

Dec
05
2024

Joint PU/IAS Number Theory

The Orbit Method and Analysis in Representation Theory
Trajan Hammonds
3:30pm|314 Fine Hall

In the 1960s, Kirillov’s orbit method provided a striking correspondence between irreducible representations of a Lie group $G$ and certain geometric objects called coadjoint orbits. In 2021, Nelson and Venkatesh profitably adapted this method to...