Previous Conferences & Workshops

Let $f$ be a polynomial of degree $d$ in $n$ variables over a finite field $\mathbb{F}$. The polynomial is said to be unbiased if the distribution of $f(x)$ for a uniform input $x \in \mathbb{F}^n$ is close to the uniform distribution over $\mathbb...

This workshop was part of the topical program "Geometric Structures on 3-Manifolds" which took place during the 2015-2016 academic year at the Institute for Advanced Study. The workshop focused on the relations between flows, 2-dimensional...

In this talk I will describe some new arithmetic invariants for pairs of torus orbits on inner forms of $\mathbf{PGL}_n$ and $\mathbf{SL}_n$. These invariants allow us to significantly strengthen results towards the equidistribution of packets of...

Over a decade ago Welschinger defined invariants of real symplectic manifolds of complex dimensions 2 and 3, which count $J$-holomorphic disks with boundary and interior point constraints. Since then, the problem of extending the definition to...

Let $G$ be a locally compact group acting by measure-preserving transformations on a probability space $(X,\mu)$. To every probability measure on $G$ there is an associated averaging operator on $L^p(X,\mu)$. Ergodic theorems describe the pointwise...

In this talk, I will describe roughly how to define a generating function arithmetic divisors (in Arakelov sense) on a unitary Shimura variety of type $(n-1,1)$. I will then briefly explain why it is modular. If time permits, I will also talk...