Previous Conferences & Workshops

Machine learning techniques based on neural networks are achieving remarkable results in a wide variety of domains. Often, the training of models requires large, representative datasets, which may be crowd-sourced and contain sensitive information...

We will describe several situations in number theory and geometry in which one recovers a sought-after structure by first constructing a “random” approximation to it.

A topological dynamical system $(X,T)$ is said to be Möbius disjointnes if \[\tag{$*$} \lim_{N\to\infty}\frac1N\sum_{n\leq N}f(T^nx)\mu(n)=0\] for all $f\in C(X)$ and $x\in X$ ($\mu$ stands for the classical Möbius function).Sarnak's conjecture from...

Given a measure preserving dynamical system, a real-valued observable determines a random process (by composing the observable with the iterates of the transformation). An important topic in ergodic theory is the study of the statistical properties...

In these lectures, we will explore what insight can be gained into the arithmetic of Galois representations in a given dimension through the geometry of a higher-dimensional locally symmetric space near a boundary component. The starting point for...

I will show an explicit construction of a binary error correcting code with relative distance $\frac{1-\epsilon}{2}$ and relative rate $\epsilon^{2+o(1)}$. This comes close to the Gilbert-Varshamov bound that shows such codes with rate $\epsilon^2$...

I will give a brief introduction to spherical varieties. With a view towards understanding the geometry of the moment map, I'll talk about the local structure theorem for spherical varieties. More concretely, if X is a spherical G-variety and B a...

Classical and quantum Hamiltonian actions of reductive groups, respectively, give rise to ubiquitous families of commuting flows and of commutative rings of operators. I will explain how a construction of Ngô (from the proof of the Fundamental Lemma...

I will show an explicit construction of a binary error correcting code with relative distance $\frac{1-\epsilon}{2}$ and relative rate $\epsilon^{2+o(1)}$. This comes close to the Gilbert-Varshamov bound that shows such codes with rate $\epsilon^2$...

Linear dynamical systems (LDSs) are a class of time-series models widely used in robotics, finance, engineering, and meteorology. I will present our "spectral filtering" approach to the identification and control of discrete-time LDSs with multi...