Previous Conferences & Workshops

We will discuss Knop's paper "The asymptotic behavior of invariant collective motion" which analyzes the moment map for a spherical variety and relates it to a Weyl group.

One of the key problem in mirror symmetry is that singular fibres in higher dimensional SYZ fibrations of sufficiently interesting spaces (e.g. the quintic 3-fold) have bad singularities. This makes it unreasonable to directly define their...

Last semester I gave a talk that was a 1-hour condensation of undergrad machine learning. https://www.ias.edu/video/membsem/2017/1127-SanjeevArora . This semester's talk will be a 1-hour treatment of some research directions in theoretical machine...

An error-correcting code is called locally repairable if any coordinate of a codeword can be recovered by accessing only few other coordinates. For locally repairable codes over small alphabets (such as binary), the optimal trade-off between...

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 $\epsilon^2$...