Past Events

Fix a positive integer $X$ and multi-sets of complex numbers $\mathcal{I}$ and $\mathcal{J}$. We study the shifted convolution sum \[ D_{\mathcal{I},\mathcal{J}}(X,1) = \sum_{n\leq X} \tau_{\mathcal{I}}(n)\tau_{\mathcal{J}}(n+1), \] where $\tau_{...

In number theory, we often consider a generalization of integers called algebraic numbers. Their definition is rather elementary, but their classification is nothing but. Algebraic numbers come in families, and we can attach each family an invariant...

Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is usually done...

Given two trees, what is the size and structure of their largest common shared subtree? This question has been a growing topic of interest in the probability/combinatorics community in recent years, with the problem having been discussed for a few...

Multiple Sclerosis (MS) is an autoimmune diseases that affects the central nervous system (CNS). It can lead to inflammation, neurodegeneration and physical or cognitive disability. To date, no cure for MS exists, but medications are available to...

The Cremona dimension of a finite group G is the minimal dimension of a rationally connected variety which admits a faithful action of G. In this talk, based on joint work with Giulio Bresciani and Angelo Vistoli, I will discuss new lower bounds on...

Sensing is a universal task in science and engineering. Downstream tasks from sensing include learning dynamical models, inferring full state estimates of a system (system identification), control decisions, and forecasting. These tasks are...

I will talk about a unification of two bounded height results around abelian varieties. The first is Silverman’s specialization theorem, which states for an abelian scheme A/C with no fixed part over a curve C, that the set of points on C where the...

We will discuss a class of ideals in a polynomial ring studied by Mark Haiman in his work on the Hilbert scheme of points and discuss how they are related to homology of affine Springer fibers, Khovanov-Rozansky homology of links, and to the ORS...

A central question in quantum chaos is how classical chaotic dynamics influence quantum behavior. On compact Riemannian manifolds, pure quantum states correspond to Laplacian eigenfunctions. The quantum unique ergodicity (QUE) conjecture of Rudnick...