Past Events

How does one describe the structure of a graph? What is a good way to measure how complicated a given graph is? Tree decompositions are a powerful tool in structural graph theory, designed to address these questions. To obtain a tree decomposition of...

Given a one-parameter degenerating family of rational maps on the projective line, it is possible to construct a non-archimedean limit which captures how this family degenerates. Recently, Luo used ultrafilters to construct limits for an arbitrary...

In recent years, harmonic analysts and fractal geometers have become increasingly interested in Ramsey-theoretic problems for subsets of Rn. Many of these were inspired by discrete analogues. Over the past 20 years, classical theorems from discrete...

Bundle gerbes on a manifold M provide geometric realizations of degree 3 cohomology classes of M. The space of infinitesimal symmetries of a bundle gerbe naturally carries the structure of a Lie 2-algebra, a deformation of the notion of Lie algebra...

The capillary energy functional models the equilibrium shape of a liquid drop meeting a substrate at a prescribed interior contact angle. We will discuss a rigidity theorem for volume-preserving critical points of the capillary energy in the half...

Cells within a population often differ in their genetic and phenotypic states, leading to variable behaviors and treatment responses—a phenomenon known as cellular heterogeneity. Understanding how these differences shape therapeutic outcomes is...

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...