Past Events

The sum-rank metric is a generalization of the well-known Hamming and rank metrics. In this talk, we introduce two new bounds on the maximal cardinality of the sum-rank-metric code with a given minimum distance. One of the bounds exploits a...

I will present some recent progress in the study of Hilbert schemes Hilb ⁡ d ( A n ) of d points in affine space. Specifically, I will describe some recent examples of elementary components of Hilbert schemes of points. One infinite family of these...

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...