Past Events

A $P$-matrix is a matrix all of whose principal minors are positive. In this talk, we demonstrate that the fractional powers of a $P$-matrix are also $P$-matrices. This insight allows us to affirmatively address a longstanding conjecture raised in [D...

The shuffle theorem is a celebrated result in algebraic combinatorics that identifies three objects: the Frobenius character of certain Sn representations, the action of the elliptic Hall algebra on symmetric functions, and a particular combinatorial...

Bounded density shifts are examples of hereditary subshifts. Bounded density shifts are defined by disallowing words whose sum of entries exceeds a value depending on the length of the word. After presenting some examples and reviewing the concepts...

I will discuss recent work with Chantal David, Alexander Dunn, and Joshua Stucky, in which we prove that a positive proportion of Hecke L-functions associated to the cubic residue symbol modulo square-free Eisenstein integers do not vanish at the...

The human population presents a unique ecosystem for studying pathogen communities, with anthropogenic activities like COVID-19 lockdowns serving as large-scale natural experiments. In this talk, I begin by exploring how host immune response...

The degeneracy of a graph is a measure of sparseness that gives important information about its Ramsey- and Turán-type properties. I will talk about the hypergraph extension of these problems. The typical notion of hypergraph degeneracy does not give...

The question of which nilpotent Lie algebras admit complex structures is far from being understood. In recent decades, progress has primarily focused on providing algebraic obstructions to the existence of such structures, with classification results...

Gradient flows have emerged as a powerful framework for analyzing machine learning and statistical inference algorithms. Motivated by several applications in statistical inference, generative models, generalization, and robustness of learning...

Current LLM alignment techniques use pairwise human preferences at a sample level, and as such, they do not imply an alignment on the distributional level. We propose in this paper Alignment via Optimal Transport (AOT), a novel method for...

I will introduce our recent work on parameterising OT problems with elastic costs, i.e. ground costs that mix the classic squared Euclidean distance with a regularizer (e.g. L1 norm). After highlighting the properties of OT maps that follow such...