Past Events

Let $d>k$ be positive integers. Motivated by an earlier result of Bugeaud and Nguyen, we let $E_{k,d}$ be the set of $(c_1,\ldots,c_k)\in\mathbb{R}_{\geq 0}^k$ such that $\vert\alpha_0\vert\vert\alpha_1\vert^{c_1}\cdots\vert\alpha_k\vert^{c_k}\geq 1$...

It is known that non-isomorphic strongly regular graphs with the same parameters must be cospectral (have the same eigenvalues). We investigate whether the spectra of higher order Laplacians associated with these graphs can distinguish them. In this...

A Lipschitz function on a graph G is a function f:V->Z from the vertex set of the graph to the integers which changes by at most 1 along any edge of the graph. Given a finite connected graph G, and fixing the value of the function to be 0 on at least...

Let $E/\mathbb{Q}$ be an elliptic curve without complex multiplication. By Serre's open image theorem, the mod $\ell$ Galois representation $\overline{\rho}_{E, \ell}$ of $E$ is surjective for each prime number $\ell$ that is sufficiently large...

The Grassmannian is studied very differently in pure and applied mathematics. From studying these two embeddings of the Grassmannian, a new variety called the squared Grassmannian arises naturally as the image of the Grassmannian in its Plücker...

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...