Past Events

In this talk we will explore the connection between the two seemingly unrelated concepts appearing in the title. Phase transitions occur when a system undergoes an abrupt change in behaviour as a consequence of a small change in parameters. While...

There is a beautiful connection between the prime numbers and the zeros of Riemann zeta- function in the complex plane, and understanding the distribution of these zeros can lead to remarkable consequences in our understanding of the primes. A famous...

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...

We consider cyclic partitions of the complete k-uniform hypergraph on a finite set V , minus a set of s edges, s ≥ 0. An s-almost t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a...

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...

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...