Past Events

We introduce a combinatorial object corresponding to a graph G, called a special rim hook G-tabloid. We construct sign-reversing maps on these special rim hook G-tabloids to prove that a family of claw-free graphs called generalized nets are Schur...

The random interlacement point process (introduced by Sznitman, generalized by Teixeira) is a Poisson point process on the space of labeled doubly infinite nearest neighbour trajectories modulo time-shift on a transient graph G. We show that the...

The size function h0 for a number field is analogous to the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. Van der Geer and Schoof conjectured that h0 attains its maximum at the trivial class of Arakelov divisors if that...

In 1962, Tutte proposed a simple method to produce a straight-line embedding of a planar graph in the plane, known as Tutte's spring theorem. This construction provides not only one embedding of a planar graph, but infinite many distinct embeddings...

An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools should therefore account for such non-linear geometry. The Riemannian geometry setting can be...

Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a developing tissue, or locusts in a swarm. Here I will focus on the specific example of...

In the late 90's, Keating and Snaith used random matrix theory to predict the exact leading terms of conjectural asymptotic formulas for all integral moments of the Riemann zeta-function. Prior to their work, no number-theoretic argument or heuristic...

The moduli space of Higgs bundles on a complex algebraic curve — an object that originates from Yang-Mills theory in theoretical physics, but which now lies at the interface of algebraic geometry and geometric representation theory — is perhaps best...

Adinkras are decorated graphs that encapsulate information about conjectural relationships between fundamental particles in physics. If we color the edges of an Adinkra with a rainbow of shades in a specific order, we obtain a special curve that we...

We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation Δu+b(α)⋅∇u=f in a bounded domain Ω⊂ℝ2containing the origin, where f∈W−1q(Ω) with q>2 and b(α):=b−αx|x|2 , b is a divergence...