Past Events

Distances between the roots of a fixed polynomial appear organically in many places in number theory. For any $f(x) \in \mathbb{Z}[x]$, let $\operatorname{sep}(f)$ denote the minimum distance between distinct roots of $f(x)$. Mahler initiated the...

Given a matching M of a hypercube, does there exist a Hamiltonian cycle that contains every edge of M? This problem was posed by Ruskey and Savage in 1993, and remains open. If M is a perfect matching a Hamiltonian cycle does exist, as shown by Fink...

Locally gentle algebras are a class of infinite-dimensional, non-connected algebras which have nice combinatorial interpretation in terms of quivers with relations. These relations ensure that each arrow is contained in a unique maximal path. In this...

Let X be an isotropic unimodal L\'{e}vy jump process on ℝ d . We develop probabilistic methods which in many cases allow us to determine whether X satisfies the elliptic Harnack inequality (EHI), by looking only at the jump kernel of X , and its...

Viral infections are social processes. Viral replication requires shared gene products that can be used by multiple viral genomes within the same cell, and hence act as public goods. This gives rise to viral cheats, a type of molecular parasite...

In this talk, I will be discussing joint work with Nathaniel Butler, Gourab Ray and Yinon Spinka on the behavior of uniformly chosen integer valued 1-lipschitz functions on regular trees, with prescribed boundary conditions on the nth generation...

Given a category C with a class of "weak equivalences" W, Dwyer and Kan constructed a simplicial localization of C that turns the morphisms in W into equivalences. We will go over this construction, its properties, and some tools to compute the...

We consider a variant of a problem first introduced by Hughes and Rudnick (2003) and generalized by Bernard (2015) concerning conditional bounds for small first zeros in a family of L-functions. Here we seek to estimate the size of the smallest...

We consider neural networks (NN) as discretizations of continuous dynamical systems. There are two relevant systems: the NN architecture on one side and the gradient flow for optimizing the parameters on the other. In both cases, stability properties...

There is now an expansive collection of mathematical work on building models for the transport of intracellular cargo by molecular motors. Commonly studied cargo undergo “saltatory” motion (bidirectional ballistic motion, intermixed with periods of...