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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...

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...

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...

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...

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...

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...

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...

The van Eeden seminar is a yearly event in which graduate students vote for their favorite statisticians. The winner is contacted by the organizing committee and invited to give a talk in the department’s seminar. The speaker spends one or two days...

In an electric grid, 'phase imbalance' refers to the unequal distribution of electrical loads across the three phases of the grid. This imbalance can lead to inefficiencies, increased power losses, and equipment damage. A helpful analogy is a three...

Since defending my PhD in the UBC Mathematics Department in 2023, I have worked as a sessional instructor both at UBC and at Corpus Christi College, which is one of UBC’s affiliate colleges, located at the northeast corner of campus. At UBC, I taught...