University of Lethbridge

The 2k-th moments I_k(T) of the Riemann zeta function have been studied extensively. In the late 90's, Keating-Snaith gave a conjecture for the size of I_k(T). At the same time Conrey-Gonek connected I_k(T) to mean values of long Dirichlet...

The first half of this talk will be a gentle introduction to the Erdős–Ko–Rado theorem (EKR) Theorem. This is a theorem that determines the size and structure of the largest collection of intersecting sets. It has become a cornerstone of extremal set...

We prove an explicit formula for the first moment of Maass form symmetric square L-functions defined over Gaussian integers. As a consequence, we derive a new upper bound for the second moment. This is joint work with Dmitry Frolenkov.

Chebyshev's bias is the surprising phenomenon that there is usually more primes of the form 4n+3 than of the form 4n+1 in initial intervals of the natural numbers. More generally, following work from Rubinstein and Sarnak, we know Chebyshev's bias...

Euler's divergent series $\sum_{n=0}^\infty n!z^n$ which converges only for $z=0$ becomes an interesting object when evaluated with respect to a p-adic norm (which will be introduced in the talk). Very little is known about the values of the series...

I give a new explicit bound for the Riemann zeta function on the critical line. This is joint work with Dhir Patel and Andrew Yang. The context of this work highlights the importance of reliability and reproducibility of explicit bounds in analytic...

Idempotent semirings have been relevant in several branches of applied mathematics, like formal languages and combinatorial optimization. They were brought recently to pure mathematics thanks to its link with tropical geometry, which is a relatively...

geometry and singularity theory. For example, one can enrich spectra of rings with new points coming from valuations defined on them and taking values in totally ordered abelian groups. Totally ordered groups are examples of idempotent semirings, and...

A Dirichlet character over Fq(t) corresponds to a curve over Fq. Using this connection to geometry, we construct families of characters whose L-functions vanish (resp. does not vanish) at the central point. The existence of infinitely many vanishing...

Let K/k be a finite Galois extension. We define a principal version of the Chebotarev density theorem which represents the density of prime ideals of k that factor into a product of principal prime ideals in K. We find explicit equations to express...