University of Lethbridge

Let L/K be a Galois extension of number fields with Galois group G, and let C⊂G be a conjugacy class. Attached to each unramified prime ideal p in OK is the Artin symbol σp, a conjugacy class in G. In 1922 Chebotarev established what is referred to...

Mathematics is often about understanding objects through their symmetries. But what do you do when the group of symmetries is nightmarishly complicated? Answer: You turn the problem into one where you can apply math’s ultimate weapon: linear algebra...

In classical q-series studies there are examples of eta quotients whose derivatives are also eta quotients. The most famous examples can be found in works of S. Ramanujan and N. Fine. In 2019, in a joint work with P. C. Toh, we have given 203 pairs...

Let E be a CM elliptic curve defined over the rational numbers. In light of the Lang-Trotter conjecture, there is a question asking for an asymptotic formula for the number of primes p x for which the reduction modulo p of E is cyclic. This has been...

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...