University of Lethbridge

I will show how the classical Beurling-Selberg extremal problem in harmonic analysis arises naturally when studying the vertical distribution of the zeros of the Riemann zeta-function and other L-functions. Using this relationship, along with...

An algebra is a vector space with a well-defined multiplication. An operator algebra is an algebra of operators acting on a Hilbert space, typically assumed closed in the norm topology. An easy example of an operator algebra is the algebra M_n(C) of...

The linear independence conjecture asserts that the multisetof positive ordinates of the zeros of automorphic L-functions is linearlyindependent over the eld of rational numbers. This deep conjectureimplies that if 1=2 + i is a zero of the Riemann...

In this talk, we give a brief overview of adelic Hilbert modular forms. Then, we show that the central values of the Rankin-Selberg convolutions, L(g otimes f, s), uniquely determine an adelic Hilbert modular form g, where f varies in a carefully...

Determining the full automorphism group of a graph is a hard problem with a long history. I will discuss some of the major results that involve finding graphs with a given automorphism group. I will then focus on circulant graphs, and describe some...

An automorphism of a Cayley graph that preserves its natural edge-colouring is called colour-preserving. We study groups G with the property that every automorphism on every connected Cayley graph on G is the composition of a left-translation and a...

In 1944, Linnik famously showed unconditionally that the least prime in an arithmetic progression a (mod q) with gcd(a,q)=1 is bounded by q^L for some absolute effective constant L>0, known as “Linnik’s constant”. Many authors have computed explicit...

Very little is known about the distribution of primitive roots of a prime p. Grosswald conjectured that the least primitive root of a prime p is less than the square root of p, minus 2, for all p greater than 409. While this is certainly true for all...

We will discuss recent progress towards the twin prime conjecture as well as highlight some recent joint work with Akshaa Vatwani the connects the parity problem with the twin prime conjecture. The talk will be accessible to a wide audience.

Given an elliptic curve E over a number field K. The Frobenius field attached to E at a prime p is the splitting field of the characteristic polynomial of the Frobenius endomorphism acting on the ell-adic Tate module of E (ell a prime different from...