University of Lethbridge

The Hardy and Littlewood k-tuple prime conjecture is one of the most enduring unsolved problems in mathematics. In 1999, Gadiyar and Padma presented a heuristic derivation of the 2-tuples conjecture by employing the orthogonality principle of...

Generalizing the original Chebyshev bias can go in many directions: one can adapt the setting to virtually any equidistribution result encoded by a finite number of L-functions. In this talk, we will discuss what happens when one needs an infinite...

Full waveform inversion (FWI) is a novel seismic wave equation-based data-driven approach characterized by exploiting full waveform information from all types of seismic data. It can image the subsurface with high resolution, up to half the...

Let ℤ be the ring of integers, and let 𝔽p[t] be the ring of polynomials in one variable defined over the finite field 𝔽p of p elements. Since the characteristic of ℤ is 0, while that of 𝔽p[t] is the positive prime number p, it is a striking theme in...

In this talk, I will discuss my on-going joint work with Xiannan Li on an unconditional asymptotic formula for the eighth moment of Γ1(q) L-functions, which are associated with eigenforms for the congruence subgroups Γ1(q). Similar to a large family...

The Selberg class consists of functions sharing similar properties to the Riemann zeta function. The Riemann zeta function is one example of the functions in this class. The estimates for logarithms of Selberg class functions and their logarithmic...

We establish a Weyl-type estimate for exponential sums over irreducible elements in function fields. As an application, we generalize an equidistribution theorem of Rhin. Our estimate works for polynomials with degree higher than the characteristic...

Graphical and Digraphical Regular Representations (GRRs and DRRs) are a concrete way to visualise the regular action of a group, using graphs. More precisely, a GRR or DRR on the group G is a (di)graph whose automorphism group is isomorphic to the...

Given an abelian variety A defined over a number field, a conjecture attributed to Serre states that the set of primes at which A admits ordinary reduction is of positive density. This conjecture had been proved for elliptic curves (Serre, 1977)...

In 1992, Erd˝os, Granville, Pomerance, and Spiro conjectured that if A is a set of integers with asymptotic density zero then the preimage of A under s(n), sum-of-proper-divisors function, also has asymptotic density zero. In this talk, we will...