University of Lethbridge

It a classical open problem in Operator Theory whether every bounded linear operator T on a Hilbert space H has a non-trivial invariant subspace (that is, a subspace Y of H such that TY is contained in Y; nontrivial means not {0} and not H). This is...

In this talk, we discuss some results on the non-vanishing in p-adic families of the central values of certain Rankin-Selberg L-functions (namely, anticyclotomic twists of L-functions) associated to automorphic forms on GL(2).

The Riemann Hypothesis predicts that all zeros of the Riemann zeta function are located on the line Re(s) = 1/2. Also, we have that the number of zeros with imaginary parts located between T and 2T is approximately (T log T)/(2pi). Therefore the...

Let h be a natural number and f an arithmetic function. The autocorrelation of f is the sum (over all n less than some x) of the product f(n) f(n+h). Such sums play an important role in analytic number theory. For instance, consider the classical...

In this talk, we will discuss order convergence and unbounded order convergence (uo-convergence) on vector lattices. In many classical function spaces, uo-convergence agrees with almost everywhere convergence. Thus, uo-convergence may be viewed as a...

For a prime p, let n(p) be the number of solutions (x, y) of y^2 = x^3 + ax + b over the finite field F_p and let a(p) = p - n(p). In 1976, Serge Lang and Hale Trotter formulated a conjecture regarding the distribution of primes p for which a(p) = A...

For a field F and a quadratic form Q defined on an n-dimensional vector space V over F, let GQ, called the quadratic graph associated to Q, be the graph with the vertex set V where vertices v, w in V form an edge if and only if Q(v-w) = 1. Quadratic...

A Cayley graph Cay(G;S) on a group G with connection set S (closed under inverses) is the graph whose vertices are the elements of G, with g adjacent to h if and only if h is in gS. If we assign a colour c(s) to each s in S so that the inverse of s...

Please bring your favourite (math) problems. Anyone with a problem to share will be given about 5 minutes to present it. We will also choose most of the speakers for the rest of the semester.

The Lang-Trotter Conjecture for primitive points predicts an expression for the density of primes p for which a fixed rational point (not torsion) of a fixed elliptic curve defined on the rational numbers is a generator of the curve reduced modulo p...