University of Lethbridge

A Hadamard matrix H of order 4n2 is said to be skew-regular if it is of skew-type and the absolute values of the row sums are all 2n. It is conjectured that for each odd integer n there is a skew-regular matrix of order 4n2. A Hadamard matrix H of...

It is known that if the negative Pell equation X2−DY2=−1 is solvable (in integers), and if (x,y) is its solution with smallest positive x and y, then all of its solutions (xn,yn) are given by the formula xn + yn√D = ±(x + y√D) 2n+1 for n∈Z...

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.

Following the framework of Rubinstein and Sarnak for Chebyshev's bias, one obtains a limiting logarithmic distribution μ. Then assuming that the zeros of the L-functions are linearly independent over Q, one can show that the distribution μ is smooth...

In this talk, I will discuss recent joint work with Wissam Raji. We show that, on average, the L-functions of cuspidal Hilbert modular forms with sufficiently large weight k do not vanish on the line segments I(s)=t0, R(s)∈(k−12,k2−ϵ)∪(k2+ϵ,k+12)...

In the past twenty years there has been a flurry of activity in the study of mean values of L-functions. This was precipitated by groundbreaking work of Keating and Snaith in which they modelled these mean values by random matrix theory. In this talk...

We will discuss several results related to transversals in Latin squares (think "Sudoku") and other Latin square-like objects. These results centre around showing the existence of, the number of, or the structure of transversals in different cases...

The relationship between independence number, chromatic number, clique number, clique cover number and their fractional analogues is well-established for perfect graphs. Here, we study the clique k-cover number cck(G) and the fractional clique k...

We shall place in a general context the following result recently (*) obtained jointly with Yuri Bilu (Bordeaux), Sanoli Gun (Chennai) and Florian Luca (Johannesburg). Theorem. Let τ(⋅) be the classical Ramanujan τ-function and let k be a positive...

For any finite group G, a natural question to ask is the order of the smallest possible automorphism group for a Cayley graph on G. A particular Cayley graph whose automorphism group has this order is referred to as an MRR (Most Rigid Representation)...