University of Lethbridge

Math Circles are the improvisational comedy of mathematics: you start with a script, and then you say “yes, and...” to all questions and queries, building an atmosphere of exploration and discovery that builds enthusiasm for mathematics. They work at...

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...

What happens when you add up the divisors of an integer? This seemingly innocuous question has motivated mathematicians across the ages, from antiquity to the present day. In this talk, we'll survey some conjectures and results on the functions s(n)...

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.

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...

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...

In this talk I will consider the discrete moments J_k(T) that are defined by summing the 2k-th power of the absolute value of the derivative of the Riemann zeta function zeta(s) at all nontrivial zeros of zeta(s) whose imaginary part has absolute...

We will discuss the Cohen-Lenstra heuristics, both in the classical and non-abelian setting. In particular we will make the connection between these heuristics and the problem of counting extensions of quadratic fields with fixed Galois groups, and...

A Digraphical Regular Representation (DRR) for a group G is a directed graph whose full automorphism group is the regular representation of G. In 1981, Babai showed that with five small exceptions, there is at least one DRR for every finite group. A...

The study of the asymptotic behaviour of the summatory function of the number of divisors of shifted primes was initiated by Titchmarsh, who used the generalised Riemann hypothesis to establish a main term and remainder for the sum of tau(p-a) for p...