University of Lethbridge

Mathematics is often about understanding objects through their symmetries. But what do you do when the group of symmetries is nightmarishly complicated? Answer: You turn the problem into one where you can apply math’s ultimate weapon: linear algebra...

Let omega(n) denote the number of distinct prime divisors of n. Let W(m) be a random integer chosen uniformly from the set of natural numbers less than or equal to m. Let X(m) be omega(W(m)). The celebrated Erdos-Kac theorem asserts that if the...

In this talk we will discuss a combinatorial approach to studying the geometry of the moduli space of Langlands parameters for GLn. We will first discuss several connections between the study of partitions and the study of nilpotent conjugacy classes...

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.

A natural way to understand groups visually is by examining objects on which the group has a natural permutation action. In fact, this is often the way we first show groups to undergraduate students: introducing the cyclic and dihedral groups as the...

Let L/K be a Galois extension of number fields with Galois group G, and let C⊂G be a conjugacy class. Attached to each unramified prime ideal p in OK is the Artin symbol σp, a conjugacy class in G. In 1922 Chebotarev established what is referred to...

The 2k-th moments I_k(T) of the Riemann zeta function have been studied extensively. In the late 90's, Keating-Snaith gave a conjecture for the size of I_k(T). At the same time Conrey-Gonek connected I_k(T) to mean values of long Dirichlet...

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)...

The first half of this talk will be a gentle introduction to the Erdős–Ko–Rado theorem (EKR) Theorem. This is a theorem that determines the size and structure of the largest collection of intersecting sets. It has become a cornerstone of extremal set...

Let q≡1(mod4) be a prime power and Fq be the finite field with q elements. Let 1/2σ1 be fixed. We consider D a monic square-free polynomial in Fq[T] and χD the Kronecker symbol associated with D. In this talk, we will discuss the distribution of...