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 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...

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...

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.

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...

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...

One version of the Polycirculant Conjecture is that every finite vertex-transitive digraph admits a non-trivial semiregular automorphism. I will give an overview of the status of this conjecture, as well as describe some recent progress with Michael...

We describe a theorem due to Jianya Liu and Yangbo Ye (Pure and Applied Mathematics Quarterly, Volume 3, Number 2, 481-497, 2007) concerning the prime number theorem for automorphic L-functions. We state the theorem and review the strategy of the...

We use properties of modular forms to extend the Ramanujan-Mordell formula. Our result yields to formulas for representation numbers by the quadratic form ∑2ai=1x2i+∑2bi=1py2i, for all non-negative integers a,b and for all odd prime p. We obtain this...

We describe a theorem due to Jianya Liu and Yangbo Ye (Pure and Applied Mathematics Quarterly, Volume 3, Number 2, 481-497, 2007) concerning the prime number theorem for automorphic L-functions. We state the theorem and review the strategy of the...