University of Lethbridge

The Erdős-Ko-Rado (EKR) theorem states that if n and k are two positive integers such that n≥2k and F is a family of k-subsets of {1,2,…,n} such that A∩B≠∅, for all A,B∈F, then |F|⩽(n−1k−1). Moreover, if n⩾2k+1, then equality holds if and only if...

In recent work with Mikko Jaskari we study the problem of finding tight explicit bounds on sums over zeros of L-functions near the 1-line with a variety of zero-free regions and zero-density estimates. As an application to demonstrate the techniques...

In principle, the zeros of two distinct Dirichlet L-functions ought to be unrelated. In fact, they turn out to be far more entangled than one expects, though not always. My talk will survey some recent results in this circle of ideas, including...

One of my favorite quotations in mathematics is due to Titchmarsh, who remarked: “The finer theory of the partial sums of the Möbius function is extremely obscure, and the results are not nearly so precise as the corresponding ones in the prime...

A c-colouring of a combinatorial design is an assignment of colours, chosen from a set of size c, to the points of the design. A c-colouring is equitable if every block of size k contains ⌊k/c⌋ or ⌈k/c⌉ points of each colour. In 2016, Luther and Pike...

L-functions appear as generating functions encapsulating information about various objects such as Galois representations, elliptic curves, arithmetic functions, modular forms, Maass forms, etc. Studying L-functions is therefore of utmost importance...

Understanding how network structure gives rise to spatiotemporal dynamics and computation is a central challenge in computational neuroscience and artificial intelligence. Despite increasingly detailed connectomic data in neuroscience and large-scale...

Vertex operator algebras (VOAs) are algebraic objects that arose in the study of infinite dimensional lie algebras, mathematical physics, and in the classification of finite simple groups. These days they are understood to give rise to vector bundles...

The prime number theorem proven independently by de la Vallée Poussin and Hadamard (1896) is an asymptotic statement about prime counting functions. It holds for sufficiently large numbers x. In 1941 Rosser authored an article giving explicit...

The study of the cohomology of line bundles on (partial) flag varieties is an important problem at the intersection of algebraic geometry, commutative algebra, and representation theory. Over fields of characteristic zero, this is well-understood...