The mathematics seminar

Upcoming seminars, spring 2024

Friday 19 April: Milica Ðukic

The seminar will take place at 15:15 in Å4005.

Title: Introduction to knot invariants

Abstract: A knot can be mathematically described as an embedding of the 1-dimensional sphere S^1 into R^3. In particular, the image is not allowed to have self-intersections. Two knots are considered equivalent if there exists a continuous deformation, i.e. path of knots, between them. Despite this seemingly simple definition, distinguishing different knots from each other is often challenging. Different ways of approaching this problem led to many interesting connections with various branches of mathematics and physics, including algebraic topology, hyperbolic and symplectic geometry, string theory, etc. In this talk, we introduce some knot invariants originating from different areas of mathematics that can be used to distinguish different knots. Along the way, we encounter interesting questions from this field, many of them still unsolved.

Friday 12 April: Kirsti Biggs

The seminar will take place at 10:15 in Å4005.

Title: Solving Diophantine equations over fractal subsets of the integers

Abstract: In this talk I will discuss subsets of the integers which are defined by restrictions on their digits in a given base. For example, in 2016, Maynard showed that there are infinitely many prime numbers with no digit 7 in their decimal expansion. Such sets of integers have fractal properties which resemble (generalised versions of) the Cantor set in several ways. In previous work, I have estimated the number of solutions to certain polynomial equations when all of the variables are required to lie in one of these fractal sets, and jointly with Julia Brandes, we developed a general framework for handling similar problems for other subsets of the integers. These results use tools from analytic number theory, particularly versions of the circle method and bounds on exponential sums.