Pure PGR

TBA

TBA

TBA

Harmonic Maps between Riemannian Manifolds are some of the most widely studied maps in Geometric Analysis. They appear as critical points of the Dirichlet Energy Functional, perhaps the simplest functional between Manifolds one can write down. They can also be viewed as generalisations of Harmonic Functions which I will introduce and discuss some of their remarkable properties. Then I will go on to generalise to Harmonic Maps and discuss some of the problems that arise from them.

Coxeter-Conway friezes and their generalisations are of interest to many mathematicians, largely thanks to their well-known connections to cluster theory and representation theory. Many such connections are motivated by the beautiful correspondence, discovered by Coxeter and Conway, between these frieze patterns and triangulations of polygons. By way of this this same correspondence, we may also make connections between these friezes and other areas of mathematics - in this talk, we discuss a connection between (particularly nice) plane curve singularities and the theory of Coxeter-Conway friezes via an invarant known as the lotus of a plane curve singularity. We will also see how the continued fraction representations of rational numbers appear in this construction.

No! (Okay, it’s slightly more complicated than that). Inspired by a recent expository paper on arXiv of the same name, my talk will give the necessary set theoretic background to consider questions about the independence of measurability of certain functions from ZFC. If time permits, I’ll give further results using large cardinal assumptions and in the context of o-minimality.

Spin of a particle is an integral notion in Quantum theory. Understanding this idea has directly influenced the development and enrichment of many topics in pure mathematics for the last century, including Algebra, Lie theory, Representation theory, Operator theory, Differential geometry, to name a few. In this talk I shall give an overview of the mathematical aspects of Spin, and discuss various pure mathematical ideas associated to it.