IMTech Colloquium by Marta Mazzocco (Univ. of Birmingham) on February 8 at 15h30 (Sala d'Actes de la FME)

Professor Marta Mazzocco (University of Birmingham) will speak at the IMTECH Colloquium on Wednesday February 8 at 15h30 at Sala d'actes de la Facultat de Matemàtiques i Estadística (FME).

Professor Mazzocco is Professor of Mathematics at University of Birmingham (UoB). She holds a PhD in Mathematical Physics from the International School of Advanced Studies (SISSA, Trieste).  She has had positions at MSRI (Berkeley), Oxford, Cambridge University, University of Manchester and Loughborough University. Professor Mazzocco is a specialist in the area of integrable systems, namely mathematical problems often motivated by Mathematical Physics, combining geometry, quantum algebra and analysis.

Title: Quantum character varieties

Abstract: In this talk we will introduce the concept of character variety in the simple example of a torus with one disk removed. We will show how this is a surface in C^3 defined by a cubic polynomial, called the Markov cubic. We will show the relation between the Markov cubic, singularity theory, Painlevé differential equations, and introduce a cluster algebra structure on it which is related to Markov numbers. We will discuss quantisation of the Markov cubic in terms of basic orthogonal polynomials and relate it to Sklyanin algebra.