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IMTech Colloquium a càrrec de Marta Mazzocco (Univ. of Birmingham)

31/01/2023

Serà el dimecres 8 de febrer a les 15h30 a la sala d'actes de l'FME.

IMTech Colloquium a càrrec de Marta Mazzocco (Univ. of Birmingham)

Quantum character varieties

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.

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