Objectes multimèdia amb l’etiqueta: Física
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Quantum character varieties
8 de febr. 2023
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.