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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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North Atlantic Noncommutative Geometry Seminar




2021-10-06 17:15

It is always interesting to find connections between NCG and other central areas of mathematics. Recent work gradually unravels deep connections between NCG and random matrix theory. In this talk, I shall explain certain techniques we have employed so far. In some cases, one can apply the Coulomb gas method to find the empirical spectral distribution and rigorously prove existence of phase transition. More recently, we applied the newly developed bootstrap technique to find the moments of certain multi-trace and multi-matrix random matrix models suggested by noncommutative geometry. Using bootstrapping, we are able to find the relationships between the coupling constants of these models and their second moments. Using the Schwinger-Dyson equations, all other moments can be expressed in terms of the coupling constant and the second moment. Explicit relations for higher moments are obtained. The talk will be a general overview of techniques we have used so far. (Based on joint works with H. Hessam and N. Pagliaroli, and separately with S. Azarfar.)