# Events for 11/10/2023 from all calendars

## Mathematical Physics and Harmonic Analysis Seminar

**Time: ** 1:50PM - 2:50PM

**Location: ** Zoom

**Speaker: **Angeliki Menegaki, IHES

**Title: ***L^2-stability for the 4-waves kinetic equation around the Rayleigh-Jeans equilibrium*

**Abstract: **We consider the four-waves spatial homogeneous kinetic equation arising in weak wave turbulence theory. In this talk I will present some new results on the existence and long-time behaviour of solutions around the Rayleigh-Jeans thermodynamic equilibrium solutions. In particular, I will present an $L^2$ stability of mild solutions on the whole frequency space for initial data close to Rayleigh-Jeans when assuming radial solutions for the equation, as well as a stability of the same kind without the radial solution-assumption but after introducing a cut-off on the frequencies. Parts of this talk are joint works with Miguel Escobedo (UPV/EHU).

## Free Probability and Operators

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 306

**Speaker: **Adrian Celestino, TU Graz

**Title: ***Antipode formulas, Schröder trees and cumulants in non-commutative probability*

**Abstract: **In a series of recent papers, Ebrahimi-Fard and Patras developed an algebraic approach for cumulants in non-commutative probability based on a combinatorial Hopf algebra of words on words on an alphabet. In particular, they showed that the combinatorial moment-cumulants formulas, expressed in terms of non-crossing partitions, can be retrieved from specific fixed-point equations involving linear functionals on a Hopf algebra.

In this talk, we discuss a combinatorial formula for the antipode in this Hopf algebra, which is represented in terms of Schröder trees, which have recently appeared in the context of non-commutative probability theory. Finally, we will see the implications of the antipode formula in non-commutative probability, namely, cumulant-moment formulas and free Wick polynomials in terms of Schröder trees. Based on an ongoing joint work with Yannic Vargas.