### Guest Speakers Seminar

Event Timings:

**16:00 – 16:10** Refreshments* (Served in the North** Mezzanine)*

**16:10 – 17:10 ** Talk by Prof. Luis Caffarelli

**17:10 – 17:30 **Refreshments Break (*20mins - Served in the North Mezzanine)*

**17:30 – 18:30** Talk by Prof Irene Martínez Gamba

Each talk will have a Q&A afterwards.

Register your interest **HERE**

## Abstract

**Title:** Topics on regularity theory for fully non-linear integro-differential equations

**Abstract****: **

*We will focus on local and non-local Monge Ampere type equations, equations with deforming kernels and convex envelopes of functions with optimal special conditions. We discuss global solutions and their regularity properties.*

**Title:** Quasilinear Conservative Collisional Transport in Kinetic Mean Field models

**Abstract****: ***We shall focus the on the interplay of nonlinear analysis and numerical approximations to mean field mo**dels in particle physics where kinetic transport flows in momentum are strongly nonlinearly modified by macroscopic quantities in classical or spectral density spaces. Two noteworthy models arise: the classical Fokker-Plank **Landau dynamics as a low magnetized plasma regimes in the modeling of perturbative non-local high order terms. The other one corresponds to perturbation under strongly magnetized dynamics for fast electrons in momentum space give raise to a coupled system of classical kinetic diffusion processes described by the balance equations for electron probability density functions (electron pdf) coupled to the time dynamics on spectral energy waves (quasi-particles) in a quantum process of their resonant interaction. Both models are rather different, yet there are derived form the Liouville-Maxwell system under different scaling. Analytical tools and some numerical simulations show a presence of strong hot tail anisotropy formation taking the stationary states away from Classical equilibrium solutions stabilization for the iteration in a three dimensional cylindrical model. The semi-discrete schemes preserves the total system mass, momentum and energy, which are enforced by the numerical scheme. Error estimates can be obtained as well.*

*Work in collaboration with Clark Pennie and Kun Huang*