**Speaker:** Irene M. Gamba

**Affiliation:** Department of Mathematics and the Institute for Computational Engineering and Sciences (ICES) at The University of Texas – Austin

**Title:** The Mathematics of statistically interacting flows

**Abstract:**

Statistical mechanics and kinetic collisional modeling were introduced in the last quarter of the nineteenth century by L. Boltzmann and J.C. Maxwell, independently. These type of evolution models concerns a class of non-local, and nonlinear problems whose rigorous mathematical treatment and approximations are still emerging in comparison to classical non-linear PDE theory. Their applications range from rarefied elastic and inelastic gas dynamics, collisional plasmas and electron transport in nanostructures, to self-organized or social interacting dynamics.

We will see that based on a Markovian framework of birth and death processes under the regime of molecular chaos propagation, their evolution is described by equations of non-linear non-local interacting type called collisional Boltzmann type equations.

We will discuss recent progress in analytical and numerical methods for initial and boundary value problems.

**Date:** September 7, 2016

**Time:** 11am -12.00 noon

**Place:** TBD