Title: Fixed point theorem and solutions for the Nonlinear Schrödinger equation.

Speaker: Luiz Gustavo Farah, GWU

Abstract: In 1933, the Austrian physicist Erwing Schrödinger was awarded the Nobel Prize in Physics. Among its notable scientific contributions he formulated one of the fundamental equations of quantum physics, now known as Schrödinger equation. In this talk, we will develop mathematical tools to prove the existence of solutions for this equation in a special case. Our exposition will be self contained and all of the mathematics needed (most of it well-known) will be introduced en route.

Bio: Luiz Gustavo Farah has been a professor of mathematics at the Federal University of Minas Gerais - UFMG (Brazil) since 2010 and is currently a visiting researcher scholar at the George Washington University. He graduated from IMPA (Brazil) with a PhD in Mathematics in 2008. During 2009 he was a postdoctoral researcher in the Department of Mathematics at the University of California, Santa Barbara. His research interests are in Harmonic Analysis and Partial Differential Equations and he has published several papers concerning the existence and asymptotic behavior of solutions to nonlinear dispersive models.