On Toda field theories

GAP Seminar

Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stiénon, Ping Xu.

Speaker: Zhaohu Nie, Utah State University

Abstract: The Liouville equation is the nonlinear second order partial differential equation $u_{xy} = -e^{2u}$. It is related to surfaces of constant curvature, and Liouville found the general solution. Toda field theories are generalizations of the Liouville equation using general simple Lie algebras. These are a typical class of integrable systems. In this talk, we will concentrate on two aspects of Toda field theories. The first one is about characteristic integrals, that is, some differential polynomials (with respect to one variable) in the unknown functions whose derivative with respect to the other variable is zero. These are conserved quantities for the system. The second is about the explicit solutions to the Toda field theories in the above spirit of Liouville. Leznov's general solutions will be presented in the most explicit form using iterated integrals.

Room Reservation Information

Room Number: 106 McAllister

Date: 03/12/2013

Time: 2:30pm - 3:30pm