An introduction to Aubry-Mather theory

Series
Research Horizons Seminar
Time
Wednesday, September 14, 2011 - 12:05pm for 1 hour (actually 50 minutes)
Location
Skiles 005.
Speaker
Rafael De La Llave – Georgia Tech.
Organizer
Amey Kaloti
Starting in the 30's Physicists were concerned with the problem of motion of dislocations or the problem of deposition of materials over a periodic structure. This leads naturally to a variational problem (minimizing the energy). One wants to know very delicate properties of the minimizers, which was a problem that Morse was studying at the same time. The systematic mathematical study of these problems started in the 80's with the work of Aubry and Mather who developed the basis to deal with very subtle problems. The mathematics that have become useful include dynamical systems, partial differential equations, calculus of variations and numerical analysis. Physical intuition also helps. I plan to explain some of the basic questions and, perhaps illustrate some of the results.