An introduction to Aubry-Mather theory

Series: 
Research Horizons Seminar
Wednesday, September 14, 2011 - 12:05
1 hour (actually 50 minutes)
Location: 
Skiles 005.
,  
Georgia Tech.
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.