4:00 pm Thursday, October 8, 2009

Rafael de la Llave (University of Texas, Austin)

We consider variational problems in media with periodic coefficients which satisfy some convexity properties. We will show that there are quasi-periodic solutions of all frequencies. We will also consider the problem of when there is a family of minimizers. The first example is the theory of Morse-Hedlund theory of geodesics on tori (and extensions by Ljusternik-Schnirelman). A later example the theory of Aubry-Mather (motivated by solid state physics and Lagrangian mechanics). An example of PDE's is homogenization theory. Families of minimizers corresponds to KAM theory.