(see
the video of the first session in Porto)
Professor
Luis Caffarelli
is Sid W. Richardson Foundation Regents Chair at
the University of Texas at Austin, and has been awarded in 2009 the
AMS Leroy P. Steele Prize for Lifetime Achievement. He is also the
Director of Mathematics at the University of Texas at Austin of the
CoLab - UTAustin|Portugal partnership program.
- July 8, 2009 - Centro de Matemática da Universidade do Porto, sala 0.07, 18:00.
(With the support of CMUP)
Title: Phase transition and minimal surfaces for non local operators.
Abstract: Movement by mean curvature , i.e, when a surface evolves with
normal speed proportional to its mean curvature, appears in the
modelling of phase transition phenomena , for instance as a limit of
phase field models In the case of slow decay of long range interactions, the corresponding
limiting transition surface moves proportionally to an "integral
version" of mean curvature.
We will describe this phenomena, and the geometric properties of the
corresponding "integral minimal surfaces".
- July 15, 2009 - Departamento de Matemática da Universidade de Coimbra, sala 17 de Abril, 14:30.
(With the support of CMUC)
Title: Fully non linear equations for nonlocal diffusions.
Abstract: Fully non linear equations arise in optimal control and game
theory, when
one is able to optimize a ( continuous) diffusion process ( or has
incomplete information about it).
A complete theory of existence and regularity for these equations was
developed in the eighties thanks to the remarkable contributions of
Krylov and Safanov ( the Harnack inequality) and of Evans- Krylov ( the
Evans_ Krylov regularity theorem)
In a series of papers , in collaboration with Luis Silvestre, we developed
the parallel theory in the case of discontinuous (Levy type) diffusion.
I plan to present the main steps of the theory, and give an idea of our
proof of the Evans Krylov theorem in this case