Lezioni Leonardesche / Felix Otto
Lunedì 20 novembre 2017, ore 16.30, in Aula Chisini, via Saldini 50,
Max Planck Institute, Leipzig
RANDOMNESS IN PARTIAL DIFFERENTIAL EQUATIONS
Abstract: In applications, we often do not know the exact details of a heterogeneous medium. Here, randomness in the coefficients of a typically elliptic partial differential equation is used to express a lack of knowledge. Nevertheless, some properties of the solution are robust under this lack of knowledge. This is the area of Stochastic Homogenization.
Thermal fluctuations typically give rise to a driving force that appears as a right-hand side in an often nonlinear parabolic partial differential equation. How to develop a notion of solution in the presence of nonlinearity and a rough right-hand side is the subject of the area of Stochastic Partial Differential Equations (SPDE).
While Homogenization capitalizes on random cancellations on large scales, SPDE copes with roughness on small scales. However, both directions have to confront similar issues in elliptic/parabolic regularity theory.
Te': ore 16.00, Sala Rappresentanza
ABOUT THE SPEAKER: Felix Otto is a leading figure in pure and applied mathematics, with numerous important contributions in the fields of partial differential equations, the calculus of variations and their applications. He is well known for his contributions to gradient flows, stochastic homogenization and to the understanding of real world problems coming from micromagnetism and material science, amongst others. His work often combines advanced analytical methods with numerical simulations. Otto’s impact on these discipline have been recognized with numerous awards, including the prestigious Leibniz Prize (2006) from the German Research Foundation, the Collatz Prize (2007) from the International Council for Industrial and Applied Mathematics and the Gauss Lectureship (2009) from the German Mathematical Society. Felix Otto received his Ph.D. from the University of Bonn under the direction of Stephen Luckhaus in 1993, held positions at the Courant Institute, Carnegie Mellon University, the University of California at Santa Barbara before returning to the University of Bonn as Professor of Applied Mathematics in 1999. In 2010, Otto was named Professor of Mathematics at the Max Planck Institute in Leipzig, where he remains today and serves as one of the directors of the institute.
In collaborazione con il : SEMINARIO MATEMATICO E FISICO DI MILANO
Per ulteriore informazioni: http://www.matematica.unimi.it/ecm/home/ricerca/lezioni-leonardesche
K. Payne e B. Ruf
Dipartimento di Matematica "F. Enriques"
Universita' degli Studi di Milano
Dipartimento di Matematica "F. Brioschi"
Politecnico di Milano
Dipartimento di Matematica e Applicazioni
Universita' di Milano Bicocca