Lezione Leonardesca / ALESSIO FIGALLI
Lunedi' 7 novembre 2016, ore 16.30, in Aula Chisini, via Saldini 50,
CONVERGENCE TO EQUILIBRIUM VIA QUANTITATIVE STABILITY
Abstract: Geometric and functional inequalities play a crucial role in several PDE problems.
Very recently there has been a growing interest in studying the stability for such inequalities. The basic question one wants to address is the following:
Suppose we are given a functional inequality for which minimizers are known. Can we prove, in some quantitative way, that if a function “almost attains the equality” then it is close to one of the minimizers?
Actually, in view of applications to PDEs, an even more general and natural question is the following: suppose that a function almost solve the Euler-Lagrange equation associated to some functional inequality. Is this function close to one one of the minimizers?
While in the first case the answer is usually positive, in the second case one has to face the presence of bubbling phenomena.
In this talk I’ll give a overview of these general questions using some concrete examples, and then present recent applications to some fast diffusion equation related to the Yamabe flow.
In my lecture, I will explain a geometric problem related to the topology of singular fibers of an abstract integrable system. The solution of this problem has been crucial for the proof of the fundamental lemma.
Te': ore 16.00, Sala Rappresentanza
ABOUT THE SPEAKER: Alessio Figalli is a brilliant and versatile mathematical analyst, who notwithstanding his tender age has made numerous fundamental contributions on a wide range of important mathematical problems. His works display an unquestioned level of originality and wealth of technical expertise. These contributions include: regularity results for optimal transport maps, optimal regularity for Alexandov solutions to related Monge Ampère equations, the regularity property for the pressure field in Brenier’s generalized incompressible flows, breakthroughs in theDi Perna-Lions theory of transport equations with rough vector fields as well as partial solutions of the Mather and Mañé conjectures in the theory of dynamical systems.Figalli’s groundbreaking work has been recognized with numerous awards, including the Peccot-Vimont Prize (2011) and Cours Peccot (2012) of the Collège de France, theEuropean Mathematical Society Prize (2012) and the Stampacchia Medal (2015). Figalli completed his Ph.D in studies in just one year, at the age of 23, under the joint supervision of Luigi Ambrosio and Cèdric Vilani and just one year later received a Hadamard Professorship at the Ecole Polytechnique in Palaiseau in 2008. Figalli went on to the University of Texas at Austin in 2009, quickly rose to hold an R.L. Moore Chiar in Mathematics and was named Professor of Mathematics at ETH Zürich in 2016.
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