# BGSMath COLLOQUIUM – FALL 2016

# BGSMath COLLOQUIUM – FALL 2016

Dates

November 23, 2016

Speaker

Michel Ledoux

Location

UB, Maths Faculty.

T1 Classroom

As is classical, the heat equation is a parabolic partial differential equation that dscribes the distribbution of heat (or variation in temperature) in a given region over time. As the prototypical parabolic partial differential equation and via its connection with Brownian motion in probability theory, the heat equation is of fundamental importance in diverse scientific fields, including (Riemannian) geometry, Lie groups, mathematical physics, graph theory, up to mechanics or biology.

Dates

november 23, 2017

Speaker

Michel Ledoux

Location

UB, Maths Faculty.

T1 Classroom

SHORT DESCRIPTION

Schedule

The three weeks in January are fixed but the daily schedule is open to debate.

*15:30h*

Balanç del primer any del programa BGSMath/María de Maeztu

*16:30h*

Pausa-Cafè

*17:00h*

Michel Ledoux

Université de Toulouse

How does the heat equation explore geometric and functional inequalities?

##### Summary

As is classical, the heat equation is a parabolic partial differential equation that dscribes the distribbution of heat (or variation in temperature) in a given region over time. As the prototypical parabolic partial differential equation and via its connection with Brownian motion in probability theory, the heat equation is of fundamental importance in diverse scientific fields, including (Riemannian) geometry, Lie groups, mathematical physics, graph theory, up to mechanics or biology.

During the last decades, the gift of ubiquity of the heat equation has developed to approach various geometric and functional inequalities. Starting from the elementary example of Hölder’s inequality, the talk will feature illustrations of the heat flow method to families of integral inequalities, Sobolev inequalities and more refined isoperimetric theorems in Euclidean and Riemannian spaces. The method developed recently in discrete Boolean analysis motivated by questions in theoretical computer science.

Professor at the University Paul Sabatier (Toulouse) and senior member of the Institut Universitaire de France, Michel Ledoux is a French mathematician specializing in the Theory of Probability. His fields of expertise encompasses Probability in Banach spaces, Gaussian processes, concentration of measure, large deviations, functional inequalities, geometry of Markov operators, random matrices, information theory and statistical mechanics, among others.

His books on “The Concentration of Measure Phenomenon” (2001), on “Probability in Banach Spaces” (2002), co-authored with Michel Talagrand, on “Analysis and Geometry of Markov Diffusion Operators (2014), with D. Bakry and I. Gentil, along with the lectures notes on “Isoperimetry and Gaussian Analysis”, based on his lectures at the Ecole d’été de Probabilités de St. Flour 1994, are references in their respective areas.