Analysis Seminar - 30/6/2015

Tuesday, 30 June 2015, 2:00 p.m.

Lecturer: Mario Milman, Florida Atlantic University, USA

Title: "Uncertainty inequalities in metric measure spaces"

Local: Room 1.6, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: I will show an extension of the classical uncertainty inequalities to connected metric measure spaces. The idea is to exploit the connection with isoperimetry. I will introduce a new class of weights (*isoperimetric weights*) and prove a new local Poincare inequality formulated in terms of the isoperimetric profi le. A reinterpretation of the notion of *isoperimetric weights* in terms of function spaces provides a diff erent method to attack the problem and also allows for explicit computation of these weights for log concave measures and other model geometries. I will try to explain all the terms in the abstract, provide examples and show connections with classical inequalities by Hardy and Strichartz.