Some emerging questions about isoperimetric type inequalities under symmetry assumption, their connections and partial results

Abstract: I will talk about the Brunn-Minkowski inequality, Ehrhard’s inequality, and some of their conjectured strengthenings — the Log-Brunn-Minkowski conjecture, the Dimensional Brunn-Minkowski conjecture, the “symmetric Ehrhard” conjecture, the B-conjecture, and all the various relations between them. In addition to mentioning many open problems, I will discuss the state of the art in this area, and explain some of my results in it. Finally, I will talk a bit about a new conjectured strengthening of the Brascamp-Leib inequality, its potential (significant) implications, and partial progress towards it.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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