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Science and Mathematics

Mathematics Faculty Candidate: On Poincaré inequalities as minimal assumptions to do variational calculus

January 27, 2020 at 4:00pm5:00pm

Carnegie Library, 122

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Sylvester Eriksson-Bique, Ph.D., from the University of California Los Angeles, is a candidate for a faculty position in the Department of Mathematics, part of the cluster hiring initiative in the BioInspired Institute.

Abstract: “Poincaré inequalities” arise as central concepts in several fields. In variational calculus they are an integral assumption de Giorgi-Nash-Moser iteration. In the Heisenberg group they lead to the theory of sets of finite perimeter, and play a role in solving questions in theoretical computer science. For hyperbolic groups and quasiconformal maps they imply rigidity. A crucial question is, what are the minimal assumptions for such an inequality to hold, or when the relevant differential calculus can be performed. I will discuss four results in this  direction, relating differentiability to Poincaré inequalities, then to curves, and then to rigidity of certain metric spaces as well as infinitesimal structure on sets of finite perimeter. Along the way we find analogies to Muckenhoupt weights.

Refreshments at 3:30 in Room 111

This event was published on January 13, 2020.

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