Measuring size and complexity of Riemannian manifolds

Conférence Nirenberg du CRM en analyse géométrique

Yevgeny Liokumovich (Université de Toronto, Canada)
Measuring size and complexity of Riemannian manifolds (18 septembre 2020 / September 18, 2020)

Résumé / Abstract : Given a Riemannian manifold how hard is it to slice it into pieces of smaller dimension? More precisely, we can ask how large in terms of their volume, diameter and topological complexity the slices have to be? These questions give rise to various notions of width of a manifold, which turn out to be closely related to questions about minimal surfaces. I will describe some recent results relating widths to other notions of size of a Riemannian manifold. The talk will be partly based on separate joint works with A. Nabutovsky, R. Rotman and B. Lishak, with G.R. Chambers, and with D. Ketover and A. Song.

Biographie / Biography : Yevgeny Liokumovich received his Ph.D. in 2015 at the University of Toronto under the supervision of A. Nabutovsky and R. Rotman. After a postdoc at MIT and the Institute for Advanced Study, he returned to Toronto in 2019 as an Assistant Professor. Yevgeny Liokumovich has obtained several major results in geometric analysis, including a solution of Gromov’s conjecture on the Weyl law for the volume spectrum in a recent joint work with F.C. Marques and A. Neves.