Umberto Hryniewicz

Universidade Federal do Rio de Janeiro; Member, School of Mathematics

January 22, 2019

In this talk I would like to explain how methods from

symplectic geometry can be used to obtain sharp systolic inequalities.

I will focus on two applications. The first is the proof of a

conjecture due to Babenko-Balacheff on the local systolic maximality

of the round 2-sphere. The second is the proof of a perturbative

version of Viterbo's conjecture on the systolic ratio of convex energy

levels. If time permits I will also explain how to show that general

systolic inequalities do not exist in contact geometry. Joint work

with Abbondandolo, Bramham and Salomao.