Symplectic methods for sharp systolic inequalities

Hryniewicz 2019 01 22

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.