Systolic Geometry and Viterbo’s Conjecture Under Finite Symmetry

Viterbo’s conjecture predicted that the ball optimizes the systolic ratio among convex domains in 𝑅2𝑛. Motivated by the recent counterexample by Haim-Kislev and Ostrover, and by the connection to Mahler conjecture, one can ask how much symmetry is needed for the conjecture to hold. I will describe a connection with systolic Finsler geometry that allows to prove Viterbo’s conjecture for 4-dimensional convex bodies invariant under the natural quaternionic group action. This is a work in progress joint with Julian Chaidez.