Convexity Seminar

---

On the combinatorial structure of 'nearly Euclidean' polytopes

Speaker: Tomer Milo, Tel Aviv University

Location: Warren Weaver Hall 1314

Date: Tuesday, September 22, 2026, 11 a.m.

Synopsis:

A general ideology in the field of asymptotic convex geometry states: if a polytope is 'close' to an Euclidean ball, then it must have many faces. This ideology can be made formal in various, non-equivalent ways. In this talk, we introduce a certain notion of 'closeness' to an Euclidean ball which is inspired by (Milman's version of) Dvoretzky's theorem, which (to my knowledge) has not been considered in the literature. We formulate conjectures and present some partial results. The work presented is a work in progress.