Combinatorics Seminar - Xavier Goaoc

16:15-18:00

Speaker: Xavier Goaoc

Title: Concentration in order types of random point sets

Abstract: The order type of a planar point set is a combinatorial structure that
encodes many of its geometric properties, for instance the face lattice
of its convex hull or the triangulations it supports. In a sense, it is
a generalization of the permutation associated to a sequence of real
numbers.

This talk will start with a quick introduction to order types. Then,
I'll discuss a concentration phenomenon that arises when taking order
types of various natural models of random point sets, and that makes
order types hard to sample efficiently. This will give us an occasion to
  revisit Klein's celebrated proof of the classification of finite
subgroups of SO(3).

This is joint work with Emo Welzl (https://arxiv.org/abs/2003.08456).