# Pure Maths Colloquium: Arnau Padrol

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

 Where: Lecture Theatre C When: Oct 31 2019 @ 16.00 Video: Not recorded
 Speaker: Arnau Padrol Institut de Mathématiques de Jussieu, Sorbonne Université Title: On Moser's shadow problem

In a famous list of problems in combinatorial geometry from 1966, Leo Moser asked for the largest $$s(n)$$ such that every $$3$$-dimensional convex polyhedron with $$n$$ vertices has a $$2$$-dimensional shadow with at least $$s(n)$$ vertices. I will describe the main steps towards the answer, which is that $$s(n)$$ is of order $$\log(n)/\log\log(n)$$, found recently in collaboration with Jeffrey Lagarias and Yusheng Luo, and which follows from 1989 work of Chazelle, Edelsbrunner and Guibas. I will also report on current work with Alfredo Hubard concerning higher-dimensional generalizations of this problem.