Alfredo Hubard: Candidate for position in Topology

Alfredo Hubard
Candidate for position in Topology

Abstract: I will explain a way in which the famous crossing number inequality can be generalized to a three-dimensional context using a combination of ideas from topology and graph theory.

Then I will explain the main ideas in the proof of the following theorem which generalizes the Borsuk-Ulam theorem and the ham sandwich theorem:
For any compact convex set in euclidean space and any prime power n=p^k there is a partition of the convex set into n convex pieces all of which have the same area and the same perimeter.

The theory of characteristic classes will play an important role.

I will try to convey some problems relating algebraic topology to combinatorial and Riemannian geometry.