Colloquium talk
Professor Pablo Soberón, CUNY Baruch College
Wednesday October 11th at 3pm
Rocky 310

Title: Art Galleries, Voting Theory, and Convex Sets

Abstract: The study of intersection patterns of convex sets is a central topic in combinatorial geometry.  In this talk, we will discuss the applications of this area to two different topics: art galleries and voting theory.  In art gallery problems we seek conditions on the blueprint of an art gallery that guarantee that few guards can keep every painting safe.  In voting theory, given a group of people such that every person has an interval of tolerance in different topics, we seek conditions that guarantee that all such intervals overlap.  We focus on connections of these two topics with quantitative Helly theorems, which characterize finite families of convex sets whose intersection is not only non-empty, but quantifiably large.