### DIMACS - Graduate Student Combinatorics Seminar

Title: Counting Convex Quadrilaterals

Speaker: **George Hauser**, Rutgers University

Date: Wednesday, November 1, 2017 12:10pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

How many convex quadrilaterals must occur among n points in the plane, no three of which are collinear? We will consider this question in a few small cases, and see how lower bounds in small cases induce lower bounds in general. But in order to beat the bounds that arise in this way, we must use more strongly the geometry of the underlying point set. We will demonstrate some recent techniques in this area. In the talk we will see how this question of counting convex quadrilaterals bears on the general combinatorial geometry of planar point sets.

See: http://www.math.rutgers.edu/~yb165/GCS.html