**Upcoming MAMS Colloquium Series**

### Fall 2024

**9/13/2024, Friday. 3:15-4:15 pm in Wickenden 321**

**Speaker**: Dr. Luis Rademacher (UC Davis)

**Title**: The k-set problem: General shapes and random point sets

**Abstract**: Given a finite set S of n points in R^d, a k-set is a subset of S of size k which can be strictly separated from the rest of S by a hyperplane. Similarly, one may consider k-facets, which are hyperplanes that pass through d points of S and have k points on one side. A notorious open problem is to determine the asymptotics of the maximum number of k-sets given n, k and d. The first part will be an introduction to basic facts and techniques about the k-set problem. The second part will be about two aspects of the problem: (1) A variation with hyperplanes replaced by algebraic surfaces. (2) For a probability distribution P on R^d, the expected number of k-facets of a sample of n random points from P. This is based on joint work with Brett Leroux.