Title:  Winding Numbers and the Generalized Lower-Bound Conjecture

Abstract:  Consider a set V of n distinct points in affinely general position in R^e. For 0 ≤ k < n−e , a k-splitter is the convex hull of a set of k points whose affine span separates the remaining points into two sets, one of which has size k. Let p be an additional point in affinely general position with respect to V . In this talk, we will discuss w_k(p), the kth winding number, which counts how many times k-splitters wrap around p in the counter clockwise direction. It is known that w_k(p) ≥ 0, as a consequence of the g-theorem. There are elementary proofs (Lee, Welzl) for some special cases (e.g. e = 2). We will discuss the ideas behind these proofs.  Then we will discuss the relationship of this work to the g-theorem.  We will then pose possible directions for further research