Geometric transversality: affine and continuous results

Florian Frick, Cornell University

Room 201 Warren Weaver Hall (Note: Not the usual room.)

April 18, 2017

Some results about intersection patterns of convex hulls of point sets in Euclidean space have a continuous relaxation, where we are allowed to continuously deform convex hulls and still expect certain intersections among them to occur. Recent progress has shown that there are important differences between the affine and continuous theory for these results. Perhaps surprisingly, whether the number of intersecting sets is a prime power plays a major role in delimiting the affine from the continuous theory. During this talk I will focus on the AP conjecture, a problem with some very recent progress, that attempts to characterize which dimensions of convex hulls must occur in r-fold intersections in any sufficiently large point set as well as continuous relaxations of this problem. Again, we observe a difference between the affine and the more general continuous results.