# 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.