Seminar:

Spring 2014, Thursdays, Blocker 113, 4:00-4:50 PM


Date: February 20

"  Helly‚Äôs theorem for systolic complexes "
  Krzysztof Swiecicki  

Abstract

Systolic complexes are connected, simply connected simplicial complexes satisfying some additional local combinatorial condition , which is a simplicial analogue of nonpositive curvature. Systolic complexes inherit lots of CAT(0)-like properties, however being systolic neither implies, nor is implied by nonpositive curvature of the complex equipped with the standard piecewise euclidean metric. There is a well known generalization of classical Helly's theorem for CAT(0) cube complexes, which inspired our study of the same phenomena for systolic complexes. In this talk I will introduce the systolic complexes and the Helly's dimension of the geodesic metric space, afterward I will present the Helly's theorem for systolic complexes.