Computer Sciences Colloquium - THE MULTI-COVER PERSISTENCE OF EUCLIDEAN BALLS

You are cordially invited to the lecture of the

Raymond and Beverly Sackler

Distinguished Lectures in Pure Mathematics

Professor Herbert Edelsbrunner
Institute of Science and Technology, Austria

Computer Science Colloquium

"THE MULTI-COVER PERSISTENCE OF EUCLIDEAN BALLS"

Abstract

Given a locally finite set X in R^d and a positive radius r, the k-fold cover of X consists of all points that have k or more points of X within distance r. The order-k Voronoi diagram decomposes the k-fold cover into convex regions, and we use the dual of this decomposition to compute homology and persistence in scale and in depth. The persistence in depth is interesting from a geometric as well as algorithmic viewpoint. The main tool in understanding its structure is a rhomboid tiling in R^{d+1} that combines the duals for all values of k into one. We mention a straightforward consequence, namely that the cells in the dual are generically not simplicial, unless k=1 or d=1,2.

Joint work with Georg Osang.

The lecture will take place on Sunday, 29 April 2018, 
at 11:00, Melamed Hall (6), Shenkar Physics Building