Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, June 04, 2013, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Zuzana Safernová (Charles University)

Helly number of a finite family of sets is *h* if any minimal subfamily with an empty intersection consist of *h* or fewer sets. (If a family has non-empty intersection then its Helly number is, by convention, 0.) Helly’s theorem then simply states that any finite family of convex sets in **R**^{d} has Helly number at most *d*+1. Such uniform bounds, that is bounds independent of the cardinality of the family, are of particular interest.

We present the following Helly-type result: if the Helly number of a finite family of sets in **R**^{d} has huge Helly number then some intersections of the sets must be topologically really complicated (in terms of its Betti numbers).

Precise statement is the following: Suppose that *F* is a finite family of arbitrary sets in **R**^{d} such that the intersection of any subfamily of *F* has the first *d*/2 Betti numbers β_{0},...,β_{d/2-1} bounded by some number *B*. Then the Helly number of *F* is bounded by some number *h=h(d,B)* that depends only on *d* and on *B*.

In the talk we will sketch a proof and say some details, since it is a continuation of a talk given by Uli a month ago.

Joint work with X. Goaoc, P. Paták, M. Tancer and U. Wagner.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login