# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, June 10, 2014, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

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

## Bounds for Pach's selection theorem

We focus on the estimates on the selection constant in the following geometric selection theorem by Pach: For every positive integer *d* there is a constant *c*_{d} > 0 such that whenever *X*_{1}, … , X_{d+1} are *n*-element subsets of **R**^{d}, then we can find a point *p* in **R**^{d} and subsets *Y*_{i} ⊂ X_{i} for every *i*=1,…, *d*+1, each of size at least *c*_{d} n, such that *p* belongs to all *rainbow* *d*-simplices determined by *Y*_{1}, … , Y_{d+1}, that is, simplices with one vertex in each *Y*_{i}.

We will discuss a lower and upper bound for the constant *c*_{d}, more concretely, *2*^{-2^{d^2 + O(d)}} ≤ c_{d} ≤ 0.9975^{d}. In order to show the upper bound, we prove the fact that the minimum solid angle of every *d*-simplex is exponentially small.

Joint work with Honza Kynčl, Pavel Paták and Martin Tancer.

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

Previous talks by year: 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