### March 17, 2017, 14:15pm

### Márton Naszódi: The Kneser--Poulsen conjecture for special contractions

The Kneser--Poulsen Conjecture states that if the centers of a family of $N$
unit balls in ${\mathbb E}^d$ is contracted, then the volume of the union
(resp., intersection) does not increase (resp., decrease).

A 'uniform contraction' is a contraction where all the
pairwise distances in the first set of points are larger than all the pairwise
distances in the second set of points. We show that
a uniform contraction of the centers does not decrease the volume of the
intersection of the balls, provided that $N\geq(1+\sqrt{2})^d$. Joint work with
Károly Bezdek.