Tverberg plus minus
Connections for Women Workshop: Geometric and Topological Combinatorics August 31, 2017  September 01, 2017
Location: SLMath: Eisenbud Auditorium
Tags/Keywords
Tverberg's theorem
sign conditions
6Barany
We prove a Tverberg type theorem: Given a set $A \subset \R^d$ in general position with $A=(r1)(d+1)+1$ and $k\in \{0,1,\ldots,r1\}$, there is a partition of $A$ into $r$ sets $A_1,\ldots,A_r$ (where $A_p\le d+1$ for each $p$) with the following property. The unique $z \in \bigcap_{p=1}^r \aff A_p$ can be written as an affine combination of the elements in $A_p$: $z=\sum_{x\in A_p}\al(x)x$ for every $p$ and exactly $k$ of the coefficients $\al(x)$ are negative. The case $k=0$ is Tverberg's classical theorem. This is joint works with Pablo Soberon.
6Barany
H.264 Video 
6Barany.mp4

Download 
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.