CAT(0) cube complexes and virtually special groups

Daniel Groves
University of Illinois, Chicago
October 27, 2015
Sageev associated to a codimension 1 subgroup $H$ of a group $G$ a cube complex on which $G$ acts by isometries, and proved this cube complex is always CAT(0). Haglund and Wise developed a theory of special cube complexes, whose fundamental groups have many favorable properties. In this talk, the basics of this theory will be described, along with applications.

A new cubulation theorem for hyperbolic groups

Daniel Groves
University of Illinois, Chicago
October 27, 2015
We prove that if a hyperbolic group $G$ acts cocompactly on a CAT(0) cube complexes and the cell stabilizers are quasiconvex and virtually special, then $G$ is virtually special. This generalizes Agol's Theorem (the case when the action is proper) and Wise's Quasiconvex Hierarchy Theorem (the case when the cube complex is a tree). This is joint work in preparation with Jason Manning.

Two-source dispersers for polylogarithmic entropy and improved Ramsey graphs I

Gil Cohen
California Institute of Technology
November 2, 2015

In his 1947 paper that inaugurated the probabilistic method, Erdős proved the existence of $2 \log(n)$-Ramsey graphs on $n$ vertices. Matching Erdős' result with a constructive proof is a central problem in combinatorics that has gained a significant attention in the literature. In this talk we will present a recent work towards this goal (http://eccc.hpi-web.de/report/2015/095/).

Two-source dispersers for polylogarithmic entropy and improved Ramsey graphs II

Gil Cohen
California Institute of Technology
November 3, 2015

In his 1947 paper that inaugurated the probabilistic method, Erdős proved the existence of $2 \log(n)$-Ramsey graphs on $n$ vertices. Matching Erdős' result with a constructive proof is a central problem in combinatorics that has gained a significant attention in the literature. In this talk we will present a recent work towards this goal (http://eccc.hpi-web.de/report/2015/095/).