Borel chromatic numbers of free groups

Abstract:

Recall that a coloring of a graph is a labeling of its vertices such that

no pair of vertices joined by an edge have the same label. The chromatic

number of a graph is the smallest number of colors for which there is a

coloring.

If G is a finitely generated group with generating set S, then for any free

action of G on a standard Borel space X, we can place a copy of the

S-Cayley graph of G onto every orbit. This results in a graph whose vertex

set is X and whose edge set is Borel measurable. We can then consider Borel

measurable colorings of this graph and the corresponding Borel chromatic

number. In this talk I will discuss Borel chromatic numbers for actions of

free groups with their standard generating set. I will focus on a

surprising theorem of Andrew Marks.

Abstract:

Recall that a coloring of a graph is a labeling of its vertices such that

no pair of vertices joined by an edge have the same label. The chromatic

number of a graph is the smallest number of colors for which there is a

coloring.

If G is a finitely generated group with generating set S, then for any free

action of G on a standard Borel space X, we can place a copy of the

S-Cayley graph of G onto every orbit. This results in a graph whose vertex

set is X and whose edge set is Borel measurable. We can then consider Borel

measurable colorings of this graph and the corresponding Borel chromatic

number. In this talk I will discuss Borel chromatic numbers for actions of

free groups with their standard generating set. I will focus on a

surprising theorem of Andrew Marks.

## Date:

Tue, 12/01/2016 - 12:00 to 13:00

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)