Reflections on the coloring and chromatic numbers

Speaker: Chris Lambie-Hanson

Abstract: Compactness phenomena play a central role in modern set theory, and

the investigation of compactness and incompactness for the coloring and chromatic

numbers of graphs has been a thriving area of research since the mid-20th century,

when De Bruijn and Erdős published their compactness theorem for finite chromatic

numbers. In this talk, we will briefly review some of the highlights in this area and then present new results indicating, firstly, that the coloring number can only exhibit a limit amount of incompactness, and, secondly, that large amounts of incompactness for the chromatic number are compatible with strong compactness statements, including compactness for the coloring number. This is joint work with Assaf Rinot.

Speaker: Chris Lambie-Hanson

Abstract: Compactness phenomena play a central role in modern set theory, and

the investigation of compactness and incompactness for the coloring and chromatic

numbers of graphs has been a thriving area of research since the mid-20th century,

when De Bruijn and Erdős published their compactness theorem for finite chromatic

numbers. In this talk, we will briefly review some of the highlights in this area and then present new results indicating, firstly, that the coloring number can only exhibit a limit amount of incompactness, and, secondly, that large amounts of incompactness for the chromatic number are compatible with strong compactness statements, including compactness for the coloring number. This is joint work with Assaf Rinot.

## Date:

Wed, 11/11/2015 - 16:00 to 18:00

Repeats every week every Wednesday until Tue Mar 28 2017 except Wed Nov 11 2015

## Location:

Ross 70