Mathematics Events
[PAST EVENT] Mathematics Colloquium - Tyrone Crisp, University of Maine
Access & Features
- Free food
- Open to the public
Coloring, Counting, and Characters
Many different kinds of problems—from solving sudoku, to making maps easier to read—can be formulated as problems about colorings of graphs. In 1912 Birkhoff introduced a polynomial function that counts graph colorings, and 60 years later Stanley pointed out the intriguing fact that Birkhoff’s polynomial also counts the acyclic orientations of the graph. Later still, Hanlon showed how to adapt Birkhoff’s and Stanley’s results to the problem of counting colorings and orientations modulo symmetry. In this talk I will give a student-friendly, expository account of this work of Birkhoff, Stanley, and Hanlon. I will also briefly present some joint work with Caleb Hill and Aidan McEnaney, in which we show that Hanlon's results have a natural interpretation and extension in the language of group representations and Hopf algebras.
Sponsored by: Mathematics
Contact
Pierre Clare