MTH 685: Topics in Algebraic Combinatorics

Instructor: Michelle Wachs Galloway

Time: Tuesdays and Thursdays, 2:00 - 3:15pm

This is the first semester of a year long sequence covering certain fundamental topics in algebraic and topological combinatorics. The first semester is an introduction to symmetric function theory and representations of the symmetric group. The second semester is based in part on the course I gave on poset topology at the IAS / Park City Mathematics Institute Graduate Summer School in Geometric Combinatorics in 2004.

Topics:

• representation theory of the symmetric group and related groups
• symmetric function theory
• topology of partially ordered sets and other combinatorial simplicial complexes

Prerequisite: MTH 562

Reference Texts:

• Bruce Sagan, The Symmetric Group, Representations, Combinatorial Algorithms & Symmetric Functions, Graduate Texts in Mathematics 203, Springer-Verlog 2001.
• William Fulton, Young Tableaux, Student Texts 35, London Mathematical Society, Cambridge University Press, 1997.
• Richard Stanley, Enumerative Combinatorics, Vols. 1 and 2, Cambridge Studies in Advanced Mathematics 50,62, Cambridge University Press, 1999.
• Michelle Wachs, Poset Topology: Tools and Applications, chapter of Geometric Combinatorics volume of IAS/ Park City Series, in press, http://www.math.miami.edu/~wachs/eprints.html