Syllabus 280-2: Combinatorics and Representation Theory
Fall 2003

Lectures: M 2:10-3:00pm, R 8:30-10:20 in Kerr 593
Instructor: Anne Schilling, Kerr Hall 578, phone: 754-9371, anne@math.ucdavis.edu
Text: Some of the material will be based on the following books:
  • B.E. Sagan, The symmetric group, second edition, Graduate Texts in Mathematics, Springer
  • L. Manivel, Symmetric functions, Schubert polynomials and degeneracy loci, SMFAMS vol. 6, American Math. Soc.
  • I.G. Macdonald, Notes on Schubert polynomials, Publications du Laboratoire de Combinatoire et d' Informatique Mathematique, Volume 6
We will also use recent papers which I will hand out or announce in class.
Grading: Every registered student is required to present a paper in class. A list of suitable papers and topics will be discussed in class.
Web: http://www.math.ucdavis.edu/~anne/FQ2003/280.html

Course description

This course will start from scratch (background on the symmetric group and symmetric functions will be helpful, but not required). Topics include:
symmetric group, Bruhat order, Schubert polynomials, Grassmannians, rc-graphs, Yang-Baxter equations, quiver varieties.
anne@math.ucdavis.edu