C&O 739

Schubert Calculus
Winter 2009

Time/Place: TTh  10:00-11:20,  MC 5045

Instructor: Prof. Kevin Purbhoo, MC 4029.

Calendar:
Tues. Jan 6: First class
Tues. Feb 10 (90210): Assignment 1 due
Feb 16-20: Reading week, no classes
Thurs. Feb 26: Deadline for choosing a course project topic
Tues. Mar 3: Assignment 2 due
Thurs. Mar 26: Assignment 3 due
Thurs. April 2: Presentations, starting at 9:30
Thurs. April 2: Last day of classes
Thurs. April 9: Course project due

References:

Wm. Fulton, "Young tableaux with applications to representation theory and geometry", Cambridge University Press, New York, 1997.

Notes on tensor products and the exterior algebra

A.S. Buch, A. Kresch and H. Tamvakis, "Littlewood-Richardson rules for Grassmannians", Adv. Math. 185 (2004), 80-90.

F. Sottile, "Pieri's formula for flag manifolds and Schubert polynomials", Ann. I. Fourier, 46 (1996), 89-110.

V.V. Deodhar, "On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells", Invent. Math. 79 (1985), 499-511.

E. Miller and B. Sturmfels, "Combinatorial Commutative Algebra", Graduate Texts in Mathematics 227, Springer, 2005.