**Lectures:** Wednesday and Friday, 1-2:30 pm,
room E17-139

**Instructor:**
Alexander Postnikov

**Synopsis:**
This is a graduate-level course in combinatorial theory. The content varies
year to year.

This year the course is about combinatorics related to the Grassmannian and flag varieties. The main players are Young tableaux, Schur polynomials and Schubert polynomials, Bruhat order, Littlewood-Richardson rule and its variations, wiring diagrams and reduced decompositions, matroids, the positive Grassmannian and positroids, quantum cohomology of the Grassmannian, quantum Schubert polynomials... We start with classical topics and (as time allows) move to topics of more recent research.

The class will be accessible to first year graduate students.

**Course Level:** Graduate

**Recommended textbooks:**

*****
W. Fulton:
*Young Tableaux*,
Cambridge University Press, 1997.

*****
R. P. Stanley:
*Enumerative Combinatorics*, Volumes 1 and 2,
Cambridge University Press, 1996 and 1999.

*****
L. Manivel:
*Symmetric Functions, Schubert Polynomials and Degeneracy Loci*,
SMF/AMS Texts and Monographs, Vol 6 and Cours Specialises Numero 3, 1998.

**Grading:** Based on several problem sets

**Problem Sets:**

- Problem Set 2 (due Friday, December 5, 2014)

**Lecture Notes** (by Carl Lian)
http://web.mit.edu/clian/www/315_notes.pdf

Additional Reading:

- Some combinatorial properties of Schubert polynomials
- Chains in the Bruhat order
- Quantum multiplication of Schur polynomials
- Affine approach to quantum Schubert calculus
- Quantum Schubert polynomials

last updated: November 21, 2014