This is an informal minicourse for Masters and advanced undergraduate students, but anyone is welcome to attend.
Lecturers: Iva Halacheva and Paul Zinn-Justin
Schedule: May 2 - 24, 2019 Thursdays: 11:00am - 12:30pm in ROOM G39, Thomas Cherry, Fridays: 1:30pm - 3:00pm in ROOM 107
Outline
LECTURE 1: Schur and Schubert polynomials, tableaux, pipe dreams, product and Littlewood-Richardson rule. (notes, last updated May 3rd)
LECTURE 2: More on Schubert polynomials and pipe dreams, the nilHecke ring, the Yang-Baxter equation, (nil)Hecke algebras. (notes, last updated May 9th)
LECTURE 3: Divided difference operators, Monk's rule, multidegrees of algebraic sets. (notes, last updated May 21st)
LECTURE 4: Matrix Schubert varieties and their multidegrees. (notes, last updated June 26th)
LECTURE 5: Partial flag varieties, Schubert varieties and their geometry, Plücker embedding.
LECTURE 6: Introduction to (equivariant) cohomology, Schubert classes.
LECTURE 7: GL(n)-representation theory, relating the Littlewood-Richardson rule to Schubert classes and GL(n).
LECTURE 8: Integrable systems.