SUMS: Nandakumar -- Combinatorics of Schubert polynomials

Schubert polynomials were introduced by Lascoux and
Schutzenberger in 1982, and since have played a very important role in
combinatorics and geometry. After defining Schubert polynomials, I
will discuss how they can be neatly expressed using the combinatorics
of pipe dreams and wiring diagrams using the nil-Hecke algebra. After
deducing some identities from these techniques, I will talk about
their relation to Schur polynomials via Grassmanian permutations. Time
permitting, I will introduce Schubert varieties, which were one of the
original geometric motivations for defining Schubert polynomials.