Colloquium
3:00 p.m., Friday (April 2nd)
Math Annex 1100
Ravi Vakil
Department of Mathematics
Stanford University
A geometric LittlewoodRichardson rule
LittlewoodRichardson coefficients are fundamental constants
in several fields of mathematics (and in nature). In combinatorics,
they appear in the ring of symmetric functions; in representation theory,
they appear in the representations of groups such as GL(n) and S_n.
In geometry they turn up in the topology of the Grassmannian, which
parametrizes subvector spaces of an ndimensional vector spaces.
(This is the "geometry behind linear algebra".) I will describe
how to interpret LittlewoodRichardson numbers in this way, and
show you the key idea behind being able to understand them with
pictures (the "geometric LittlewoodRichardson rule"). I'll conclude
with a list of applications in several fields, but the main goal of
this talk will be to communicate the flavor of the ideas involved.
In particular, no background will be assumed.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
