Date:      October 2, 2003

Speaker:   Ravi Vakil (Stanford University)

Title:     A geometric Littlewood Richardson rule

Abstract:  Littlewood-Richardson coefficients are fundamental
constants in several fields of mathematics.  In combinatorics, they
appear in the ring of symmetric functions.  In representation theory,
they appear in the representations of groups such as the general
linear group and the symmetric group. In geometry, they turn up in the
topology of the Grassmannian, which parametrizes sub-vector spaces of
an n-dimensional vector spaces.  (This is the ``geometry behind linear
algebra''.)  I will describe how to interpret Littlewood-Richardson
numbers in this way, and show you the key idea behind being able to
understand them with pictures (the "geometric Littlewood-Richardson
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.