Mathematical Conversations

The theory of quantum cohomology was developed in the early 1990s by physicists working in the field of superstring theory.

Mathematicians then discovered applications to enumerative geometry, counting the number of rational curves of a given degree satisfying certain incidence conditions, but the impact now extends into many other aspects of algebraic geometry, combinatorics, representation theory, number theory, and even back to physics. In this talk, we will define the Grassmannian of k-planes in n-space, its Schubert cells, and do some basic Schubert calculus, all by example.  Our goal is to state the “rim hook rule” which gives a fun combinatorial way to calculate the quantum cohomology of the Grassmannian.  This talk will be very concrete and assumes only basic linear algebra.