(October 27) Ed Swartz: Matroids - This lecture is the first of two. The first lecture is an exposition of the theory of matroids. The second will be about a relation discovered by the speaker between matroids and linear quotients of spheres.

(April 19) Allen Knutson: Sums of hermitian matrices and honeycombs - In 1912 Hermann Weyl first addressed the following question; given two Hermitian matrices with known eigenvalues, what might be the eigenvalues of the sum. For example, the largest eigenvalue of the sum is at most the sum of the two individual largest eigenvalues. A great advance ws made recently be Klyachko in answering this, but the exact list of conditions was still unknown. We define a honeycomb, a combinatorial object analogous to a triple of Hermitian matrices wiht zero sum. With these we (1) refine the results of Klyachko to a minimal list of conditions,(2) prove Horn's 1962 conjcture, which gives a different (and much more explicit list), and (3) prove that the corresponding "quantum" problem (about tensor products of U(n) representations) is no harder than this classical problem. This work is joint work with Terence Tao and Chris Woodward.

(May 17) Lisa Traynor: Contact homology for Legendrian tangles - There are two classical integer invariants that can be assigned to a legendrian curve in a contact manifold. Recently, a notion of invariant homology groups for legendrian knots has been developed using the theory of holomorphic curves. Instead of focusing on legendrian knots, I will discuss legendrian tangles. For these tangles, it is possible to define two notions of homology; one defined via holomorphic curves and another via the theory of generating functions. I will compare and contrast these two homology theories for l class of tangles related by flypes.