Title: Young tableaux and the geometry of algebraic curves

 

Abstract:  A classical computation of Castelnuovo in enumerative geometry (made rigorous in the 1980s) shows that, for certain choices of numerical invariants, the number of linear series on a general curve of genus g is equal to the number of standard Young tableaux on a certain rectangular partition. Later proofs show that this equality becomes a bijection when the algebraic curve degenerates in a particular way. I will discuss joint work with Melody Chan, Alberto Lopez, and Montserrat Teixidor i Bigas, in which we prove that in the case where the variety of linear series is 1-dimensional rather than a finite set of points, then the holomorphic Euler characteristic of this variety can be computed by an analogous enumeration of tableaux. Time permitting, I will explain how similar methods translate other aspects of the geometry of algebraic curves to enumeration of tableaux.