3:45PM: Higher Homotopies and Golod RingsJesse BurkeLet Q be a commutative ring, R = Q/I a quotient ring, and M an Rmodule. Let A be a Qprojective resolution of R and G a Qprojective resolution of M. I will explain the Qlinear A∞algebra structure on A and an A∞ Amodule structure on G using higher homotopies. From these one can: build an Rprojective resolution of M from A and G, modify A and G to obtain Qfree resolutions for all Rsyzygies of M, and, when Q is local and A and G are min imal, describe the differentials in the EilenbergMoore spectral sequence for M. These methods work especially well for Golod modules, and show that if the inequality traditionally used to define Golod modules is an equality in the first dim Q+1 degrees, then the module is Golod. Finally, we give an explicit construction of the minimal Rfree resolution of every finitely generated module, when R is Golod.

5:00PM: The GreenLazarsfeld Gonality Conjecture (after EinLazarsfeld)Justin ChenWe show that a small variant of the methods used by Voisin in her study of canonical curves leads to a surprisingly quick proof of the gonality conjecture of Green and the second author, asserting that one can read off the gonality of a curve C from its resolution in the embedding defined by any one line bundle of sufficiently large degree. More generally, we establish a necessary and sufficient condition for the asymptotic vanishing of the weight one syzygies of the module associated to an arbitrary line bundle on C.
