3:45PM: The maximum likelihood degree of a toric varietySerkan HostenThe maximum likelihood degree (ML degree) of a projective variety is the number of complex critical points of the likelihood function with generic data. We consider the ML degree of projective toric varieties. For this, we look at "scaled" toric varieties given by a monomial parametrization involving arbitrary complex coefficients. We show that for generic choice of coefficients the ML degree of such a scaled toric variety is equal to the degree of the original toric variety. We also prove that the ML degree drops if and only if the scaling vector is on the hypersurface defined by the principal Adeterminant. With this tool in our hand, we will compute the ML degree of various classical toric varieties, of toric hypersurfaces, and toric varieties arising in graphical models.

5:00PM: GenusOne LandauGinzburg/CalabiYau CorrespondenceDustin RossFirst suggested by physicists in the late 1980's, the LandauGinzburg/CalabiYau correspondence studies a relationship between spaces of maps from curves to the quintic 3fold (the CalabiYau side) and spaces of curves with 5th roots of their canonical bundle (the LandauGinzburg side). The correspondence was put on a firm mathematical footing in 2008 when Chiodo and Ruan proved a precise statement for the case of genuszero curves, along with an explicit conjecture for the highergenus correspondence, which is determined from genuszero data alone. In this talk, I will begin by describing the motivation and the mathematical formulation of the LG/CY correspondence, and I will report on recent work with Shuai Guo that verifies the highergenus correspondence in the case of genusone curves.
