Title: The supersingular locus of some unitary Shimura varieties Speaker: Sungyoon Cho (Northwestern University) Faculty Sponsor: Liang Xiao
Time: Wednesday, September 26, 2018 at 11:15 am Place: MONT 313Abstract: A version of the Arithmetic Gan-Gross-Prasad conjecture predicts a relation between the intersection number of a certain arithmetic cycle in unitary Shimura variety to the non-vanishing of the central derivative of a certain L-function. Here, the supersingular locus plays an important role. In this talk, I will explain the geometric structure of the supersingular locus of the relevant unitary Shimura variety at a place with bad reduction.

Title: Symmetric and skew symmetric degeneracy loci and constructions of hyperkahler manifolds Speaker: Kristian Ranestad (University of Oslo) Faculty Sponsor: Jerzy Weyman
Time: Friday, September 28, 2018 at 10:00 am Place: MONT 214Abstract: Minors of matrices are defining equations for many classical varieties, which are therefore called degeneracy loci. Starting with Kummer surfaces, I shall explain a relation between symmetric and skew symmetric degeneracy loci. I shall go on to show how hyperkahler manifolds can be constructed from such degeneracy loci, in reporting on work with A. Iliev, G. Kapustka and M. Kapustka.