3:45PM: Residual Intersections and DualityDavid EisenbudLet J be an ideal generated by s elements in an sdimensional regular local ring. If dim S/J = 0, so that J is a complete intersection, then S/J is Gorenstein  that is, it is selfdual. I will explain an extension of this result to residual intersections  cases where S/J can have any dimension (and is not even pure dimensional). This is joint work with Bernd Ulrich, inspired by an idea of Duco van Straten.

5:00PM: Higher discriminants and the topology of algebraic mapsVivek ShendeWe introduce `higher discriminants' of a morphism of complex algebraic varieties. These are defined in terms of transversality conditions, and we show: (1) the support of any summand of a projective pushforward of the IC sheaf is a component of a higher discriminant, and (2) any component of the characteristic cycle of a proper pushforward of the constant function is a conormal variety to a component of a higher discriminant. This talk presents joint work with Luca Migliorini.
