Nicholas Lindell has been selected as a 2019 Presidential Award of Excellence Scholar. 

Abstract: Ring of conditions is a version of intersection theory defined by De Concini and Procesi for spherical homogeneous spaces. In the case of an algebraic torus (C^*)^n, the ring of conditions has a convex geometric description as a ring generated by the volume polynomial on the space of polytopes. One can extend this description to the case of horospherical homogeneous spaces using an analogue of Bernstein-Kouchnirenko theorem for toric bundles. In my talk I will explain these results.

Abstract: The classical degree-genus formula computes the genus of a nonsingular algebraic curve in the complex projective plane. The well-known Thom conjecture posits that this is a lower bound on the genus of smoothly embedded, oriented and connected surface in CP2. The conjecture was first proved twenty-five years ago by Kronheimer and Mrowka, using Seiberg-Witten invariants. In this talk, we will describe a new proof of the conjecture that combines contact geometry with the novel theory of bridge trisections of knotted surfaces.

This is a workshop for graduate students of the AWM who identify as female. Contact Sarah Blackwell for more details.