Combinatorics and Probability Seminar
Hunter Spink
Stanford
The additive structure of algebraic (and other nice) sets at infinity
Abstract: If X and V are closed sets in R^n, then the closure of X+V can be covered by X+V itself together with a "Frontier set" of points limited to by a sequence x_i+v_i with the individual sequences (x_i) and (v_i) tending to infinity. If V has additional structure like being an algebraic variety then the Frontier set can be (surprisingly) shown to be a union of lines, via the model-theoretic technique of "infinitesimal stabilizers" introduced by Peterzil and Starchenko. In joint work with Spencer Dembner using more subtle properties of the Frontier set, we resolve a conjecture of Gallinaro on the structure of the topological image-closure of a complex algebraic variety under the coordinate-wise complex-exponential map.
Monday October 17, 2022 at 2:00 PM in 636 SEO