Title: Lower bounds on the initial degrees and containments of ideals
Abstract: Chudnovsky’s Conjecture and Demailly’s Conjecture suggest lower bounds for the degrees of hypersurfaces passing through a given set of points in a projective space. In this talk, we shall discuss some recent developments on these conjectures with focus on results for general points. We shall also discuss how solutions to the ideal containment problem can be used to investigate these questions. This is based on our joint work with Sankhaneel Bisui, Eloísa Grifo, and Tài Huy Hà.
