Time: 9:30 -- 11:00, May 22nd, 2024

Venue: Room 612, A6

Abstract: What is the smallest degree of a homogeneous polynomial that vanishes on a finite set of points to a given order? Chudnovsky’s Conjecture and Demailly's Conjecture suggest lower bounds for such degrees. To study the above interpolation question, one can study containment between symbolic powers and ordinary powers of the defining ideal of the set of points. In this talk, we will discuss some recent developments on these conjectures with focus on results for general points. I will also present results from our joint work with Sankhaneel Bisui, Eloísa Grifo and Tài Huy Hà.