Seminar on Complex Analysis and Complex Geometry - Fall 2022

On Wednesday when no extramural speaker is listed, the members of the complex geometry group may meet for a working seminar. For more information, send an email to Gordon Heier.

Friday, October 21, 2022, 2-3pm, PGH 646A

Title: Multi-types and Bloom conjecture

Speaker: Xiaojun Huang, Rutgers University

Abstract: Motivated by the subelliptic estimates for a bounded smooth pseudoconvex domain in C^2, Kohn introduced three boundary invariant measuring the non-degeneracy of the Levi-form of weakly pseudoconvex domain. It turns out all these invariants are the same. Kohn's three types can also be similarly defined for a hypersurface in C^n, called the s-contact type a_s, the s-commutator type t_s and the Levi-form type c_s. Bloom conjectured in 1979 that a_s=t_s=c_s for $n\ge 3$. In ths talk, I will discuss a joint work with Wanke Yin in which we answered the conjecture in the affirmative when $n=3$. We also discuss a related problem of D'Angelo.