中央研究院數學研究所

Seminar on Geometry and Several Complex Variables

The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds

2025/11/13 (Thu.) 16:00~17:00

Date : 2025/11/13 (Thu.) 16:00~17:00
Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
Speaker : Dr. Yoshiaki Suzuki (University of Osaka)
Organizer : Jih-Hsin Cheng (AS)
Abstract : In 2004, Folland studied the compact quotients of the Heisenberg group by its lattice, known as Heisenberg nilmanifolds, in the context of CR geometry. He determined the eigenvalues and eigenfunctions of the Folland-Stein operator (gives the Kohn Laplacian essentially) on Heisenberg nilmanifolds. In this talk, with the aim of extending Folland's work, we study Heisenberg Bieberbach manifolds, which are given by the quotients of Heisenberg nilmanifolds by finite groups. Using Folland's method, we calculate the eigenvalues and the dimensions of the eigenspaces of the Folland-Stein operator on some examples of Heisenberg Bieberbach manifolds.