Focused Research Group | Workshop on Hypoelliptic Operators
Sep 23th - Sep 25th
Washington University in St. Louis
The overall goals of the project will be clearer, simpler and more powerful understanding of the algebraic and functional analytic foundations of hypoelliptic Laplacian; the extensive development of its applications to tempered representation theory, including the Harish-Chandra Plancherel formula and the Mackey bijection; and a deepened understanding of the geometric and topological invariants of singular spaces. Specific goals for the proposed project period will include:
A new analytic foundation for the hypoelliptic Laplacian, using techniques borrowed from non- commutative geometry to obtain subelliptic and spectral estimates.
A new approach Harish-Chandra’s spherical Plancherel formula, and an analysis of its correspondence with both the classical approaches and other geometric approaches.
Analysis and characterization of the tempered duals of real reductive groups from the noncommutative geometric point of view, using higher orbital integrals to determine the Hochschild complex of Harish-Chandra’s Schwartz space via (higher) orbital integrals.
Development of the noncommutative geometry and spectral theory of coefficient systems, constructible and coherent sheaves as they arise in the theory of real and complex singular spaces.
Schedule:
09/23 3:00 p.m.-4:00 p.m. Higson
4:00 a.m. -5:30 p.m. discussion
09/24 9 a.m.-9:30 a.m. coffee/tea
9:30 a.m.-10:30 a.m. Wei
10:30 a.m.-12 p.m. discussion
09/24 2:00 p.m.- 4:00 p.m. discussion
09/25 9 a.m.- 9:30 a.m. coffee/tea
9:30 a.m. - 10:15 a.m. Zhu
11:00 a.m.-11:45 a.m. Roman
PIs: Nigel Higson (Penn State) Yanli Song (Wash U) Xiang Tang (Wash U) Zhizhang Xie (Texas A&M)
Local Organizers: Yanli Song, Xiang Tang
We gratefully acknowledge funding from the National Science Foundation under the aegis of DMS-1952557, DMS-1952551, DMS-1952669 and DMS-1952693.