International Micro-Workshop on the Hypoelliptic Laplacian

May 7-10, 2019
Department of Mathematics
Penn State University

This was a small gathering to discuss Bismut’s hypoelliptic Laplacian and its applications. Each day began with an informal lecture, which was followed either by other informal lectures, or by even more informal discussions. The event was open to all.

Visiting Participants

  • Iakovos Androulidakis, National and Kapodistrian University of Athens
  • Bingxiao Liu, Max Planck Institute, Bonn
  • Shu Shen, Institut de Mathématiques de Jussieu
  • Yanli Song, Washington University in St Louis
  • Shilin Yu, Texas A&M University

Penn State Participants

  • Rui Bao
  • Michael Francis
  • Nigel Higson
  • Shiqi Liu
  • Yiannis Loizides
  • Jesus Sanchez
  • Jianchao Wu
  • Zelin Yi


Lectures and discussions took place in 106, McAllister Building, 10:00am-5:00pm.

Tuesday May 7

10:00 Nigel Higson
Hypoelliptic operators and nilpotent groups

11:00 Iakovos Androulidakis
Hypoelliptic operators and singular foliations

2:00 Bingxiao Liu
Correction term in Bismut’s hypoelliptic Laplacian

3:00 Shu Shen
Mathai-Quillen form on the free loop space

Wednesday May 8

10:00 Yanli Song
Bismut formula / Plancherel formula: Compact groups and SL(2,R)

11:00 Yanli Song
Bismut formula / Plancherel formula: Spherical formula for real rank one groups

2:00 Yiannis Loizides
The noncommutative Weil algebra and the cubic Dirac operator

Thursday May 9

10:00 Shu Shen
Hypoelliptic Laplacian and stochastic methods

2:00 Zelin Yi
Tangent groupoids, relative tangent groupoids and Getzler’s rescaling

Friday May 10

10:00 Bingxiao Liu
Computations for SL(2,R) (the good, the bad and the ugly)

11:00 Shu Shen
Hypoelliptic Laplacian and local index theory on a complex Hermitian manifold

2:00 Nigel Higson
Some challenges in tempered representation theory and slightly beyond

3:00 Yanli Song
Orbital integrals and characters