Xiang Tang, professor of mathematics and statistics in Arts & Sciences, has received a $252,305 grant from the National Science Foundation (NSF).
To explain the research, Tang asks: How does the sound of a bell determine its shape, or vice versa? The collection of frequencies at which a geometric structure resonates is called its spectrum. The spectrum contains a great deal of information, but it’s difficult to extract. A new approach, based on a concept called the hypoelliptic Laplacian, has shown great promise. The overall goal of this research is a clearer and more powerful understanding of the algebraic and functional analytic foundations of the hypoelliptic Laplacian; extensive development of its applications to tempered representation theory; and a deepened understanding of the geometric and topological invariants of singular spaces.
The grant is part of a focused research team also funded by the NSF. The team consists of four principal investigators: Nigel Higson, of Pennsylvania State University; Tang and Yanli Song of Washington University; and Zhizhang Xie of Texas A&M University.
