Special functions and Shimura varieties of orthogonal/unitary type

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

This project involves several topics in Number Theory, and more specifically the Kudla Program. The Kudla Program is an important part of research in modern Number Theory. It seeks to understand the deep connections between arithmetic and analysis on certain geometric objects called Shimura Varieties. Number theory focuses on the properties of whole numbers, including the primes, which have proved essential, resulting in far-reaching and unexpected connections to other fields such as electronic communications and cryptography, among others. The Principal Investigator is actively involved in the training of future mathematicians, including several PhD students who work on related projects. The Principal Investigator and his collaborators will continue fundamental research on the Kudla Program, including CM values of higher Green functions, and the construction of Green currents for Kudla special cycles of co-dimension larger than one and proof of their modularity. The relative trace formula and (arithmetic) Gan-Gross-Prasad theory is another very important direction in which the Principal Investigator will work, as well as the interactions between these two programs, resulting in a new line of fundamental research. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.