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Research Spending & Results

Award Detail

Doing Business As Name:University of Minnesota-Twin Cities
  • Tsao-Hsien Chen
  • (773) 895-6449
Award Date:07/11/2020
Estimated Total Award Amount: $ 175,703
Funds Obligated to Date: $ 59,766
  • FY 2020=$59,766
Start Date:07/15/2020
End Date:06/30/2023
Transaction Type:Grant
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Higgs Bundles, Real Quasi-Maps, and Automorphic L-Functions
Federal Award ID Number:2001257
DUNS ID:555917996
Parent DUNS ID:117178941
Program Officer:
  • James Matthew Douglass
  • (703) 292-2467

Awardee Location

Street:200 OAK ST SE
Awardee Cong. District:05

Primary Place of Performance

Organization Name:University of Minnesota-Twin Cities
Street:127 Vincent Hall, 206 Church Str
Cong. District:05

Abstract at Time of Award

This mathematics research project naturally sits at the intersection of representation theory and geometry. Representation theory is a branch of mathematics studying symmetries of mathematical objects and structures. Methods from geometry have been very successful in answering questions in representation theory. The main goal of the project is to study open questions in representation theory using geometric methods. Specifically, the investigator plans to use and develop geometric tools to attack several longstanding problems in the study of representations of Lie groups, Higgs bundles and representations of fundamental groups, and the Langlands program. In more detail, the research centers on three projects: (1) Hitchin morphisms for higher dimensional varieties, (2) real quasi-maps and applications, and (3) nonlinear Fourier transforms and the Braverman-Kazhdan program. In project (1), the investigator will develop the theory of Hitchin morphisms for higher dimensional varieties and apply it to the study of the Simpson correspondence. This project is closely related to deep questions in invariant theory, higher-dimensional algebraic geometry, and representations of fundamental groups. In project (2), the investigator will explore the geometric structure of real quasi-maps and establish applications to the study of representation theory of real groups, the Kostant-Sekiguchi correspondence, and Springer theory for symmetric spaces. In project (3), the investigator will study the Braverman-Kazhdan approach to meromorphic continuation and functional equations of automorphic L-functions. Based on results on nonlinear Fourier transforms and the Braverman-Kazhdan conjecture in the finite field and D-modules setting, the project aims to construct nonlinear Fourier kernels in the local fields setting. 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.

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