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Research Spending & Results

Award Detail

Doing Business As Name:Brandeis University
  • Carolyn Abbott
  • (607) 342-4523
Award Date:06/17/2021
Estimated Total Award Amount: $ 263,986
Funds Obligated to Date: $ 263,986
  • FY 2021=$263,986
Start Date:07/01/2021
End Date:06/30/2024
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:Group Actions on Hyperbolic Spaces
Federal Award ID Number:2106906
DUNS ID:616845814
Parent DUNS ID:055986020
Program Officer:
  • Krishnan Shankar
  • (703) 292-4703

Awardee Location

Street:415 SOUTH ST MAILSTOP 116
Awardee Cong. District:05

Primary Place of Performance

Organization Name:Brandeis University
Street:415 South St.
Cong. District:05

Abstract at Time of Award

The collection of symmetries of an object form an algebraic object called a group. A simple example of a group is that of reflections and rotations of a square, as in the case of a 90 degree rotation, which leaves it unchanged. Studying groups can lead to many interesting questions. One could ask, for instance, how many different groups act on a square? What do such groups have in common? Geometric group theory aims to answer such questions by translating the geometric properties of spaces on which a group acts into algebraic properties of the group. The project will use these techniques to work towards understanding certain classes of groups, all of which act on spaces that have a particular geometric structure, called hyperbolicity. This project also seeks to support and encourage student involvement in mathematics, through support for graduate students, outreach to the local community, and support for a seminar series. In more detail, this projects fits into the broad goal of understanding groups that act on hyperbolic, or negatively curved, spaces. This goal is approached in three distinct ways: first, through understanding all actions of a given group on hyperbolic metric spaces; next, through an in-depth study of two particular actions of big mapping class groups, a class of groups in which there has recently been an explosion of interest; and finally, by seeking to prove a strong stability result for quotients of hierarchically hyperbolic groups, a class of groups which can be completely described by their actions on hyperbolic metric spaces. Parts of this project involve tools from other areas of mathematics, including descriptive set theory and (often non-commutative) ring theory. 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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