| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | September 15, 2011 |
| Latest Amendment Date: | June 23, 2021 |
| Award Number: | 1107452 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Tomek Bartoszynski
tbartosz@nsf.gov (703)292-4885 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 15, 2011 |
| End Date: | August 31, 2022 (Estimated) |
| Total Intended Award Amount: | $3,082,251.00 |
| Total Awarded Amount to Date: | $2,572,091.00 |
| Funds Obligated to Date: |
FY 2012 = $564,833.00 FY 2013 = $421,802.00 FY 2015 = $510,160.00 FY 2016 = $478,862.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
506 S WRIGHT ST URBANA IL US 61801-3620 (217)333-2187 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
506 S WRIGHT ST URBANA IL US 61801-3620 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): |
OFFICE OF MULTIDISCIPLINARY AC, INFRASTRUCTURE PROGRAM |
| Primary Program Source: |
01001213DB NSF RESEARCH & RELATED ACTIVIT 01001314DB NSF RESEARCH & RELATED ACTIVIT 01001415DB NSF RESEARCH & RELATED ACTIVIT 01001516DB NSF RESEARCH & RELATED ACTIVIT 01001617DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
GEometric structures And Representation varieties (GEAR)
This award supports a Research Network in the Mathematical Sciences. The GEometric structures And Representation varieties (GEAR) network encompasses mathematicians with backgrounds in diverse areas such as classical Teichmüller theory, discrete subgroups of Lie groups, 3- manifold topology, harmonic maps, dynamics, and moduli spaces of Higgs bundles and gauge theory. In recent years researchers in these areas have converged on common problems clustered around locally homogeneous structures on manifolds and moduli spaces of representations of finitely generated groups. New techniques and tools in one area have led to advances in another, and the contrasting points of view have highlighted new questions.
The goals of the GEAR network are to spur cross-pollination of ideas from one area to another, to build a research community transcending current divisions, to train students and researchers to cross traditional boundaries, and by these means to advance the mathematics targeted by the network. The main programs of the network include visits and exchanges among researchers at different locations, focused meetings and workshops designed to bridge gaps between targeted subspecialties or to address specific problems, network-wide retreats to help forge a common research community, graduate student internships and summer research experiences, and cyber-networking activities. Spread over 46 locations in the US, Canada and Europe, the nodes of the network cover a wide range of institutions, including several with historically low levels of resources for research. The nodes are arranged around central hubs at The University of Illinois at Urbana-Champaign, The University of Maryland, and Stanford University, with the lead hub in Urbana-Champaign.
GEAR Research Network home page: http://www.gear.math.illinois.edu
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The GEAR (GEometric structures And Representation varieties) Network brought together mathematicians with a wide range of backgrounds but with common interests in a specific set of research questions. The mathematical focus of the network was the topology, geometry, and dynamics of character varieties. The core mathematics, namely the theory of locally homogeneous geometric structures, flat bundles, and their deformation spaces has a long and distinguished history. More recently the subject acquired a multifaceted flavor with insights and techniques from several distinct sources being brought to bear on emerging problems. The goals of the GEAR Network were to:
(1) Understand all aspects of deformation spaces of geometric structures, representation varieties and moduli space of Higgs bundles,
(2) Facilitate and promote cross-pollination of ideas among research communities,
(3) Build a research community transcending extant divisions,
(4) Train students and researchers to cross traditional mathematical boundaries.
The main activities supported by the network were visits between GEAR members, either to collaborate on projects or to facilitate mentoring of junior members by senior researchers. Other activities included three network-wide retreats. Each retreat had two parts, namely a one-week junior retreat consisting of mini-courses and lectures designed for graduate students and postdocs, followed by a one-week meeting for all members. In addition, four `log cabin' workshops were organized entirely by junior members for junior members. In each of these, a group of about 20 junior GEAR members got together in a large `log-cabin' for the purpose of learning about a topic at the leading edge of GEAR research. The training mission of the network was further enhanced by a summer `research experiences' program which paired graduate students with senior GEAR members.
Complete records of the retreats, the log-cabin workshops, the summer programs, and much other information about the network, has been recorded on the website http://gear.math.illinois.edu
The network was administratively structured around three hubs, in the mathematics departments of the University of Illinois at Urbana-Champaign, the University of Maryland at College Park, and Stanford University. No-cost extensions and extensions related to the COVID pandemic allowed the network to operate from 2012 till August 31, 2022. By the end of its lifespan the network included over 180 senior members and approximately the same number of junior members (postdocs and graduate students) located at over 100 centers around the globe.
The tangible outcomes of the network include close to 1000 publications authored by at least one GEAR member and published in a peer-reviewed journal. Less tangible, but perhaps more far-reaching, was the impact on the cohort of young mathematicians who came of age and launched research careers during the GEAR era. The programs of the GEAR network greatly increased their opportunities to witness and participate in research at the cutting edge of highly active areas of mathematics. Moreover, because of the network's emphasis on building bridges between different communities, this generation internalized a much broader view of mathematics than would have otherwise been possible. The mathematics profession will be reaping the rewards for many years to come.
Last Modified: 01/30/2023
Modified by: Steven B Bradlow
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