Award Abstract # 1502632
RTG: Analysis on Manifolds

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: NORTHWESTERN UNIVERSITY
Initial Amendment Date: April 23, 2015
Latest Amendment Date: July 8, 2022
Award Number: 1502632
Award Instrument: Continuing Grant
Program Manager: Christopher Stark
DMS
 Division Of Mathematical Sciences
MPS
 Directorate for Mathematical and Physical Sciences
Start Date: July 1, 2015
End Date: June 30, 2023 (Estimated)
Total Intended Award Amount: $2,185,074.00
Total Awarded Amount to Date: $2,185,074.00
Funds Obligated to Date: FY 2015 = $377,915.00
FY 2016 = $440,706.00

FY 2017 = $528,638.00

FY 2018 = $635,861.00

FY 2019 = $201,954.00
History of Investigator:
  • Ezra Getzler (Principal Investigator)
    getzler@northwestern.edu
  • Laura DeMarco (Co-Principal Investigator)
  • Benjamin Weinkove (Co-Principal Investigator)
  • Aaron Naber (Co-Principal Investigator)
  • Jared Wunsch (Co-Principal Investigator)
Recipient Sponsored Research Office: Northwestern University
633 CLARK ST
EVANSTON
IL  US  60208-0001
(312)503-7955
Sponsor Congressional District: 09
Primary Place of Performance: Northwestern University
2033 Sheridan Road
Evanston
IL  US  60208-2730
Primary Place of Performance
Congressional District:
09
Unique Entity Identifier (UEI): EXZVPWZBLUE8
Parent UEI:
NSF Program(s): GEOMETRIC ANALYSIS,
ANALYSIS PROGRAM,
WORKFORCE IN THE MATHEMAT SCI
Primary Program Source: 01001920DB NSF RESEARCH & RELATED ACTIVIT
01001516DB NSF RESEARCH & RELATED ACTIVIT

01001819DB NSF RESEARCH & RELATED ACTIVIT

01001617DB NSF RESEARCH & RELATED ACTIVIT

01001718DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 7301
Program Element Code(s): 126500, 128100, 733500
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.049

ABSTRACT

Analysis on manifolds is a broad area of mathematics that arose historically in the nineteenth and twentieth centuries from the study of physical problems. It relates to questions such as the shape of a soap bubble, the overtones of a drum, and even to basic questions in number theory, such as the distribution of primes. The gravitational force is described with great success by Einstein's theory of General Relativity, and the theory of the recently discovered Higgs boson also depends on the study of differential equations on manifolds. This Research Training Group project aims to increase the number of US students interested in pursuing the study of analysis, and more specifically, analysis on manifolds.

This grant will support a rich educational environment, for undergraduates, graduate students, and postdoctoral fellows in the field of analysis on manifolds, mentored by junior and senior faculty in the area. We will establish a summer workshop for advanced undergraduates and students at the threshold of graduate study, to increase their fluency in the language of modern analysis. We will enhance the courses in analysis available to our undergraduate students, and expand the range of research experiences for undergraduates. We will also conduct outreach activities among high school students and teachers in the Chicago region. The larger goal is to increase the number of well-prepared US citizens who pursue careers in the mathematical sciences, with a particular effort to increase the numbers of under-represented minorities in this field.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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(Showing: 1 - 10 of 29)
Nicholas McCleerey and Jian Xiao "Polar Transform and Local Positivity for Curves" Annales de la Faculté des Sciences de Toulouse , v.(6) 29 , 2020 , p.247
Moritz Doll, Oran Gannot and Jared Wunsch "Refined Weyl law for homogeneous perturbations of the harmonic oscillator" Communications in Mathematical Physics , v.362 , 2018 , p.269 https://doi.org/10.1007/s00220-018-3100-5
Nicholas Lohr "Scaling Asymptotics of Wigner Distributions of Harmonic Oscillator Coherent States" Communications in PDE , 2023
Nicholas McCleerey "Envelopes with Prescribed Singularities" Journal of Geometric Analysis , 2019
Nicholas McCleerey "Volume of Perturbations of Pseudoeffective classes" Pure and Applied Mathematics Quarterly , 2018
Nicholas McCleerey and Valentino Tosatti "Pluricomplex Green's functions and Fano manifolds" Épijournal de Géométrie Algébrique , v.3 , 2019 , p.Article N
Oran Gannot "Resolvent estimates for spacetimes bounded by Killing horizons" Analysis & PDE , v.12 , 2019 , p.537
Oran Gannot "The null-geodesic flow near horizons" Transactions of the American Mathematical Society , v.371 , 2019 , p.4769
Oran Gannot and Jared Wunsch "Resonance-free regions for diffractive trapping by conormal potentials" American Journal of Mathematics , v.5 , 2021 , p.1339
Oran Gannot and Michal Wrochna "Propagation of singularities on AdS spacetimes for general boundary conditions and the holographic Hadamard condition" Journal of the Institute of Mathematics of Jussieu , v.21 , 2021
Perry Kleinhenz "Stabilization rates for the damped wave equation with Holder regular damping" Communications in Mathematical Physics , v.369 , 2019 , p.1187-1205
(Showing: 1 - 10 of 29)

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 "Analysis on Manifolds" RTG provided training opportunities at
every level from undergraduate to postdoctoral, helping to move a
whole generation of US students and postdocs through the pipeline
toward advanced study and research in geometric analysis.

Research Experiences for Undergraduates programs provided an entry
into the field for interested undergraduates.  On a larger scale, the
RTG also funded several summer schools, including some large "Summer
Northwestern Analysis Programs" (SNAP) meetings, as follows: 2015
(Geometric Analysis summer school); 2017 (SNAP on Partial Differential
Equations); 2018 (SNAP on Probability Theory and Connections to
Analysis); and 2019 (SNAP on Semiclassical Analysis).  These programs
brought together undergraduates, graduate students, and
researchers at all levels.  Exit surveys for these programs revealed
them to be excellent venues for early-career training; survey
responses such as "this was a very important experience for me to
transition from undergraduate to graduate level mathematics" were the
norm.

The grant also supported a weekend conference in October, 2015, for 50
American women undergraduates in mathematics.  This was the pilot of
what later become the (separately) NSF-funded GROW ("Graduate Research
Opportunities Workshop"); GROW has since expanded beyond Northwestern and
continues to receive NSF support.

The RTG sponsored research conferences in microlocal analysis and in homotopical methods
in mathematical physics.  It also brought seminar visitors to Northwestern's
Analysis Seminar, Informal Geometric Analysis Seminar, and Dynamical
Systems Seminar. These activities  exposed graduate students and postdocs to the cutting
edge of the field.

The grant funded all or part of the training of seven postocs and 15
graduate students in Northwestern's vibrant and supportive geometric
analysis group.  Outplacement has been excellent, and includes tenure
track jobs posts at Temple, Binghamton, Carnegie Mellon, Penn State.


Last Modified: 11/26/2023
Modified by: Jared Wunsch

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