Award Abstract # 1942302
CAREER: Intrinsic and Extrinsic Conditions in Several Complex Variables

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: LOUISIANA STATE UNIVERSITY
Initial Amendment Date: January 23, 2020
Latest Amendment Date: January 23, 2020
Award Number: 1942302
Award Instrument: Continuing Grant
Program Manager: Cesar Silva
DMS
 Division Of Mathematical Sciences
MPS
 Directorate for Mathematical and Physical Sciences
Start Date: September 1, 2020
End Date: January 31, 2021 (Estimated)
Total Intended Award Amount: $400,000.00
Total Awarded Amount to Date: $114,349.00
Funds Obligated to Date: FY 2020 = $0.00
History of Investigator:
  • Andrew Zimmer (Principal Investigator)
    amzimmer2@wisc.edu
Recipient Sponsored Research Office: Louisiana State University
202 HIMES HALL
BATON ROUGE
LA  US  70803-0001
(225)578-2760
Sponsor Congressional District: 06
Primary Place of Performance: Louisiana State University & Agricultural and Mechanical College
202 Himes Hall
Baton Rouge
LA  US  70803-2701
Primary Place of Performance
Congressional District:
06
Unique Entity Identifier (UEI): ECQEYCHRNKJ4
Parent UEI:
NSF Program(s): ANALYSIS PROGRAM
Primary Program Source: 01002021DB NSF RESEARCH & RELATED ACTIVIT
01002122DB NSF RESEARCH & RELATED ACTIVIT

01002223DB NSF RESEARCH & RELATED ACTIVIT

01002324DB NSF RESEARCH & RELATED ACTIVIT

01002425DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 1045, 9150, 9251
Program Element Code(s): 128100
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.049

ABSTRACT

This project concerns complex analysis, which combines complex numbers with the theory of calculus. Complex analysis is a fundamental tool in many applications. In particular, it is used in physics (for instance: studying the flow of air past an airfoil and dispersion relations in optics), engineering (for instance: signal processing and control theory), and computer science (for instance: image processing and quantum computation). Complex analysis of a single variable is a classical and well understood mathematical subject, but when additional variables are introduced many mysteries remain. In this project, the PI will further the theoretical understanding of complex analysis of several variables. This project also has a substantial educational component: The PI will develop a research experience in data science for first year undergraduate students at Louisiana State University (LSU). This program will prepare participants for a career in STEM, solidify their knowledge of basic mathematics, and give them an opportunity to learn about data science.

In the research part of this project, the PI will study bounded domains in complex Euclidean space and relate intrinsic geometric conditions (e.g. the geometry of the Kaehler-Einstein metric) to extrinsic geometric conditions (e.g. the CR-geometry of the boundary). Many classical results in the subject consider bounded domains in complex Euclidean space, assume that the boundary is smooth, and make assumptions about the CR-geometry of the boundary. For domains with non-smooth boundary, the PI will prove new variants of classical results by assuming geometric conditions on the Kaehler-Einstein metric instead of conditions on the boundary. Using this approach, the PI will be able to study classes of domains which are typically outside the reach of the standard analytic methods and also make progress on old problems. This approach is motivated by the great success of geometric group theory where metric space techniques applied to group theory not only lead to progress on old problems, but also many new and interesting examples.

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.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Zimmer, Andrew "The automorphism group and limit set of a bounded domain II: the convex case" Journal of the London Mathematical Society , 2021 https://doi.org/10.1112/jlms.12435 Citation Details

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