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Project Information

FRG: COLLABORATIVE RESEARCH: HOMOTOPICAL METHODS IN ALGEBRAIC GEOMETRY

Agency:
NSF

National Science Foundation

Project Number:
0966824
Contact PI / Project Leader:
WEIBEL, CHARLES A
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
The Principal Investigators will join in a collaborative effort to investigate fundamental questions in algebraic geometry using modern homotopical techniques; a unifying thread in these questions is the importance of various classes of invariants ranging from purely algebro-geometric to purely topological. First, the PIs propose to investigate the structure of morphism spaces between real algebraic varieties, especially unstable and stable homotopy types of spaces of "real algebraic" morphisms. Second, the PIs will examine the cohomology of various discrete and arithmetic groups, including algebraic versions of homotopy invariance for cohomology and the related Friedlander-Milnor conjecture. Third, the PIs propose to investigate invariants of singularities arising from methods involving the cdh-topology, continuing the recent flurry of activity in this subject. Finally, motivated by comparisons between algebro-geometric and topological invariants, the PIs will investigate semi-topological or morphic invariants of algebraic varieties, which lie partway between the worlds of algebraic geometry and topology.

Algebraic geometry, one of the oldest branches of mathematics, has at its heart the goal of studying the structure of solutions to systems of polynomial equations; these collections of solutions are called algebraic varieties. Homotopy theory, sometimes called rubber sheet geometry, attempts to study those aspects of geometric objects that are independent of the way they are pulled or twisted; one way to do this is to attach "invariants," e.g., numbers (or more general algebraic structures), to these objects. Algebraic varieties arising from equations with real or complex coefficients can be studied by means of homotopy theory, and the invariants that arise are necessarily somewhat restricted. The goal of this project is to study classical questions in algebraic geometry using invariants of algebraic varieties arising from homotopy theory. A major aim of this project is to convey some of the enthusiasm, techniques, and mathematical goals of the principal investigators to the next generation of mathematicians represented by graduate students and postdoctoral fellows. Methods to recruit and involve early career mathematicians will include the organization of a large international conference, the running of several workshops, the sharing of travel funds, and activities involving visitors from other institutions.
Project Terms:
career; Collection; Complex; Educational workshop; Equation; Funding; Goals; graduate student; Heart; Institution; International; Mathematics; Methods; next generation; Postdoctoral Fellow; Principal Investigator; Recruitment Activity; Research; Rubber; Running; Solutions; Structure; symposium; System; Techniques; theories; Travel

Details

Contact PI / Project Leader Information:
Name:  WEIBEL, CHARLES A
Other PI Information:
Not Applicable
Awardee Organization:
Name:  RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK
City:  NEW BRUNSWICK    
Country:  UNITED STATES
Congressional District:
State Code:  NJ
District:  06
Other Information:
Fiscal Year: 2010
Award Notice Date: 27-Apr-2010
DUNS Number: 001912864
Project Start Date: 01-Jun-2010
Budget Start Date:
CFDA Code: 47.049
Project End Date: 31-May-2013
Budget End Date:
Agency: ?

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National Science Foundation
Project Funding Information for 2010:
Year Agency

Agency: The entity responsible for the administering of a research grant, project, or contract. This may represent a federal department, agency, or sub-agency (institute or center). Details on agencies in Federal RePORTER can be found in the FAQ page.

FY Total Cost
2010 NSF

National Science Foundation

$395,932

Results

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