NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF CHICAGO
Initial Amendment Date:	June 29, 2001
Latest Amendment Date:	March 3, 2003
Award Number:	0100108
Award Instrument:	Continuing Grant
Program Manager:	Andrew Pollington adpollin@nsf.gov  (703)292-4878 DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 2001
End Date:	June 30, 2004 (Estimated)
Total Intended Award Amount:	$405,000.00
Total Awarded Amount to Date:	$405,000.00
Funds Obligated to Date:	FY 2001 = $131,000.00 FY 2002 = $135,000.00 FY 2003 = $139,000.00
History of Investigator:	Vladimir Drinfeld (Principal Investigator) drinfeld@math.uchicago.edu Alexander Beilinson (Co-Principal Investigator)
Recipient Sponsored Research Office:	University of Chicago 5801 S ELLIS AVE CHICAGO IL  US  60637-5418 (773)702-8669
Sponsor Congressional District:	01
Primary Place of Performance:	University of Chicago 5801 S ELLIS AVE CHICAGO IL  US  60637-5418
Primary Place of Performance Congressional District:	01
Unique Entity Identifier (UEI):	ZUE9HKT2CLC9
Parent UEI:	ZUE9HKT2CLC9
NSF Program(s):	ALGEBRA,NUMBER THEORY,AND COM
Primary Program Source:	01000102DB NSF RESEARCH & RELATED ACTIVIT app-0102  app-0103
Program Reference Code(s):	0000, OTHR
Program Element Code(s):	126400
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT


The principal investigators conduct research in the following areas:
global geometric Langlands correspondence, local Langlands
correspondence in the de Rham setting, conformal field theories
related to Hecke chiral algebras, families of Tate spaces and
related infinite-dimensional algebraic varieties. They explore
analogs of the local Langlands correspondence in the de Rham
setting relating representations of Kac-Moody affine algebras
with de Rham local systems for the Langlands dual group on the
formal punctured disc. They study the representation theory of
chiral Hecke algebras and related global non-rational conformal
field theories in which the correlator D-modules form Hecke
eigensheaves in order to understand the global geometric Langlands
correspondence in the de Rham setting. They construct and study the
universal family of Langalnds transforms of GL(2) local systems.
They study the algebraic geometry of infinite-dimensional algebraic
varieties similar to the space of maps from the punctured formal
disk to a smooth algebraic variety.

The subject of the research lies on the intersection of several
domains of modern mathematics and mathematical physics - the
Langlands program, geometric representation theory, infinite-
dimensional algebraic geometry, and conformal field theory. The
blend of complementary ideas and methods is very fruitful - in
particular, it leads to construction of a geometric version of
Hecke eigenforms by means of an appropriate quantum field theory.

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