NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	OKLAHOMA STATE UNIVERSITY
Initial Amendment Date:	July 16, 2001
Latest Amendment Date:	July 16, 2001
Award Number:	0100438
Award Instrument:	Standard Grant
Program Manager:	Joe W. Jenkins DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	August 1, 2001
End Date:	July 31, 2004 (Estimated)
Total Intended Award Amount:	$87,420.00
Total Awarded Amount to Date:	$87,420.00
Funds Obligated to Date:	FY 2001 = $87,420.00
History of Investigator:	Dave Witte (Principal Investigator) dwitte@math.okstate.edu
Recipient Sponsored Research Office:	Oklahoma State University 401 WHITEHURST HALL STILLWATER OK  US  74078-1031 (405)744-9995
Sponsor Congressional District:	03
Primary Place of Performance:	Oklahoma State University 401 WHITEHURST HALL STILLWATER OK  US  74078-1031
Primary Place of Performance Congressional District:	03
Unique Entity Identifier (UEI):	NNYDFK5FTSX9
Parent UEI:
NSF Program(s):	ANALYSIS PROGRAM
Primary Program Source:	01000102DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s):	0000, OTHR
Program Element Code(s):	128100
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT


Abstract
Witte
One focus of this project is the study of tessellations of homogeneous spaces. Namely, if G/H is a non-compact, simply connected homogeneous space of a connected Lie group G, the question is whether there is a properly discontinuous subgroup D of G, such that the orbit space D\G/H is compact. Some special cases were studied by L. Auslander, Y. Benoist, G. A. Margulis, R. J. Zimmer, and others. In collaboration with H. Oh and A. Iozzi, the PI has recently made progress in understanding the case where G is a semisimple Lie group of real rank two, including a detailed study of the case where G = SO(2,2n) or SU(2,2n). The PI will continue this research, both for real rank two and higher real rank. He will also continue his study of actions of arithmetic groups on the circle, and related questions.
This project studies crystals in mathematical spaces other than the 3-dimensional universe that we live in. (A crystal is a material whose atomic structure is very symmetric.) The most fundamental problem in this subject is to decide which spaces contain crystals, and which do not. (For this question, the most interesting spaces are homogeneous, which means that every point of the space looks exactly like all of the other points.) Mathematicians have made substantial progress on this problem in recent years, and this project will continue the work. In cases where crystals do exist, the project will investigate the algebraic properties of the group formed by the symmetries of a crystal.

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