NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	PRESIDENT & TRUSTEES OF WILLIAMS COLLEGE
Initial Amendment Date:	November 10, 1992
Latest Amendment Date:	September 27, 1995
Award Number:	9214077
Award Instrument:	Continuing Grant
Program Manager:	Joe W. Jenkins DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	November 15, 1992
End Date:	April 30, 1996 (Estimated)
Total Intended Award Amount:	$98,582.00
Total Awarded Amount to Date:	$98,582.00
Funds Obligated to Date:	FY 1993 = $32,144.00 FY 1994 = $32,144.00 FY 1995 = $34,294.00
History of Investigator:	Dave Witte (Principal Investigator) dwitte@math.okstate.edu
Recipient Sponsored Research Office:	Williams College 880 MAIN ST WILLIAMSTOWN MA  US  01267-2600 (413)597-4352
Sponsor Congressional District:	01
Primary Place of Performance:	Williams College 880 MAIN ST WILLIAMSTOWN MA  US  01267-2600
Primary Place of Performance Congressional District:	01
Unique Entity Identifier (UEI):	JVZEJJ6N5EM8
Parent UEI:
NSF Program(s):	MODERN ANALYSIS, COMPUTATIONAL MATHEMATICS, ANALYSIS PROGRAM
Primary Program Source:	app-0194  app-0195
Program Reference Code(s):	0000, 9178, 9229, 9251, OTHR, SMET
Program Element Code(s):	126200, 127100, 128100
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

The classical crystallographic groups of ordinary Euclidean space are basic examples of discrete subgroups of Lie groups. The crystallographic groups arising in the very rigid geometric structures known as locally symmetric spaces of higher rank have been classified by Margulis. Witte will investigate whether these important groups can be realized as symmetries of one-dimensional spaces. Witte will also investigate the crystallographic groups that arise in homogeneous spaces other than the usual symmetric spaces. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.

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