Mathematical Sciences: Formal Systems and Combinatorics
{'Code': '03040200', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause'}
Timothy Carlson's work in finite and infinite combinatorics             provides powerful unifying generalizations of various so-called                 Ramsey theorems.  The simplest Ramsey theorem is the following:                 if six points in space are connected in all possible ways by                    straight line segments and each segment is painted either red or                green, then there will always be an entire triangle whose sides                 are of the same color.  This theorem has been generalized beyond                easy recognition in a variety of different ways, but all such                   generalizations are referred to as Ramsey theorems.  They have a                host of significant consequences in geometry and number theory                  and elsewhere, and it is very useful to have unifying principles                which provide economical derivations for these corollaries.                     Further results of this nature will be sought.
{'FirstName': 'Timothy', 'LastName': 'Carlson', 'EmailAddress': 'carlson.6@asc.ohio-state.edu', 'StartDate': '05/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Ohio State University Research Foundation -DO NOT USE', 'CityName': 'Columbus', 'ZipCode': '432101016', 'PhoneNumber': '6146888734', 'StreetAddress': '1960 KENNY RD', 'CountryName': 'United States', 'StateName': 'Ohio', 'StateCode': 'OH'}
{'Code': '1268', 'Text': 'FOUNDATIONS'}
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