Mathematical Sciences: Presidential Young Investigator Award
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Gary Cornell', 'PO_EMAI': None, 'PO_PHON': None}
This research overlaps the areas of combinatorics,                         representation theory and homological algebra.  A fundamental                   aspect is the use of supercomputers.  Algorithms are designed                   that use a mix of algebraic and combinatorial methods.  The                     results of these computations give valuable insight into the                    solutions of the ongoing research problems described now.  The                  first problem is to compute the Lie algebra cohomology of the                   tensor product of a finite dimensional complex Lie algebra L with               a certain polynomial quotient ring.  If L is semisimple, a                      solution to this problem would imply the Macdonald root-system                  conjectures.  Partial results and strong computer evidence points               to a complete solution when L is either semisimple or nilpotent.                The second problem is to determine the algebra structure of the                 symplectic and orthogonal centralizer algebras defined by Richard               Brauer.  These algebras are fundamental to the representation                   theory of the symplectic and orthogonal groups and are rich in                  combinatorial structure.  Again, strong computer evidence and                   partial results suggest that a complete solution to this                        structure problem will have and elegant combinatorial statement.                     This research investigates the combinatorial structure of                  algebraic problems.  Many of these questions can be described as                determining certain coefficients of certain polynomials which on                the one hand are defined in a complicated algebraic way but on                  the other hand have a simple combinatorial interpretation.                      Hanlon has in his short career become one of the world's leading                authorities on this important subject.  His use of the                          supercomputers to aid this work is very innovative.  His research               will certainly have the most profound affect.
{'FirstName': 'Philip', 'LastName': 'Hanlon', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Philip J Hanlon', 'EmailAddress': 'hanlon@math.lsa.umich.edu', 'NSF_ID': '000168935', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Regents of the University of Michigan - Ann Arbor', 'CityName': 'ANN ARBOR', 'ZipCode': '481091079', 'PhoneNumber': '7347636438', 'StreetAddress': '1109 GEDDES AVE, SUITE 3300', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Michigan', 'StateCode': 'MI', 'CONGRESSDISTRICT': '06', 'CONGRESS_DISTRICT_ORG': 'MI06', 'ORG_UEI_NUM': 'GNJ7BBP73WE9', 'ORG_LGL_BUS_NAME': 'REGENTS OF THE UNIVERSITY OF MICHIGAN', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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