Mathematical Sciences: Classification and Moduli Problems inAlgebraic Geometry
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{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
Professor Morrison will carry out research into several                    questions in the classification of isolated terminal quotient                   singularities in dimension four and possible extensions of this                 classification to higher dimensions.  Extensive computer assisted               calculations have been and will continue to be used in the search               for these singularities.  In collaboration with David Morrison,                 he will study the stability of Hilbert points of K3 surfaces and                will use the results of this study to describe compactifications                of moduli spaces of such surfaces.  With Dave Bayer, he will                    implement a universally standard basis algorithm for the                        construction of state polytopes of projective varieties and use                 it to produce and study such polytopes.  A superior algorithm for               computing these polytopes has been found and will be exploited in               these researches.  On the bases of these examples, he will                      attempt to find a geometric refinement of the Hilbert-Mumford                   criterion suited to the study of stability of Hilbert points of                 projective varieties.  In further joint work with Bayer, he will                use these examples to investigate the relationship between the                  state polytopes of a variety and the complexity of standard or                  Grobner basis calculations for the ideal of the variety.
{'FirstName': 'Ian', 'LastName': 'Morrison', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Ian Morrison', 'EmailAddress': 'morrison@murray.fordham.edu', 'NSF_ID': '000092184', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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[{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}, {'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}]
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