Mathematical Sciences: Hodge Theory
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Eduardo Cattani and Aroldo Kaplan will continue their work                 in Hodge theory. This involves the study of topological and                     geometric invariants connected with an algebraic variety. Hodge                 theory yields a method of describing the space of differential                  forms on a manifold. This theory has seen very rapid developments               in recent years. Most notably, on the construction of functorial                Hodge structures on appropriate cohomology and homotopy spaces.                 The work of Cattani and Kaplan in cooperation with Wilfried                     Schmid has been at the forefront of research in variations of                   Hodge structures.                                                                    Cattani and Kaplan will build on their recent results which                bring the several variable case within reach of applications.                   They will apply these results to the study of the behaviour of                  integral cycles in an algebraic family of varieties. They will                  also study the structure of modular varieties. This work will                   focus on the characterization of maximal integral submanifolds                  for the horizontal distribution in a classifying space for Hodge                structures.
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{'Name': 'University of Massachusetts Amherst', 'CityName': 'AMHERST', 'ZipCode': '010039252', 'PhoneNumber': '4135450698', 'StreetAddress': '101 COMMONWEALTH AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'MA02', 'ORG_UEI_NUM': 'VGJHK59NMPK9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF MASSACHUSETTS', 'ORG_PRNT_UEI_NUM': 'VGJHK59NMPK9'}
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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