Mathematical Sciences: RUI: Geometry
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{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
Frank Morgan will continue his studies of the behavior and                 structure of m-dimensional area minimizing surfaces. Soap films                 are the prototypical examples of such surfaces. Much current work               is directed towards the study of their singularities.                           Singularities occur at points where there is no well defined                    tangent plane. Work of Almgren has established upper bounds on                  the sizes of the singularity sets, but so far little is known                   about their structure. In particular they may even turn out to                  have fractional dimension. Morgan will involve undergraduate                    students in these investigations and thereby expose them to the                 excitement of modern mathematical research. They will be involved               in various computational and experimental aspects of the work.                  Morgan will be joined by Colin Adams whose work is of a more                    topological nature. He will study the cusp volumes of hyperbolic                three dimensional manifolds.                                                         The techniques to be employed by Morgan belong to geometric                measure theory. This is an extremely powerful theory which is                   accessible to relatively few mathematicians. Morgan will use                    these methods to study the structure of singularity sets of m                   dimensional area minimizing currents. In addition he will use                   calibrations to find further examples of area minimizing                        surfaces. These are closed differential forms which take extreme                values on the tangent spaces of such surfaces. They have recently               been used to great effect in the study of submanifolds of                       Grassmannians.
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{'Name': 'Williams College', 'CityName': 'WILLIAMSTOWN', 'ZipCode': '012672600', 'PhoneNumber': '4135974352', 'StreetAddress': '880 MAIN ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'MA01', 'ORG_UEI_NUM': 'JVZEJJ6N5EM8', 'ORG_LGL_BUS_NAME': 'PRESIDENT & TRUSTEES OF WILLIAMS COLLEGE', 'ORG_PRNT_UEI_NUM': 'JVZEJJ6N5EM8'}
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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