Mathematical Sciences: The K-Theory and Isomorphism         Invariants of Toeplitz Algebras
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{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
The situation of a group acting on a space, for instance the               group of real numbers acting by time evolution on the state space               of a physical system, is encountered quite often in mathematics                 and its applications.  In the physics example, every possible                   configuration of the system lies on a line flowing from remote                  past to distant future.  One is interested in what happens                      overall, in the long run, which may be quite difficult to infer                 solely from what happens over short intervals of time.  For                     purposes of analysis, the available information can be encoded in               several different ways: by differential equations or vector                     fields or foliations or, as is the case in Professor Xia's                      research project, by an algebra of operators on Hilbert space.                       Professor Xia will study a rather general Toeplitz algebra                 construction that has recently been developed for  (non-                        commutative) dynamical systems; this is related to the more                     familiar notion of a crossed product.  The specific objectives of               his work are to calculate the K-groups of Toeplitz algebras and                 their associated commutator ideals, and to see whether the                      Toeplitz algebra is a complete isomorphism invariant of the                     underlying dynamical system.
{'FirstName': 'Jingbo', 'LastName': 'Xia', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Jingbo Xia', 'EmailAddress': 'jxia@acsu.buffalo.edu', 'NSF_ID': '000168012', 'StartDate': '06/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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