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An Analytic Grothendieck-Riemann-Roch Theorem


Speaker: Ronald G. Douglas, Texas A&M University
Location: 2112 MSB
Start time: Thu, Feb 19 2015, 3:10PM

About 15 years ago, Bill Arveson suggested a way of associating an analytic object to a homogeneous polynomial ideal, namely its closure in the Bergmann space on the unit ball. He conjectured that the multiplication operators on this space are essentially normal, which would yield an odd K-homology class for the projective variety. Having such, the next issue is calculating the class. This can be viewed as an index theorem analogous to the Grothendieck-Riemann-Roch Theorem. In this talk I present a very concrete case of these issues for which the proofs reduce to mostly calculations. This illustrates some recent results of Xiang Tang, Guoliang Yu, and myself. After presenting the concrete case I will examine the analogous statements and ideas for the general case.