An unexpected application of algebraic number theory to operator algebras
Marta Asaeda (UC Riverside)

An Operator algebra is an algebra of bounded linear operators on a Hilbert space. Subfactors are pairs of operator algebras with certain properties. It belongs to the area of functional analysis, however since Jones' discovery on Jones polynomials, it evolved dramatically, having connection to other areas of mathematics such as low dimensional topology, representation theory, mathematical physics, and Topological quantum field theory. Subfactors with certain properties had been conjectured to exist. 9 years ago I proved that two of the conjectured subfactors do exist, with Haagerup. I will talk about my recent result with Yasuda that proves that none of the others exist except one. It uses classical theory of ramification of prime ideals in field extension.

Colloquium, Department of Mathematics, Rice University
November 13, 2008, 4-5PM, HB 227

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