Jody Trout's Research Interests:

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My areas of research are in functional analysis, operator algebras, noncommutative topology/geometry, and mathematical physics. Specifically, I am interested in issues revolving around the Atiyah-Singer Index Theorem, such as elliptic differential operators on manifolds, asymptotic morphisms of C*-algebras, and their Connes-Higson bivariant E-theory (which also relates K-homology and K-theory), noncommutative topology/geometry of infinite-dimensional spaces and manifolds, and the use of operator algebras in quantum theory and quantization.

Here is a fun essay by the mathematical physicist John Baez on "What are C*-algebras good for?" See also Mark Tomforde's interesting A Survey of Operator Theory .

Nigel Higson and Jon Roe (Penn State) have written excellent math survey articles on operator algebras and the Atiyah-Singer Index Theorem.

For the bible on Noncommutative Geometry, click here and pray that the 654 page download doesn’t crash your server, or go to Alain Connes’ website first for more information.

This research has been supported by the National Science Foundation (NSF Research Grants DMS-0071120 and DMS-9706767).

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