Dr. J. Phillips
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John Phillips, Ph.D. (Ore.), Professor
Research Interests: Operator Algebras, Noncommutative Geometry.
Recent Students
- Magdalena Georgescu, PhD 2006-present, Spectral Flow Formulas for Unbounded Fredholm Modules
and Analyticity.
- Robert Harrison, MSc 1995, Normal Approximants for Certain
Toeplitz Matrices and Toeplitz Operators.
- Tao Cao, MSc 1992, Introduction to AF Algebras and their Dimension Groups.
- Alison Nishihara, MSc 1990, On the Proofs of the Bott Periodicity Theorem.
- Hong-sheng Yin, PhD 1985, Classification of C*-crossed Products Associated with Characters on Free Groups.
- Mahmood Khoshkam, PhD 1982, Perturbations of Operator Algebras.
Selected Recent Publications
- A. Carey, J. Phillips, and A. Rennie, Twisted Cyclic Theory and an Index Theorem for the Gauge Invariant
KMS State on Cuntz Algebras, Submitted Jan. 2008, 27 LaTeX pages.
- A. Carey, J. Phillips, and A. Rennie, A Noncommutative Atiyah-Patodi-Singer Index Theorem in KK-Theory,
Submitted Nov. 2007, 40 LaTeX pages.
- A. Carey, J. Phillips, A. Rennie, and F. Sukochev, The Chern Character of Semifinite Spectral Triples,
J. Noncomm. Geometry, 2 (2008), 141-193.
- M.-T. Benameur, A. Carey, J. Phillips, A. Rennie, F. Sukochev, and K. P. Wojciechowski, An Analytic Approsch to Spectral Flow in
von Neumann Algebras, Proceedings of a Conference in Honour of K. P.
Wojciechowski, 50 years--Analysis and Geometry of Boundary Value Problems, in
Analysis, Geometry and Topology of Elliptic Operators, World Scientific (2006), 297-352.
- A. Carey, J. Phillips, A. Rennie, and F. Sukochev, The Local Index Formula in Semifinite von Neumann Algebras II:
The Even Case, Advances in Math., 202 (2006), 517-554.
- A. Carey, J. Phillips, A. Rennie, and F. Sukochev, The Local Index Formula in Semifinite von Neumann Algebras I:
Spectral Flow, Advances in Math., 202 (2006), 451-516.
- B. Booss-Bavnbek, M. Lesch, and J. Phillips, Unbounded Fredholm Operators and Spectral Flow,
Canadian J. Math., 57 no. 2 (2005), 225-250.
- A. Carey, J. Phillips, A. Rennie, and F. Sukochev, The Hochschild Class of the Chern Character for Semifinite Spectral Triples
, J. Functional Analysis, 213, no. 1 (2004), 111-153.
- A. Carey and J. Phillips, Spectral Flow in Fredholm Modules, Eta Invariants and the JLO Cocycle
, K-Theory, 31 (2004), 135-194.
- A. Carey, J. Phillips, and F. Sukochev, Spectral Flow and Dixmier Traces,
Advances in Math., 173 (2003), 68-113.
- A. Carey, J. Phillips, and F. Sukochev, On Unbounded p-Summable Fredholm Modules,
Advances in Math., 151 (2000), 140-163.
- A. Carey and J. Phillips, Unbounded Fredholm Modules and Spectral Flow, Can. J. Math., 50, no. 4(1998), 673-718 (invited paper).
- A. Carey, T. Coulhon, J. Phillips, and V. Mathai, Von Neumann Spectra Near the Spectral Gap, Bull. Math. Sci. France, 122, no. 3(1998), 1-40.
- J. Phillips, Spectral Flow in Type I and II Factors - A New Approach, Fields Institute Communications, 17(1997), 137-153
(invited paper).
- J. Phillips, Self-Adjoint Fredholm Operators and Spectral Flow, Can. Math.
Bull., 39 (1996), 460-467.
- J. Phillips and I. Raeburn, An Index theorem for Toeplitz Operators with Noncommutative Symbol Space, J. of Functional Analysis 120, (1994), 239-263.
- J. Phillips and I. Raeburn, Semigroups of Isometries, Toeplitz Algebras and Twisted Crossed Products,
J. Integral Eqns. and Operator Theory, 17 (1993), 579-602.
- A. Carey and J. Phillips, Algebras Almost Commuting with Clifford Algebras in a Semifinite Factor, K-Theory 4, (1991), 445-478.
- J. Phillips, K-Theory Relative to a Semifinite Factor, Indiana Univ. Math. J. 39, (1990), 339-354.