|
|
Adam Rennie
- Position
Lecturer, Australian Research Fellow
- Research interests
Noncommutative geometry via
spectral triples. Analytic index theory, relation to KK-theory, index theory for unbounded
traces and weights, residue formulae for the index.
Manifold type structures for spectral triples. Metrics, differentiable structures, curvature,
nonunital algebras/noncompact spaces.
Extensions and applications of noncommutative geometry. Standard model of particle physics,
Lorentzian spectral triples,
statistical mechanics and quantum field theory, semifinite and type III index theory,
equivariant index theory.
-
- Email Address
- Adam.Rennieatmaths.anu.edu.au
- Postal Address
- Centre for Mathematics and its Applications, Mathematical Sciences Institute
- Australian National University, Canberra, ACT 0200, Australia.
- Phone
- (61-2) 6125 0717
- FAX
- (61-2) 6125 5549
Publications
Commutative Geometries are Spin Manifolds Reviews in
Mathematical Physics, vol 13, no. 4, pages 409-464, 2001
Smoothness and Locality for
Nonunital Spectral Triples K-Theory, vol 28, pages 127-165, 2003
Summability for Nonunital Spectral Triples
K-Theory, vol 31, pages 71-100, 2004
Nonunital Spectral Triples Associated
to Degenerate Metrics
Reviews in Mathematical Physics, Vol 16 No. 1 (2004) 125--146
The Hochschild Class of the
Chern Character of Semifinite Spectral Triples
, with A. Carey, J. Phillips, F. Sukochev, Journal of Functional Analysis, vol 213,
pages 111-153, 2004
The Local Index Formula for
Semifinite Spectral Triples I: Spectral Flow
, with A. Carey, J. Phillips, F. Sukochev, Advances in Mathematics, vol 202,
pages 451-516, 2006
The Local Index Formula for
Semifinite Spectral Triples II: The Even Case
, with A. Carey, J. Phillips, F. Sukochev, Advances in Mathematics, vol 202,
pages 517-554, 2006
The Noncommutative Geometry of Graph
C*-Algebras I: The Index Theorem
, with D. Pask, Journal of Functional Analysis, vol 233,
pages 92-134, 2006
An Analytic Approach to
Spectral Flow in von Neumann Algebras
, with M-T. Benemeur, A. Carey, J. Phillips, F. Sukochev,
K. Wojciechowski, in `Analysis, Geometry and Topology of
Elliptic Operators-Papers in Honour of K. P. Wojciechowski', World
Scientific, pages 297-352, 2006
Asymptotic of Zeta Functions and Dixmier
Traces
, with A. Carey, A. Sedaaev, F. Sukochev, Journal of Functional Analysis, vol 249,
pages 253-283, 2007
To appear
The Noncommutative Geometry of k-Graph
C*-Algebras
, with D. Pask, A. Sims, to appear in Journal of K-Theory
The Chern Character of
Semifinite Spectral Triples
, with A. Carey, J. Phillips, F. Sukochev, to appear in Journal of Noncommutative Geometry
Orbifolds are not Commutative Geometries,
with J. Varilly, to appear in the Journal of the Australian Mathematical Society
Semifinite Spectral Triples Associated with Graph
C*-Algebras,
with A. Carey, J. Phillips, to appear in `Traces in Geometry,
Number Theory and Quantum Fields', to be published by Vieweg, editors
S. Albeverio, M. Marcolli, S. Paysha, ca 22pp
Noncommutative Manifolds from Graph
and k-Graph
C*-Algebras
, with D. Pask, A. Sims, to appear in Communications in Mathematical Physics
Preprints
Reconstruction of Manifolds in
Noncommutative Geometry, with J. Varilly
KK-Theory and Spectral Flow
in von Neumann Algebras, with J. Kaad, R. Nest
A Noncommutative Atiyah-Patodi-Singer
Index Theorem in KK-Theory, with A. Carey, J. Phillips
Twisted cyclic theory and an index theory for
the gauge invariant KMS
state on Cuntz algebras, with A. Carey, J. Phillips
Spectral flow invariants and twisted cyclic
theory from the Haar state on SU_q(2), with A. Carey, K. Tong
- Links
-
Mathematical Sciences Institute, ANU
|
