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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.
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- Email Address
- Adam.Rennieatanu.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
1. Commutative geometries are spin manifolds Reviews in
Mathematical Physics, vol 13, no. 4, pages 409-464, 2001
2. Smoothness and locality for
nonunital spectral triples K-Theory, vol 28, pages 127-165, 2003
3. Summability for nonunital spectral triples
K-Theory, vol 31, pages 71-100, 2004
4. Nonunital spectral triples associated
to degenerate metrics
Reviews in Mathematical Physics, Vol 16 No. 1 (2004) 125--146
5. 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
6. 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
7. 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
8. The noncommutative geometry of graph
C*-algebras I: the index theorem
, with D. Pask, Journal of Functional Analysis, vol 233,
pages 92-134, 2006
9. 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
10. Asymptotic of zeta functions and Dixmier
traces
, with A. Carey, A. Sedaaev, F. Sukochev, Journal of Functional Analysis, vol 249,
pages 253-283, 2007
11. The noncommutative geometry of k-graph
C*-algebras
, with D. Pask, A. Sims, Journal of K-Theory, Vol 1, no. 2 (2008), pages 259-304
12. The Chern character of
semifinite spectral triples
, with A. Carey, J. Phillips, F. Sukochev, Journal of Noncommutative Geometry, Vol 2, no. 2 (2008),
pages 253-283
13. Orbifolds are not commutative geometries,
with J. Varilly, Journal of the Australian Mathematical Society, Vol 84, no. 1 (2008), pages 109-116
14.
Semifinite Spectral triples associated with graph
C*-algebras,
with A. Carey, J. Phillips, in `Traces in Number Theory,
Geometry and Quantum Fields', Vieweg, editors
S. Albeverio, M. Marcolli, S. Paycha, J. Plazas, (2008) pages 35-56
To appear
Noncommutative Atiyah-Patodi-Singer boundary conditions and
index pairings in KK-Theory, with A. Carey, J. Phillips, to appear in Journal
fur die reine und angewandte Mathematik
Twisted cyclic theory and an index theory for
the gauge invariant KMS
state on Cuntz algebras, with A. Carey, J. Phillips, to appear in Journal of K-Theory
Spectral flow invariants and twisted cyclic
theory for the Haar state on SU_q(2), with A. Carey, K. Tong, to appear in Journal of Geometry and Physics
Twisted cyclic theory, equivariant KK-theory and KMS
states, with
A. Carey, S. Neshveyev, R. Nest, to appear in Journal
fur die reine und angewandte Mathematik
Noncommutative manifolds from graph
and k-graph
C*-algebras
, with D. Pask, A. Sims, to appear in Communications in Mathematical Physics
Preprints
KK-Theory and spectral flow
in von Neumann algebras, with J. Kaad, R. Nest
Modular index invariants of Mumford curves,
with A. Carey, M. Marcolli
- Links
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Mathematical Sciences Institute, ANU
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One of my colleagues' brain
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