Lectures on group-valued moment maps and Verlinde formulas.
Preprint (submitted),
35 pages, January 2012.
PDF file.
Dirac Lie groups,
with D. Li-Bland. Preprint (submitted),
46 pages, October 2011
ArXiV
On the Verlinde formulas for SO(3)-bundles,
with D. Krepski. Quarterly Journal of Mathematics
(to appear).
16 pages, June 2011
ArXiV
Twisted K-homology and group-valued moment maps.
International Mathematics Research Notices (to appear).
38 pages, August 2010
ArXiV
The cubic Dirac operator for infinite-dimensional Lie algebras.
Canadian Journal of Mathematics 63 (3) (2011), 1364--1387
PDF file
Dirac structures and Dixmier-Douady bundles,
with A. Alekseev. International Mathematics Research Notices (to appear). PDF file
Courant algebroids and Poisson geometry,
with D. Li-Bland. International Mathematics Research Notices 11
(2009), 2106-2145. PDF file
Tilings defined by affine Weyl
groups. Pacific Journal of Mathematics 2 (2009), 333-343 PDF file
The Atiyah algebroid of the path
fibration over a Lie group,
with A. Alekseev. Letters in Mathematical Physics 90
(2009), 23-58.
PDF file
Quantization of q-Hamiltonian
SU(2)-spaces.
Geometric Aspects of Geometry and Mechanics (in honor of
the 65th birthday of Hans Duistermaat), Birkhaeuser, 2011.
Pages 257--293. PDF
file
Pure spinors on Lie groups,
with A. Alekseev and H. Bursztyn. Astérisque 327
(2009), 131--199. PDF file
On the quantization of conjugacy
classes. L'Enseignement Mathematique
55 (2009), 33-75. PDF file
Lectures on pure spinors
and moment maps. Poisson Geometry and Mathematical Physics,
Contemporary Mathematics 450 (2008), 199--222
PDF file
On the Kashiwara-Vergne conjecture,
with A. Alekseev.
Inventiones Mathematicae 164 (2006), 615--634
ArXiV
Ginzburg-Weinstein via Gelfand-Zeitlin,
with A. Alekseev.
Journal of Differential Geometry 76 (2007), 1--34.
ArXiV
Equivariant cohomology and the Cartan model,
Overview article for the
Encyclopedia of Mathematical Physics, Elsevier (2006). PDF file
Equivariant cohomology and the Maurer-Cartan equation,
with A. Alekseev.
Duke Mathematical Journal,
130 (3) (2005), 479-522 ArXiV
Witten's formulas for intersection pairings
on moduli spaces of flat G-bundles,
Advances in Mathematics,
197 (1) (2005), 140-197 ArXiV
Lie theory and the Chern-Weil homomorphism,
with A. Alekseev.
Ann. Sci. Ecole Norm. Sup.
38 (2) (2005), 303-338 Postscript file
The basic gerbe over a compact simple Lie group,
L'Enseignement Mathematique
49 (2003), 307--333. Postscript file
Clifford algebras and the classical dynamical Yang-Baxter equation,
with A. Alekseev.
Mathematical Research Letters
10 (2003), 253--268. Postscript file
Poisson Geometry and the Kashiwara-Vergne conjecture,
with A. Alekseev.
C. R. Acad, Sci. Paris.
335 (2002), 723--728.
Postscript file
Clifford algebras and the Duflo isomorphism,
Proceedings of the ICM Beijing 2002, volume II: Invited lectures.
Postscript file
Duistermaat-Heckman measures and moduli spaces of flat
bundles over surfaces,
with A. Alekseev, C. Woodward.
Geometric and Functional Analysis
12 (2002), 1--31.
Postscript file
Linearization of Poisson actions and singular values of matrix products,
with A. Alekseev, C. Woodward.
Annales Institut Fourier 51 (2001), 1691--1717.
Postscript file
Quasi-Poisson manifolds,
with A. Alekseev, Y. Kosmann-Schwarzbach.
Canadian Journal of Mathematics 54 (2002), 3--29.
Postscript file
The Verlinde formulas as fixed point formulas,
with A. Alekseev, C. Woodward.
Journal of Symplectic Geometry 1 (2001), 1--46.
Postscript file
Verlinde formulas for non-simply connected groups,
preliminary version, with A. Alekseev, C. Woodward.
May 2000. Pdf file
Group-valued equivariant localization,
with A. Alekseev, C. Woodward.
Inventiones Mathematicae 140 (2000), 327--350.
The non-commutative Weil algebra,
with A. Alekseev.
Inventiones Mathematicae 139 (2000), 135--172.
An elementary derivation of certain classical dynamical r-matrices,
with A. Alekseev.
Advances in the Mathematical Sciences 201 L. D. Faddeev's Seminar on Mathematical Physics.
A.M.S., 2000.
Canonical bundles for Hamiltonian loop group spaces,
with C. Woodward.
Pacific Journal of Mathematics 198 (2001), 477--487
Hamiltonian loop group actions and Verlinde factorization,
with C. Woodward.
Journal of Differential Geometry 50 (1999), 417--470
Cobordism for Hamiltonian loop group actions and flat connections
on the punctured two-sphere,
with C. Woodward.
Mathematische Zeitschrift 231 (1999), 133--168
Lie group valued moment maps,
with A. Alekseev, A. Malkin.
Journal of Differential Geometry 48 (1998), 445--495.
Moduli spaces of flat connections on 2-manifolds, cobordism, and
Witten's volume formulas,
with C. Woodward.
Advances in Geometry, Progr. Math. 172 271--295, Birkhaeuser Boston, 1999.
Singular reduction and quantization,
with R. Sjamaar.
Topology 38 (1999), 699-763.
Non-abelian convexity by symplectic cuts
with E. Lerman, S. Tolman, C. Woodward.
Topology 37 (1998), 245--259.
Symplectic surgery and the Spin-c Dirac operator.
Advances in Mathematics 134 (1998), 240--277
Symplectic reduction and Riemann-Roch for circle actions,
with H. Duistermaat, V. Guillemin, S. Wu.
Mathematical Research Letters 2 (1995), 259-266.
On Riemann-Roch formulas for multiplicities.
Journal of the American Mathematical Society 9 (1996), 373-390.
Vielfachheitsformeln fuer die Quantisierung von Phasenraeumen.
Ph.D. Thesis, Freiburg (1994).
Toeplitz quantization of Kaehler manifolds,
with M. Bordemann, M. Schlichenmaier.
Communications in Mathematical Physics 165 (1994), 281--296.
Coherent states and classical limits.
Journal of Physics A 27 (1994), 3257-3265.
Maslov indices for periodic orbits.
Conference Proceedings
Salamanca 1992 Vol.II, CIEMAT (1993), 414-417
Trace formulas and the Conley-Zehnder index.
Journal of Geometry and Physics (1994), 1-15.
Semiclassical principal symbols and Gutzwiller's trace formula.
Reports in Mathematical Physics 31 (1992), 279-295.
