Publications and Preprints:
- Matrix Factorisation of Morse-Bott functions
- Dirac Families for Loop groups as Matrix
Factorizations C.R. Acad. Sci. Paris, 353 (2015)
- Gauge theory and mirror symmetry ICM Seoul, 2014
- Geometric Langlands correspondence near opers (with
- Relative quantum field theory
(with D. Freed)
- Open-closed field theories, string topology, and Hochschild homology (with A. Blumberg and R. Cohen)
- Gromov-Witten Gauge Theory I
(with E. Frenkel and A.J. Tolland)
- Topological Quantum Field Theories from Compact Lie Groups
(with D. Freed, M. Hopkins and J. Lurie)
- Topological Field Theories in 2 dimensions European Congress of Mathematics, 197-210, EMS 2010
- An update on
semi-simple quantum cohomology and F-manifolds (with Yu. Manin
and C. Hertling) Proc. Steklov Inst. 264
- Structure of 2D semi-simple
Field theories, Invent. Math 188, 2012; directly from Springer
- Branching of Hitchin's Prym
cover for SL(2)
- Loop Groups and twisted
K-theory I (with D. Freed and M Hopkins) J. Topol.
- Consistent Orientations
of Moduli Spaces (with D. Freed and M Hopkins) In:
The many facets of geometry, Oxford, 2010
- The Newstead-Ramanan
conjecture on Chern classes (with C. Woodward; now incorporated in
the "Index formula" paper)
- The strong
Macdonald conjecture and Hodge theory on the Loop Grassmannian
(with S. Fishel and I. Grojnowski) Ann. of Math. 168,
- Loop groups
and twisted K-theory II (with D. Freed and M. Hopkins)
JAMS 26, 2013
of Verma modules and differential forms on Opers (with E. Frenkel)
Compositio Math 142.
- The Index
formula on the moduli of G-bundles (with C. Woodward)
Ann. of Math. 170, 2009
- Loop Groups
and twisted K-theory III (with D. Freed and M. Hopkins)
Ann. Math 174, 2011.
of the moduli of principal bundles on a surface and deformations
of the Verlinde algebra.
Topology, Geometry and
Quantum Field Theory: Proceedings of the 2002 Oxford Symposium
in Honour of the 60th Birthday of Graeme Segal. (U.L. Tillmann,
- Twisted equivariant
K-theory with complex coefficients (with D. Freed
and M. Hopkins). J. Top. 1 (2008)
bundles, products of conjugacy classes and Gromov-Witten invariants
(with C. Woodward). Ann. Inst. Fourier (Grenoble)
- Some Hodge
theory from Lie algebras. Motives, polylogarithms and
Hodge theory, Part II (Irvine, CA, 1998), 731–744, Int.
Press Lect. Ser. 3
- The quantization
conjecture revisited. Ann. of Math. (2) 152 (2000),
theory for loop groups (Short survey of # 17,18,19).
Theory on the moduli of G-bundles over a curve. Invent.
Math. 134 (1998), 1–57
factorization and Lie algebra cohomology. Invent. Math.
126 (1996), 249–263
algebra Cohomology and the Fusion Rules. Comm. Math. Phys.
173 (1995), 265–311
- Limiting tangent spaces and a criterion for µ-constancy
(w. D. O'Shea) Stratifications, singularities and
differential equations, II (Marseille, 1990; Honolulu, HI,
1990), 79-85, Travaux en Cours, 55, Hermann, Paris, 1997