**Publications and Preprints:**

- Matrix Factorisation of Morse-Bott functions
- Dirac Families for Loop groups as Matrix
Factorizations C.R. Acad. Sci. Paris,
**353**(2015) link - Gauge theory and mirror symmetry ICM Seoul, 2014
- Geometric Langlands correspondence near opers (with E. Frenkel)
- 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.***4**, 2011 - 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**, 175–220. - Loop groups
and twisted
*K*-theory II (with D. Freed and M. Hopkins)*JAMS***26**, 2013 - Self-extensions
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. *K*-theory 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, Ed.)- Twisted equivariant
*K*-theory with complex coefficients (with D. Freed and M. Hopkins).*J. Top.***1**(2008) - Parabolic
bundles, products of conjugacy classes and Gromov-Witten invariants
(with C. Woodward).
*Ann. Inst. Fourier (Grenoble)***53**(2003) - 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), 1–43 - Borel-Weil-Bott theory for loop groups (Short survey of # 17,18,19).
- Borel-Weil-Bott
Theory on the moduli of
*G*-bundles over a curve.*Invent. Math.***134**(1998), 1–57 - Verlinde
factorization and Lie algebra cohomology.
*Invent. Math.***126**(1996), 249–263 - Lie
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*79-85, Travaux en Cours, 55,

differential equations, II (Marseille, 1990; Honolulu, HI, 1990),*Hermann, Paris,*1997