Publications and Preprints:

  1. Coulomb branches in gauge theory
  2. Matrix Factorisation of Morse-Bott functions
  3. Dirac Families for Loop groups as Matrix Factorizations C.R. Acad. Sci. Paris, 353 (2015) link
  4. Gauge theory and mirror symmetry ICM Seoul, 2014
  5. Geometric Langlands correspondence near opers (with E. Frenkel)
  6. Relative quantum field theory (with D. Freed)
  7. Open-closed field theories, string topology, and Hochschild homology (with A. Blumberg and R. Cohen)
  8. Gromov-Witten Gauge Theory I (with E. Frenkel and A.J. Tolland)
  9. Topological Quantum Field Theories from Compact Lie Groups (with D. Freed, M. Hopkins and J. Lurie)
  10. Topological Field Theories in 2 dimensions European Congress of Mathematics, 197-210, EMS 2010
  11. An update on semi-simple quantum cohomology and F-manifolds (with Yu. Manin and C. Hertling) Proc. Steklov Inst. 264
  12. Structure of 2D semi-simple Field theories, Invent. Math 188, 2012; directly from Springer
  13. Branching of Hitchin's Prym cover for SL(2)
  14. Loop Groups and twisted K-theory I (with D. Freed and M Hopkins) J. Topol. 4, 2011
  15. Consistent Orientations of Moduli Spaces (with D. Freed and M Hopkins) In: The many facets of geometry, Oxford, 2010
  16. The Newstead-Ramanan conjecture on Chern classes (with C. Woodward; now incorporated in the "Index formula" paper)
  17. The strong Macdonald conjecture and Hodge theory on the Loop Grassmannian
    (with S. Fishel and I. Grojnowski) Ann. of Math. 168, 175–220.
  18. Loop groups and twisted K-theory II (with D. Freed and M. Hopkins) JAMS 26, 2013
  19. Self-extensions of Verma modules and differential forms on Opers (with E. Frenkel) Compositio Math 142.
  20. The Index formula on the moduli of G-bundles (with C. Woodward) Ann. of Math. 170, 2009
  21. Loop Groups and twisted K-theory III (with D. Freed and M. Hopkins) Ann. Math 174, 2011.
  22. 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.)
  23. Twisted equivariant K-theory with complex coefficients (with D. Freed and M. Hopkins). J. Top. 1 (2008)
  24. Parabolic bundles, products of conjugacy classes and Gromov-Witten invariants (with C. Woodward). Ann. Inst. Fourier (Grenoble) 53 (2003) 
  25. Some Hodge theory from Lie algebras. Motives, polylogarithms and Hodge theory, Part II (Irvine, CA, 1998), 731–744, Int. Press Lect. Ser. 3
  26. The quantization conjecture revisited. Ann. of Math. (2) 152 (2000), 1–43
  27. Borel-Weil-Bott theory for loop groups (Short survey of # 17,18,19).
  28. Borel-Weil-Bott Theory on the moduli of G-bundles over a curve. Invent. Math. 134 (1998), 1–57
  29. Verlinde factorization and Lie algebra cohomology. Invent. Math. 126 (1996), 249–263
  30. Lie algebra Cohomology and the Fusion Rules. Comm. Math. Phys. 173 (1995), 265–311
  31. 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