Publications and Preprints:

  1. Topological Symmetry in Quantum Field Theory (with D. Freed and G. Moore)
  2. Coulomb branches for quaternionic representations
  3. The Haagerup category is not a gauge theory
  4. Gapped Boundary Conditions in Three Dimensions (with Dan Freed) Commun. Math. Phys. 388 (2021), 3497–3520
  5. Topological dualities in the Ising model (with Dan Freed) Geom. Topol. 26 (2022)
  6. Coulomb branches in gauge theory JEMS 23 (2021), 3947–3520 link
  7. Matrix Factorisation of Morse-Bott functions Duke Math. J.169 (2020) No. 3, 533–549
  8. Dirac Families for Loop groups as Matrix Factorizations (with D. Freed) C.R. Acad. Sci. Paris 353 (2015) link
  9. Gauge theory and mirror symmetry Proceedings of the ICM&emdash;Seoul 2014, Vol. II, 1309–1332
  10. Geometric Langlands correspondence near opers (with E. Frenkel) J. Ramanujan Math. Soc. 28A (2013), 123–147
  11. Relative quantum field theory (with D. Freed) Commun. Math. Phys. 326 (2014), 459–476
  12. Open-closed field theories, string topology, and Hochschild homology (with A. Blumberg and R. Cohen)
  13. Gromov-Witten Gauge Theory(with E. Frenkel and A.J. Tolland) Adv. Math. 288 (2016), 201–239
  14. Topological Quantum Field Theories from Compact Lie Groups (with D. Freed, M. Hopkins and J. Lurie) A celebration of the mathematical legacy of Raoul Bott, CRM Proc. Lecture Notes 50 367–403 (2010)
  15. Topological Field Theories in 2 dimensions European Congress of Mathematics, 197-210, EMS 2010
  16. An update on semi-simple quantum cohomology and F-manifolds (with Yu. Manin and C. Hertling) Proc. Steklov Inst. 264
  17. Structure of 2D semi-simple Field theories, Invent. Math 188, 2012; directly from Springer
  18. Branching of Hitchin's Prym cover for SL(2)
  19. Loop Groups and twisted K-theory I (with D. Freed and M Hopkins) J. Topol. 4, 2011
  20. Consistent Orientations of Moduli Spaces (with D. Freed and M Hopkins) In: The many facets of geometry, Oxford, 2010
  21. The Newstead-Ramanan conjecture on Chern classes (with C. Woodward; now incorporated in the "Index formula" paper)
  22. The strong Macdonald conjecture and Hodge theory on the Loop Grassmannian (with S. Fishel and I. Grojnowski) Ann. of Math. 168, 175–220.
  23. Loop groups and twisted K-theory II (with D. Freed and M. Hopkins) JAMS 26, 2013
  24. Self-extensions of Verma modules and differential forms on Opers (with E. Frenkel) Compositio Math 142.
  25. The Index formula on the moduli of G-bundles (with C. Woodward) Ann. of Math. 170, 2009
  26. Loop Groups and twisted K-theory III (with D. Freed and M. Hopkins) Ann. Math 174, 2011.
  27. 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.)
  28. Twisted equivariant K-theory with complex coefficients (with D. Freed and M. Hopkins). J. Top. 1 (2008)
  29. Parabolic bundles, products of conjugacy classes and Gromov-Witten invariants (with C. Woodward). Ann. Inst. Fourier (Grenoble) 53 (2003) 
  30. Some Hodge theory from Lie algebras. Motives, polylogarithms and Hodge theory, Part II (Irvine, CA, 1998), 731–744, Int. Press Lect. Ser. 3
  31. The quantization conjecture revisited. Ann. of Math. (2) 152 (2000), 1–43
  32. Borel-Weil-Bott theory for loop groups (Short survey of the three articles below).
  33. Borel-Weil-Bott Theory on the moduli of G-bundles over a curve. Invent. Math. 134 (1998), 1–57
  34. Verlinde factorization and Lie algebra cohomology. Invent. Math. 126 (1996), 249–263
  35. Lie algebra Cohomology and the Fusion Rules. Comm. Math. Phys. 173 (1995), 265–311
  36. 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