Publications and preprints available online are below, mostly in pdf format. The papers are ordered by date of release. Comments are very welcome. Note that the published versions in some cases contain substantial revisions, feel free to ask me for an offprint.

55. (With G. Xu) An open quantum Kirwan map. 110 pages. (Version June 2018).

54. (With J. Palmer) Floer cohomology and Maslov flow. 60 pages. (Version June 2018).

53. (With E. Gonzalez and P. Solis) Properness for scaled gauged maps 53 pages. J. Algebra, 490:104--157, 2017. (Version July 2017)

52. (With E. Gonzalez and P. Solis) Stable gauged maps 34 pages. To appear in Proc. Symposia AMS. Version February 2018.

(This and the paper above were meant to be one paper intended as a survey, but the paper eventually got too long and was split. There is still substantial overlap. )

51. (With F. Charest) Floer theory and flips 169 pages. (Version June 2018)

50. (With F. Charest) Floer trajectories and stabilizing divisors. 61 pages. Jour. Fixed Point Theory. June 2017, Volume 19, Issue 2, pp 1165--1236 (Version October 17; a paragraph of clarification was added to the published version.)

49. (With S. Venugopalan) Classification of affine vortices. 39 pages. Duke Math. J. Volume 165, Number 9 (2016), 1695-1751. (Version December 2014)

48. (With E. Gonzalez) A wall-crossing formula for Gromov-Witten invariants under variation of git quotient. Submitted. 45 pages. (Version June 2017)

47. (With E. Gonzalez) Quantum cohomology and toric minimal model programs. Submitted. 47 pages. (Version March 2013)

44-46. Quantum Kirwan morphism and Gromov-Witten invariants of quotients. Part 1 . Part 2 . Part 3 . Transformation Groups 20 (2015) 507-556, 881-920, 1155-1193. Split into parts at the request of the journal. (Corrected version June 2017)

43. (With Glen Wilson) Quasimap Floer cohomology and varying symplectic quotients. Canadian Jour. of Math. 65 (2013) 467--480. (Version April 2012)

42. Gauged Floer theory of toric moment fibers. 74 pages. GAFA Vol21-3 (2011), 680-749. Errata. on the published version. (The arxiv version was corrected, version March 2015.)

41. Moment maps and geometric invariant theory. 57 pages, 5 figures. Notes from a course given at CIRM, Luminy, in April 2009. Les cours du CIRM, 1 no. 1: Hamiltonian Actions: invariants et classification (2010), p. 55-98

(Version November 2011)

40. (with S. Ma'u and K. Wehrheim) A-infinity functors for Lagrangian correspondences. 84 pages. Selecta Math. July 2018, Volume 24, Issue 3, p. 1913--2002 Selecta Math. (Version February 2018).

39. (with K. Nguyen and F. Ziltener) Morphisms of cohomological field theory algebras and quantization of the Kirwan map. 33 pages. Symplectic, Poisson, and Noncommutative Geometry , MSRI Publications Volume 62, 2014, 131-170. (Version June 2014).

38. (with C. Manolescu) Floer homology on the extended moduli space. Perspectives in analysis, geometry, and analysis. Progr. Math., 96, Birkhauser-Springer, New York 2012. (Version November 2010)

37. (with K. Wehrheim) Exact triangle for fibered Dehn twists. 81 pages. Res. Math. Sciences 3:17, 2016.

36. (with K. Wehrheim) Floer field theory for tangles. 40 pages. Under revision. (Version March 2016)

35. (with K. Wehrheim) Floer field theory for coprime rank and degree. 43 pages. To appear in Indiana Math. Jour. 2019. (Version July 2018)

34. (with E. Gonzalez) Gauged Gromov-Witten theory for small spheres. Math. Zeit. (2013) 273 pp 485--514. (Version March 2012).

33. (with E. Gonzalez) Quantum Witten localization and abelianization of qde solutions. 45 pages. (Version June 2016)

32. (with E. Gonzalez) Deformations of symplectic vortices 44 pages. Annals of Global Anal. and Geom. 39 (2011) 45--82. (Version August 2010)

31. (with S. Ma'u) Geometric realizations of the multiplihedron. 30 pages. Compositio Math 146 (2010). (Version March 2009)

30. (with K. Wehrheim) Orientations for pseudoholomorphic quilts. 69 pages. arxiv:1503.07803. Version January 2016.

29. (with K. Wehrheim) Functoriality for Floer theory in Lagrangian correspondences. 33 pages, 2.4M. Quantum Topology (2010). (Version May 2009. The original version of this paper was expanded and then broken into four parts, below.)

28. (with K. Wehrheim) Pseudoholomorphic quilts. Journal of Symplectic Geometry 13 (2015) 745-764. (Version January 2015)

27. (with K. Wehrheim) Floer Cohomology and Geometric Composition of Lagrangian Correspondences. 41 pages, 2.4M. Adv. Math. 230 (2012) 177-228. (Version May 2009)

26. (with K. Wehrheim) Quilted Floer cohomology. 43 pages, 2.4M. Geometry and Topology (2010). (Version May 2009) Corrigendum: Quilted Floer trajectories with constant components . Geometry & Topology 16 (2012) 127-154.

25. (with Y. Taylor) Spherical tetrahedra and invariants of 3-manifolds. . 18 pages. (Version June 2004). This manuscript was never published.

24. (with C. Teleman) The Index Formula on the Moduli of G-bundles. 25 pages, 568K. Annals Math. 170 (2009) 495-527. (Version August 2007)

23. Localization for the norm-square of the moment map and the two-dimensional Yang-Mills integral . 39 pages. Jour. Sympl. Geom. 3 (2005) 17-54. (Version December 2005)

22. (with A. Knutson and T. Tao) A positive proof of the Littlewood-Richardson rule using the octahedron recurrence . 16 pages, 309K. Electron. J. Combin. 11 (2004), Research Paper 61, 18 pp. (electronic). (Version June 2003)

21. (with Y. Taylor) 6j symbols for U_q(sl_2) and non-Euclidean tetrahedra . 34 pages, 941K. Selecta Math. (11) (2005) 539 - 571. The Maple code for generation of the graph in Figure 3 can be found here . An erratum . (Version January 2006)

20. The Yang-Mills heat flow on the moduli space of framed bundles on a surface . 52 pages, 572K. Amer. J. Math. (28) (2006) 311--359. (version January 2006)

19. On D. Peterson's comparison theorem for Gromov-Witten invariants . 10 pages, 196K. Proc. of the Amer. Math. Soc. 133 (2005) 1601-1609. (Version January 2005)

18. (with W. Fulton) On the quantum product of Schubert classes . 18 pages, 312K. J. Algebraic Geom. 13 (2004), no. 4, 641--661. (Version December 2001)

17. (with A. Knutson and T. Tao) The honeycomb model of GL(n) tensor products II: Facets of the Littlewood-Richardson cone, . 24 pages, 460K. J. Amer. Math. Soc. 17 (2004), no. 1, 19--48. (Version July 2002)

16. (with C. Teleman) Parabolic bundles, products of conjugacy classes, and quantum cohomology . 23 pages, 483K. Ann. Inst. Fourier (Grenoble) (53) (2003), 713--748. Offprint available. Erratum . (Version October 2002)

15. (with A. Alekseev and E. Meinrenken) Linearization of Poisson actions and singular values of matrix products . Ann. Inst. Four. (51) (2001) 1691--1717. (Version December 2000)

14. (with A. Alekseev and E. Meinrenken) Formulas of Verlinde type for non simply-connected groups . (Version May 2000) This manuscript was never published.

13. (with A. Alekseev and E. Meinrenken) A fixed point formula for loop group actions . Jour. of Symplectic Geometry 1, 1--46 (2001), (2), 427--434 (2001). (Version December 2001)

12. (with A. Alekseev and E. Meinrenken) Duistermaat-Heckman distributions for group-valued moment maps . Geom. funct. anal. 12 (2002) 1--31. (Version March 1999)

11. (with A. Canas and V. Guillemin) On the unfolding of folded symplectic structures . Math. Res. Lett. 7 (2000) 35--53. (Version October 1998)

10. (with E. Meinrenken) Canonical bundles for Hamiltonian loop group actions . Pacific J. Math. 198 (2001) 477--487. (Version May 2005).

9. (with A. Alekseev and E. Meinrenken) Group-valued equivariant localization . Invent. math. 140 (2000) 2, 327-350. (Version May 1999).

8. (with S. Agnihotri) Eigenvalue inequalities for products of unitary matrices and quantum Schubert calculus Math. Res. Lett. 5 (1998), 817--836. (Version August 1998) .

7. (with E. Meinrenken) Cobordism for Hamiltonian loop group actions and flat connections on the punctured two-sphere Math. Z. 231 (1999), 133--168. (Version August 1998)

6. (with E. Meinrenken) Moduli spaces of flat connections on 2-manifolds, cobordism, and Witten's volume formulas in Advances in geometry, 271--295, Progr. Math., 172, Birkhauser, Boston, Boston, MA. (Version August 1998).

5. (with E. Meinrenken) Hamiltonian loop group actions and Verlinde factorization. J. Differential Geom. 50 (1998), 417--469. (398k). (Version August 1998)

4. (With E. Lerman, E. Meinrenken, and S. Tolman) Non-abelian convexity by symplectic cuts. Topology 37 (1998). (Version August 1998)

3. Spherical varieties and existence of invariant Kaehler structure. Duke Math. Jour. 93 (1998) (Version August 1998)

2. Multiplicity-free Hamiltonian actions need not be Kaehler. Inventiones Math. 131 (1998). (Version August 1998)

1. The classification of transversal multiplicity-free group actions. Ann. Global Ann. Geom 14 (1996), 3--42. (Version August 1998)

All files are in Postscript format.

Back to my homepage .