Research: Algebraic geometry, homological algebra, string theory Teaching:
All the papers below are also available from the Mathematics ArXiv.
- The cup product in orbifold Hochschild cohomology
(with Shengyuan Huang), arXiv:2101.06276.
- Categorical Enumerative Invariants, I: String vertices
(with Kevin Costello and Junwu Tu), arXiv:2009.06673, submitted.
- Categorical Enumerative Invariants, II: Givental formula
(with Junwu Tu), arXiv:2009.06659, submitted (see series of 5 talks about the above two papers).
Categorical enumerative invariants:
- Categorical primitive forms and Gromov-Witten invariants of An singularities
(with Si Li and Junwu Tu), International Mathematics Research Notices, rnz315, https://doi.org/10.1093/imrn/rnz315
- Computing a categorical Gromov-Witten invariant
(with Junwu Tu), Compos. Math. 156 (2020), no. 7, 1275-1309 (see video of talk about this paper).
Derived algebraic geometry and interactions with Lie theory:
- Formality of derived intersections and the orbifold HKR isomorphism
(with Dima Arinkin and Marton Hablicsek), J. Algebra 540 (2019), pp. 100-120, issn: 0021-8693, doi:10.1016/j.jalgebra.2019.08.002.
- Derived intersections and the Hodge theorem
(with Dima Arinkin and Marton Hablicsek), Algebraic Geometry 4 (2017), 394-423
- On the Lie algebroid of a derived self-intersection
(with Damien Calaque and Junwu Tu) Adv. Math. 262 (2014), 751--783
- When is the self-intersection of a subvariety a fibration?
(with Dima Arinkin) Adv. Math. 231 (2012), no. 2, 815--842
- Curved A-infinity algebras and Landau-Ginzburg models
(with Junwu Tu) New York J. Math. 19 (2013), 305-342
- PBW for an inclusion of Lie algebras
(with Damien Calaque and Junwu Tu) J. Algebra 378 (2013), 64-79
Hochschild homology and cohomology:
- Algebraic deformations arising from orbifolds with discrete torsion
(with Anthony Giaquinto and Sarah Witherspoon) J. Pure Appl. Algebra 187 (2004), no. 1-3, 51--70.
- The Mukai pairing, I: a categorical approach
(with Simon Willerton) New York J. Math. 16 (2010), 61-98
- The Mukai pairing, I: the Hochschild structure
math.AG/0308079, superseded by the paper above
- The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism
Adv. in Math. 194 (2005), no. 1, 34-66
Non-birational derived equivalences:
- GLSM realizations of maps and intersections of Grassmannians and Pfaffians
(with Johanna Knapp and Eric Sharpe), J. High Energ. Phys. (2018) 2018: 119, also arXiv:1711.00047
- Intersections of two Grassmannians in P9
(with Lev Borisov and Alex Perry), J. reine angew. Math. (Crelle), 760 (2020), 133-162
- Non-birational Calabi-Yau threefolds that are derived equivalent
Internat. J. Math. 18 (2007), no. 5, 491-504
- The Pfaffian-Grassmannian derived equivalence
(with Lev Borisov) J. Algebraic Geom. 18 (2009), no. 2, 201-222
Elliptic fibrations, K3 surfaces, and twisted sheaves:
- Derived categories of twisted sheaves on elliptic threefolds
J. reine angew. Math. 544 (2002), 161-179
- Fiberwise stable bundles on elliptic fibrations with relative Picard number one
CR Acad. Sci. Paris Ser. I 334 (2002), no. 6, 469-472
- Non-fine moduli spaces of sheaves on K3 surfaces
Internat. Math. Res. Notices 2002 (2002), no. 20, 1027-1056
Physics and string theory:
- D-branes, B-fields and Ext groups
(with Sheldon Katz and Eric Sharpe) Adv. Theor. Math. Phys. 7 (2003), no. 3, 381-404.
- Non-birational twisted derived equivalences in abelian GLSMs
(with Jacques Distler, Simeon Hellerman, Tony Pantev and Eric Sharpe) Comm. Math. Phys. 294 (2010), no. 3, 605-645
- Derived categories of twisted sheaves on Calabi-Yau manifolds
Ph.D. Thesis, Cornell University, May 2000
- Derived categories of sheaves: a skimming
Snowbird lectures in algebraic geometry, 43-75, Contemp. Math., 388, Amer. Math. Soc., Providence, RI, 2005