![]() |
Andrei Căldăraru
|
Research: Algebraic geometry, homological algebra, string theory Teaching:
Publications: All the papers below are also available from the Mathematics ArXiv. Recent papers:
- Categorical primitive forms and Gromov-Witten invariants of An singularities
(with Si Li and Junwu Tu), submitted, arXiv:1810.05179- Computing a categorical Gromov-Witten invariant
(with Junwu Tu), submitted, also arXiv:1706.09912 (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, to appear, also arXiv:1412.5233- 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), 64-79Hochschild 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
Preprint, math.AG/0308079, superseded by the paper above- The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism
Adv. in Math. 194 (2005), no. 1, 34-66Non-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), to appear, J. reine angew. Math. (Crelle), also arXiv:1707.00534- 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, 201-222Elliptic 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, 1027-1056Physics 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, 605-645Ph.D. thesis:
- Derived categories of twisted sheaves on Calabi-Yau manifolds
Ph.D. Thesis, Cornell University, May 2000General expository:
- Derived categories of sheaves: a skimming
Snowbird lectures in algebraic geometry, 43-75, Contemp. Math., 388, Amer. Math. Soc., Providence, RI, 2005