Andrei Căldăraru

Research: Algebraic geometry, homological algebra, string theory Teaching:
Publications: All the papers below are also available from the Mathematics ArXiv. Recent preprints:
 Intersections of two Grassmannians in P^{9}
(with Lev Borisov and Alex Perry), submitted, also arXiv:1707.00534 Computing a categorical GromovWitten invariant
(with Junwu Tu), submitted, also arXiv:1706.09912 Formality of derived intersections and the orbifold HKR isomorphism
(with Dima Arinkin and Marton Hablicsek), submitted, also arXiv:1412.5233Video:
 Video of a talk I gave at IAS about the paper "Computing a categorical GromovWitten invariant" above.
Derived algebraic geometry and interactions with Lie theory:
 Derived intersections and the Hodge theorem
(with Dima Arinkin and Marton Hablicsek), Algebraic Geometry 4 (2017), 394423 On the Lie algebroid of a derived selfintersection
(with Damien Calaque and Junwu Tu) Adv. Math. 262 (2014), 751783 When is the selfintersection of a subvariety a fibration?
(with Dima Arinkin) Adv. Math. 231 (2012), no. 2, 815842 Curved Ainfinity algebras and LandauGinzburg models
(with Junwu Tu) New York J. Math. 19 (2013), 305342 PBW for an inclusion of Lie algebras
(with Damien Calaque and Junwu Tu) J. Algebra 378 (2013), 6479Hochschild homology and cohomology:
 Algebraic deformations arising from orbifolds with discrete torsion
(with Anthony Giaquinto and Sarah Witherspoon) J. Pure Appl. Algebra 187 (2004), no. 13, 5170. The Mukai pairing, I: a categorical approach
(with Simon Willerton) New York J. Math. 16 (2010), 6198 The Mukai pairing, I: the Hochschild structure
Preprint, math.AG/0308079, superseded by the paper above The Mukai pairing, II: the HochschildKostantRosenberg isomorphism
Adv. in Math. 194 (2005), no. 1, 3466Nonbirational derived equivalences:
 Nonbirational CalabiYau threefolds that are derived equivalent
Internat. J. Math. 18 (2007), no. 5, 491504 The PfaffianGrassmannian derived equivalence
(with Lev Borisov) J. Algebraic Geom. 18 (2009), no. 2, 201222Elliptic fibrations, K3 surfaces, and twisted sheaves:
 Derived categories of twisted sheaves on elliptic threefolds
J. reine angew. Math. 544 (2002), 161179 Fiberwise stable bundles on elliptic fibrations with relative Picard number one
CR Acad. Sci. Paris Ser. I 334 (2002), no. 6, 469472 Nonfine moduli spaces of sheaves on K3 surfaces
Internat. Math. Res. Notices 2002 (2002), no. 20, 10271056Physics and string theory:
 Dbranes, Bfields and Ext groups
(with Sheldon Katz and Eric Sharpe) Adv. Theor. Math. Phys. 7 (2003), no. 3, 381404. Nonbirational twisted derived equivalences in abelian GLSMs
(with Jacques Distler, Simeon Hellerman, Tony Pantev and Eric Sharpe) Comm. Math. Phys. 294 (2010), no. 3, 605645Ph.D. thesis:
 Derived categories of twisted sheaves on CalabiYau manifolds
Ph.D. Thesis, Cornell University, May 2000General expository:
 Derived categories of sheaves: a skimming
Snowbird lectures in algebraic geometry, 4375, Contemp. Math., 388, Amer. Math. Soc., Providence, RI, 2005