Andrei Căldăraru

Research: Algebraic geometry, homological algebra, string theory Teaching:
Publications: All the papers below are also available from the Mathematics ArXiv. Recent papers:
 Effective categorical enumerative invariants
(with Junwu Tu), arXiv:2404.01499, supersedes the two papers CEI I, II below. Moonshine at LandauGinzburg points
(with Yunfan He and Shengyuan Huang), to appear in Proc. AMS, arXiv:2107.12405. The cup product in orbifold Hochschild cohomology
(with Shengyuan Huang), under revision, Adv. Math., arXiv:2101.06276.Categorical enumerative invariants:
 Categorical enumerative invariants, I: String vertices
(with Kevin Costello and Junwu Tu), arXiv:2009.06673, superseded by the Effective CEI paper above. Categorical enumerative invariants, II: Givental formula
(with Junwu Tu), arXiv:2009.06659, superseded by the Effective CEI paper above.
(see series of 5 talks about the above two papers) Categorical primitive forms and GromovWitten invariants of A_{n} singularities
(with Si Li and Junwu Tu), International Mathematics Research Notices, rnz315, https://doi.org/10.1093/imrn/rnz315 Computing a categorical GromovWitten invariant
(with Junwu Tu), Compos. Math. 156 (2020), no. 7, 12751309 (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. 100120, issn: 00218693, doi:10.1016/j.jalgebra.2019.08.002. 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
math.AG/0308079, superseded by the paper above The Mukai pairing, II: the HochschildKostantRosenberg isomorphism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:
 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 P^{9}
(with Lev Borisov and Alex Perry), J. reine angew. Math. (Crelle), 760 (2020), 133162 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