Andrei Caldararu Department of Mathematics  University of Wisconsin, Madison  480 Lincoln Dr Madison WI 53706-1388   email: andreic@math.wisc.edu  Office: van Vleck 605 Phone: (608) 262-2880 Fax: (608) 263-8891

Teaching:

Fall 2008	MATH 275 Topics in Calculus, I
Spring 2008	MATH 234 Calculus - Functions of Several Variables	MATH 542 Abstract Algebra
Fall 2007	MATH 763 Introduction to Algebraic Geometry
Fall 2006	MATH 234 Calculus - Functions of Several Variables	MATH 541 Abstract Algebra
Fall 2005	MATH 114 Algebra and Trigonometry	MATH 750 Homological Algebra
Spring 2005 (at UPenn)	MATH 240 Calculus, part III	MATH 725 Topics in Algebraic Geometry

Ph.D. Thesis:

• Derived Categories of Twisted Sheaves on Calabi-Yau Manifolds
  Ph.D. Thesis, Cornell University, May 2000

Elliptic Fibrations:

• 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

K3 surfaces:

• Non-fine moduli spaces of sheaves on K3 surfaces
  Internat. Math. Res. Notices 2002 (2002), no. 20, 1027-1056

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) Preprint, arXiv:0707.2052, submitted to Invent. Math.
• 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  Preprint, math.AG/0308079, superseded by the paper above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, 34-66

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) Preprint, arXiv:0709.3855

General Expository:

• Derived categories of sheaves: a skimming
  Snowbird lectures in algebraic geometry, 43-75, Contemp. Math., 388, Amer. Math. Soc., Providence, RI, 2005

Non-birational derived equivalences:

• 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) To appear in J. Alg. Geom.

Invited lectures:

• Western Algebraic Geometry Seminar (WAGS 2007), Fort Collins, Colorado, October 20-21, 2007
• Hochschild Cohomology of Algebras: Structure and Applications, BIRS, Banff, Canada, September 2-7, 2007
• Non-linear Integral Transforms: Fourier and Nahm, CRM, Montréal, Canada, August 27-31, 2007
• Derived Categories in Mathematics and Physics, AMS Summer Research Conference, Snowbird, UT, June 16-21, 2007
• Homological Mirror Symmetry and Applications, Institute for Advanced Studies, Princeton, NJ, January 22-26, 2007
• Workshop on Algebraic Geometry and Physics 2006: Gerbes, Groupoids, and Quantum Field Theory, ESI, Vienna, May 9-13, 2006
• Generalized McKay Correspondences and Representation Theory, MSRI, Berkeley, California, March 20-24, 2006
• Thick Subcategories - Classifications and Applications, Mathematisches Forschungsinstitut Oberwolfach, Germany, February 19-25, 2006
• Progress in algebraic geometry inspired by physics, BIRS, Banff, Canada, October 8-13, 2005
• Summer Institute in Algebraic Geometry, Seattle, Washington, July 25-29, 2005
• Algebraic Geometry and Categories, (a conference for André Hirschowitz' 60th birthday), Nice, France, June 6-10, 2005
• Algebraic Geometry and Derived Categories, 27th Autumn School in Algebraic Geometry, Lukecin, Poland, September 19-25, 2004
• EAGER 2003, Aussois, France, September 6-11, 2003
• Workshop on algebraic structures and moduli spaces, CRM Montréal, Canada, July 14-20, 2003
• Euroconference VBAC 2003, Porto, Portugal, July 1-5, 2003
• Workshop and Conference SWAGP 2003, Salamanca, Spain, June 18-27, 2003
• Higher Dimensional Geometry Programme at the Newton Institute, Cambridge, UK, February-July, 2002
• Workshop on Algebraic Geometry and Physics (WAGP) 2002, Genova, Italy, June 18-21, 2002
• Summer school on symplectic geometry, Nordfjordeid, Norway, June 11-15, 2001
• 2001 EAGER conference, Nordfjordeid, June 16-22, 2001
• Workshop on Vector Bundles on Algebraic Curves, Roma, Italy, September 11-15, 2001
• Conference on Hilbert Schemes, Vector Bundles and their Interplay with Representation Theory, Columbia, Missouri, April 5-7, 2002
• Higher Dimensional Complex Geometry, Newton Institute, Cambridge, UK, June 24-28, 2002
• K-Theory, Derived Categories and Strings, 2002 Workshop on Algebraic Geometry and Physics, Genova, Italy, June 18-21, 2002