Justin Sawon

Department of Mathematics
University of North Carolina
Chapel Hill, NC 27599-3250
USA

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Office:
Hours:
Phone:
Fax:
Email:
Chapman 441
Wednesday 2-4pm
(919) 962 1294 (department)
(919) 962 2568
sawon -at- email -dot- unc -dot- edu


Workshop on New developments in moduli and Geometric Invariant Theory, UNC, 20th November to 22nd November 2015

Workshop on Moduli spaces, derived geometry, and geometric representation theory, UNC, 31st October to 2nd November 2014


Teaching:

Spring 2016:
Fall 2015:
Spring 2015:
Fall 2014:
 
Spring 2014:
 
Fall 2013:
Spring 2013:
Fall 2012:
 
Spring 2012:
 
Spring 2011:
Fall 2010:
Spring 2010:

MATH782 Differential Geometry
MATH231 Calculus of Functions of One Variable I (section 4)
MATH681 Introductory Topology
MATH548 Combinatorial Mathematics
MATH676 Modules, Linear Algebra, and Groups
MATH381 Discrete Mathematics (section 1)
MATH578 Algebraic Structures
MATH680 Geometry of Curves and Surfaces
MATH681 Introductory Topology
MATH233 Calculus of Functions of Several Variables (section 6)
MATH381 Discrete Mathematics (section 3)
MATH381 Discrete Mathematics
MATH578 Algebraic Structures
MATH782 Differential Geometry
MATH381 Discrete Mathematics
MATH681 Introductory Topology


Publications (click on titles for abstracts and to download):

  1. "Moduli spaces of sheaves on K3 surfaces", preprint arXiv:1603.00785.
  2. "A bound on the second Betti number of hyperkähler manifolds of complex dimension six", preprint arXiv:1511.09105.
  3. "Isotrivial elliptic K3 surfaces and Lagrangian fibrations", preprint arXiv:1406.1233.
  4. with Kelly McKinnie, Sho Tanimoto, and Anthony Várilly-Alvarado, "Brauer groups on K3 surfaces and arithmetic applications", preprint arXiv:1404.5460.
  5. with Rebecca Glover, "Generalized twistor spaces for hyperkähler manifolds", Journal of the London Mathematical Society (2) 91 (2015), no. 2, 321-342.
  6. "A finiteness theorem for Lagrangian fibrations", Journal of Algebraic Geometry, to appear.
  7. "Fourier-Mukai transforms, mirror symmetry, and generalized K3 surfaces", preprint arXiv:1209.3202.
  8. "On Lagrangian fibrations by Jacobians II", Communications in Contemporary Mathematics 17, 1450046 (2015).
  9. "Fibrations on four-folds with trivial canonical bundles", Geometriae Dedicata 171 (2014), 93-117.
  10. "On Lagrangian fibrations by Jacobians I", Journal für die reine und angewandte Mathematik (2013), DOI: 10.1515/crelle-2013-0023.
  11. "Foliations on hypersurfaces in holomorphic symplectic manifolds", International Mathematics Research Notices (2009), no. 23, 4496-4545.
  12. "Deformations of holomorphic Lagrangian fibrations", Proceedings of the AMS 137 (2009), no. 1, 279-285.
  13. "Twisted Fourier-Mukai transforms for holomorphic symplectic four-folds", Advances in Mathematics 218 (2008), no. 3, 828-864.
  14. "On the discriminant locus of a Lagrangian fibration", Mathematische Annalen 341 (2008), no. 1, 201-221.
  15. "Lagrangian fibrations on Hilbert schemes of points on K3 surfaces", Journal of Algebraic Geometry 16 (2007), no. 3, 477-497.
  16. "Perturbative expansion of Chern-Simons theory", Geometry and Topology Monographs, Vol. 8 (2006), The interaction of finite-type and Gromov-Witten invariants (Banff 2003), 145-166.
  17. "Derived equivalence of holomorphic symplectic manifolds", in Algebraic Structures and Moduli Spaces: CRM Workshop, Montreal 14-20 July 2003, CRM Proceedings & Lecture Notes Series, Volume 38 (2004), 193-211.
  18. "Abelian fibred holomorphic symplectic manifolds", Turkish Journal of Mathematics 27 (2003), No. 1, 197-230. (Proceedings of the Ninth Gokova Geometry-Topology Conference, Turkey, 27th to 31st May 2002.)
  19. with Justin Roberts, "Generalizations of Rozansky-Witten invariants", Geometry and Topology Monographs, Vol. 4 (2002), Invariants of knots and 3-manifolds (Kyoto 2001), 263-279.
  20. with Michael Eastwood, "The Borel-Weil theorem for complex projective space", in Invitations to Geometry and Topology, Oxford Graduate Texts in Mathematics, OUP (2002), 126-145.
  21. "Topological quantum field theory and hyperkähler geometry", Turkish Journal of Mathematics 25 (2001), No. 1, 169-194. (Proceedings of the Seventh Gokova Geometry-Topology Conference, Turkey, 29th May to 3rd June 2000.)
  22. "A new weight system on chord diagrams via hyperkähler geometry", Proceedings of the Second Meeting on Quaternionic Structures in Mathematics and Physics, Rome 6-10 September 1999, World Scientific (2001), 349-363.
  23. with Nigel Hitchin, "Curvature and characteristic numbers of hyperkähler manifolds", Duke Mathematical Journal 106 (2001), no. 3, 599-615.
  24. "When is a Lie algebra not a Lie algebra?", Proceedings of the IXth Oporto Meeting on Geometry, Topology and Physics, September 29th to October 2nd, 2000, 1-16.
  25. "The Rozansky-Witten invariants of hyperkähler manifolds", Proceedings of the 7th International Conference on Differential Geometry and Applications, Satellite Conference of ICM in Berlin, Aug. 10-14, 1998, Brno, Czech Republic (1999), 429-436.
  26. "Homomorphisms of semiholonomic Verma modules: an exceptional case", Acta Mathematica Universitatis Comenianae 68 (1999), no. 2, 257-269.

Dissertations:

Unpublished:

Other:


To the University of North Carolina Mathematics Department front page.

To Sawon Enterprise Company.


Past teaching:

Fall 2009:
 
Spring 2009:
Fall 2008:
Spring 2008:
Fall 2007:
 
Spring 2007:
Fall 2006:
 
Spring 2006:
Fall 2005:
Fall 2004:
 
Spring 2004:
Fall 2003:
 
Spring 2003:
 
Fall 2002:

MATH369 Linear Algebra (section 3)
MATH676 (section 1) Topics in Riemannian Geometry
MATH670 Introduction to Differentiable Manifolds
MATH161 Calculus II (sections 4, 5, 7)
MATH567 Abstract Algebra II
MATH495 (section 1) GRE Preparation
MATH566 Abstract Algebra I
M369 Linear Algebra (section 3)
M369 Linear Algebra (section 1)
M400D Topology
MAT 542 Complex Analysis I
MAT 125 Calculus A (LEC1, ELC5)
MAT 260 Problem Solving in Mathematics (plus Putnam competition information)
MAT 590 Problem Seminar
MAT 645 Topics in Differential Geometry (Hyperkähler manifolds)
MAT 123 Intro to Calculus
MAT 590 Problem Seminar
MAT 305 Calculus IV
MAT 569 Differential Geometry II
MAT 566 Differential Topology

Colorado State:
Math Club
The William Lowell Putnam Mathematical Competition
Western Algebraic Geometry Seminar, Fall '07

Stony Brook:
Geometry and Topology Seminar
Mathematical Physics Learning Seminar