Reading seminar in algebraic geometry: The Hitchin system, character varieties, and related topics.
Spring 2015.

The seminar will meet on Mondays, 3:00PM-4:00PM in LGRT 206.




Schedule

1/23. Organizational meeting, 4:30PM, LGRT 1634.

2/2. Snow day.

2/9. Snow day.

2/17. Paul Hacking. Stable bundles and integrable systems. 3:00PM, LGRT 206.
Note that we are meeting on Tuesday (= UMass Monday) due to Presidents' day.

2/23. Eyal Markman. Meromorphic Higgs pairs. 3:00PM, LGRT 206.

3/2. Alexei Oblomkov. The Hitchin system for the projective line. 3:00PM, LGRT 206.

3/9. Tassos Vogiannou. Character varieties. 3:00PM, LGRT 206.

3/16. No meeting (Spring break).

3/23. Jenia Tevelev. Geodesic flow on an ellipsoid. 3:00PM, LGRT 206.

3/30. Kien Nguyen. Geodesic flow on an ellipsoid. II. 3:00PM, LGRT 206.

4/6. Franz Pedit. Harmonic maps, spectral curves and completely integrable systems. 3:00PM, LGRT 206.

4/13. Huy Le. 3:00PM, LGRT 206.

4/20. No meeting (Patriots' day).

4/27. Franz Pedit. Harmonic maps, spectral curves and completely integrable systems. II. 3:00PM, LGRT 206.




References

N. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), no. 1, 59--126.

N. Hitchin, Stable bundles and integrable systems, Duke Math. J. 54 (1987), no. 1, 91--114.

N. Hitchin, Harmonic maps from a 2-torus to the 3-sphere, J. Differential Geom. 31 (1990), no. 3, 627--710.

C. Simpson, Harmonic bundles on noncompact curves, J. Amer. Math. Soc. 3 (1990), no. 3, 713--770.

R. Donagi, E. Markman, Spectral covers, algebraically completely integrable, Hamiltonian systems, and moduli of bundles, in Integrable systems and quantum groups (Montecatini Terme, 1993), 1--119, Lecture Notes in Math. 1620, Springer, 1996. arxiv.





Links to the seminar from previous semesters.

Holomorphic symplectic varieties and Hyperkahler manifolds, Fall 2014
Syzygies, Spring 2014
Toric varieties, Fall 2013
Derived categories in algebraic geometry, Spring 2013
Deformation theory, Fall 2012
Curves, K3 surfaces, and Fano 3-folds, Spring 2012
Topics in algebraic geometry, Fall 2011
Surfaces of general type, Spring 2011
Algebraic surfaces, Fall 2010.
Stability conditions on derived categories and wall crossing, Spring 2010
Mirror symmetry and tropical geometry, Fall 2009
Deformation theory, Fall 2008
Green's Conjectures, Spring 2008
Bridgeland Stability, Fall 2007.
Minimal Model Program, Spring 2007
Commutative Algebra and Polyhedra Seminar, Spring 2006.
Geometry and Algebra of Polyhedra Seminar, Fall 2005.
Commutative Algebra Seminar, 2004-2005



The page is maintained by Paul Hacking