MRC CONFERENCE on BIRATIONAL GEOMETRY AND MODULI SPACES will take place in Snowbird, Utah June 12-18, 2010. For more information see the conference webpage(BIRATIONAL)
Teaching:
In Fall 2008 I will be teaching
Math 417 Complex Analysis with applications and Math 552 Introduction to Algebraic Geometry. You can find the course materials for Complex Analysis here (math417). You can find the course materials for Algebraic Geometry here (math552).
Seminars:
The UIC Algebraic Geometry Seminar Fall 2008
(AGS)
The UIC Graduate Student Algebraic
Geometry Seminar (GradAGS)
Comments, corrections and
suggestions are always welcome.
Towards Mori's program for the moduli space of stable maps (joint with Dawei Chen, with an appendix by Charley Crissman) (pdf). Submitted. Any comments, corrections and suggestions very welcome.
Stable base locus decompositions of Kontsevich moduli spaces (joint with Dawei Chen) (pdf). Submitted. Any comments, corrections and suggestions very welcome.
Rational curves on smooth cubic hypersurfaces (joint with Jason Starr) (pdf). To appear in Int. Math. Res. Not. as article RNP102.
Restriction varieties. (pdf). A revised version. Submitted. Any comments, corrections and suggestions very welcome.
The quantum cohomology of flag varieties and the periodicity of the Schubert structure constants. (pdf) Submitted. Any comments, corrections, suggestions are welcome.
A Littlewood-Richardson rule for partial flag varieties. (pdf). Currently under revision. This is a preliminary version of a Littlewood-Richardson rule for arbitrary partial flag varieties. Any comments, corrections and suggestions are welcome. GALLERY (html)
A Littlewood-Richardson rule for two-step flag varieties (pdf). For examples see Gallery (html). Old version is available here: (pdf).
Inventiones Mathematicae volume 176, no 2 (2009) p. 325--395 DOI: 10.1007/s00222-008-0165-3
Geometric positivity in the cohomology of homogeneous
spaces and generalized Schubert calculus (joint with Ravi Vakil) (pdf). Algebraic Geometry, Seattle 2005 volume 1, p. 77--124.
The cohomology of the space of k-planes on
quadrics. Coming soon
Divisors on the space of maps to Grassmannians (joint with
Jason Starr). (pdf). International Mathematics Research Notices, vol. 2006, Article ID 35273, 25 pages, 2006.
The effective cone of the Kontsevich moduli space (joint
with Joe Harris and Jason Starr). (pdf). Canadian Mathematical Bulletin. vol. 51 no. 4 (2008), pages 519-534.
The ample cone of the Kontsevich moduli space (joint with Joe
Harris and Jason Starr) (pdf).
Canadian Journal of Mathematics. vol. 61 no. 1 (2009), pages 109-123.
Gromov-Witten invariants of jumping curves (pdf). Transactions of the American Mathematical Society. 360 (2008), p. 989-1004.
Degenerations of surface scrolls and Gromov-Witten invariants of
Grassmannians (pdf).
Journal of Algebraic Geometry. 15 (2006), p. 223-284.
The enumerative geometry of Del Pezzo surfaces via degenerations
(pdf). American
Journal of Mathematics. vol. 128 no. 3 (2006), p. 751-786.
The arithmetic and the geometry of Kobayashi hyperbolicity (pdf). Snowbird lectures in algebraic geometry. Contemporary Mathematics, vol 388 (2005) p. 77-88.
A first glimpse at the minimal model program (pdf). (with 8 coauthors) Snowbird lectures in algebraic geometry. Contemporary
Mathematics, vol 388 (2005) p. 17-42.
Degenerations of scrolls and Del Pezzo surfaces and applications
to enumerative geometry, Thesis, Harvard University, 2004.
Past Conferences:
The Modern Moduli Theory Workshop, February 23-27, 2009 (MODULI)
A Conference to celebrate Robin Hartshorne's 70th birthday, April 11-13 2008
(HARTSHORNE)
