In the spring semester I will be teaching 18.726 Algebraic
Geometry (html), the second semester of the
first year graduate algebraic geometry sequence.
Seminars:
BAGS -- The Baby Algebraic Geometry Seminar
(html)
Comments, corrections and
suggestions are always welcome.
Geometric positivity in the cohomology of homogeneous
spaces and generalized Schubert calculus (joint with Ravi Vakil) (pdf). Submitted to the Seattle
Proceedings.
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).
To appear in the Canadian Mathematical Bulletin.
The ample cone of the Kontsevich moduli space (joint with Joe
Harris and Jason Starr) (pdf).
To appear in the Canadian Journal of Mathematics.
Gromov-Witten invariants of jumping curves (pdf).
To appear in the Transactions of the American Mathematical Society.
A Littlewood-Richardson rule for two-step flag varieties Revised version (pdf). Submitted. NEW
Gallery (html).
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 Semesters:
Math 18.727--Topics in Algebraic Geometry: Positivity in Algebraic
Geometry (html)
Math 18.727--Topics in Algebraic Geometry: Intersection theory on
moduli spaces. Spring 2006 (html).