Sept 13   3:00 pm P-131	Sorin Popescu, SUNY at Stony Brook. Equations of modular curves Modular curves are compactifications of quotients of the upper half space by arithmetic subgroups acting via Moebius transformations. Several of their natural embeddings have been extensively studied starting perhaps with Felix Klein. I will survey some of the related beautiful algebraic geometry and discuss new results (joint with L. Borisov and P. Gunnells) concerning a natural embedding of the modular curve $X_1(p)$.
Sept 20   3:00 pm P-131	Calin-Iuliu Lazaroiu, ITP, SUNY. Mirror symmetry and string field theory I discuss the physical origins of the homological mirror symmetry conjecture and how one can extract a generalization of this conjecture from string theory considerations
Sept 27   3:00 pm P-131	Calin-Iuliu Lazaroiu, ITP, SUNY. Mirror symmetry and string field theory, II
Oct 4   3:00 pm P-131	Blaine Lawson, SUNY at Stony Brook. The de Rham-Federer Theory of Differential Characters
Oct 11   3:00 pm P-131	Blaine Lawson, SUNY at Stony Brook. The de Rham-Federer Theory of Differential Characters, II
Oct 18   3:00 pm P-131	Blaine Lawson, SUNY at Stony Brook. The de Rham-Federer Theory of Differential Characters, III
Oct 25   3:00 pm P-131	A. Moroianu, SUNY at Stony Brook. Spin Geometry and Contact Manifolds The aim of this talk is to outline some results obtained in contact geometry by means of spinorial methods and in particular to exhibit relations between (complex) contact structures and (K{\"a}hlerian) Killing spinors.
Nov 3   1:00 pm 5-127	Martin Rocek, SUNY, ITP. Twistors and hyperkahler quotients (PLEASE NOTE: TIME, DAY, AND PLACE ARE DIFFERENT THAN USUAL)
Nov 6   2:30 pm P-131	Dan Abramovich, Boston University. Factorization of birational maps PLEASE NOTE DIFFERENT DAY AND TIME FROM USUAL
Nov 15   3:00 pm P-131	Lev Borisov, Columbia University. Toric varieties and modular forms Toric varieties are special algebraic varieties defined by some combinatorial data. It turns out that these data also define certain modular forms on the upper half plane, which we call toric forms. Linear span of toric forms has non-trivial number-theoretic properties, related to the conjecture of Birch and Swinnerton-Dyer.
Nov 17   12:30 pm 5-127	Martin Rocek, SUNY, ITP. Twistors and hyperkahler quotients, II
Nov 20   3:00 pm P-131	Robert Friedman, Columbia University. Exceptional groups and del Pezzo surfaces It has long been known that there is a deep connection between del Pezzo surfaces of degrees $3$, $2$, $1$ and the exceptional groups $E_6$, $E_7$, $E_8$. This talk describes an explicit link between the surfaces and the groups: given a smooth del Pezzo surface $X$, there is a tautological holomorphic principal $G$-bundle over $X$, where $G$ is an appropriate conformal form of the group $E_r$. There is a generalization of this construction to the case where $X$ is allowed to have rational double points. Finally, restricting to hyperplane sections gives a concrete model for the moduli space of all holomorphic semistable $E_r$-bundles over a smooth elliptic curve.
Nov 29   3:00 pm	No Meeting This Week.
Dec 8   2:00 pm 5-127	Takashi Kimura, Boston University. Cohomological Field Theories and Intersection Theory We will explain the construction of intersection theoretic realizations of cohomological field theories, an axiomatization (by Kontsevich-Manin) of the expected factorization properties of correlators in physical models of topological gravity. The relevant moduli spaces are compactifications of moduli spaces of decorated Riemann surfaces. We will discuss the relationship between such theories and their connections with integrable systems.
Dec 13   3:00 pm P-131	Ravi Vakil, MIT. Branched covers of the projective line and the Chow ring of the moduli space of curves Branched covers of the sphere have recently proved a powerful tool in understanding the Chow ring of the moduli space of pointed curves. I will briefly describe the moduli space and its cohomlogy, Chow, and tautological rings. I will then define Hurwitz numbers (counting branched covers of the sphere, and describe their links to Gromov-Witten theory, and the connection discovered by Ekedahl et al. to the tautological ring. I'll give several consequences, including a verfication of predictions of a remarkable question/conjecture of Hain/Looijenga/Faber/Pandharipande that the tautological ring ``should be a combinatorial object''. (This is joint work with T. Graber.)