Algebraic Geometry Seminar Fall 2010

The seminar meets on Fridays at 2:25 pm in Van Vleck B305.

Fall 2010

date	speaker	title	host(s)
sept 24	Xinyi Yuan (Harvard)	Calabi-Yau theorem and algebraic dynamics	Tonghai
oct 1	Dawei Chen (UIC)	Geometry of Teichmuller curves	Andrei
oct 22	Zhiwei Yun (Berkeley)	Springer representation and Hitchin fibration	Shamgar
oct 29	Christian Schnell (UIC)	TBA	Laurentiu
nov 5	Daniel Erman (Berkeley)	TBA	Jordan
nov 19	Alina Marian (UIC)	TBA	Andrei
dec 10	Izzet Coskun (UIC)	TBA	Andrei

Abstracts

Xinyi Yuan Calabi-Yau theorem and algebraic dynamics

The uniqueness part of the Calabi-Yau theorem asserts that the Monge-Ampere measure of a (complex) positive hermitian line bundles determines the hermitian metric up to constant. Here we introduce a p-adic analogue of the theorem. Combinning with the equidistribution theory, we obtain the rigidity of preperiodic points on algebraic dynamical systems.

Dawei Chen Geometry of Teichmuller curves

We study Teichmuller curves parameterizing square-tiled surfaces (i.e. covers of elliptic curves with a unique branch point).

The results can be applied to the following problems in algebraic geometry and complex dynamics: (a) construct rigid curves on the moduli space of pointed rational curves; (b) bound the effective cone of the moduli space of genus g curves; (c) verify the invariance of Siegel-Veech constants; (d) calculate the Lyapunov exponents of the Hodge bundle.

Zhiwei Yun Springer representation and Hitchin fibration

Classical Springer representation is the action of the Weyl group on the cohomology of certain subvarieties of the flag variety. I will construct a global analogue of this action, namely, an action of the graded double affine Hecke algebra on the cohomology of parabolic Hitchin fibers. Examples in SL(2) will be described in details. This construction is motivated by Ngo's proof of the fundamental lemma, and has applications to the harmonic analysis on p-adic groups.