Algebraic Geometry Seminar Fall 2010
The seminar meets on Fridays at 2:25 pm in Van Vleck B305.
|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|
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.