Great Lakes Geometry Conference Schedule - University of Notre Dame

Great Lakes Geometry Conference Schedule All talks will be held in Hayes-Healy 127
Saturday, April 17, 2004
9:00-9:45 am	Registration, Coffee and Bagels
9:45-10:00 am	Opening remarks and organizational details.
10:00-11:00 am	Speaker: Huai-Dong Cao - Title: "Ricci flow on Kähler Manifolds" Abstract: In this talk, I will first review the preliminaries of the Ricci flow on compact Kaehler manifolds and then report some recent developments on the subject, in particular applications of Perelman's entropy functionals and local injectivity radius estimates.
11:30-12:30 noon	Speaker: Alexander Varchenko - Title: "Critical Points of Functions, Lie Algebra Representations, and Fuchsian Differential Equations" Abstract: The master function is a function associated to a simple Lie algebra and a collection of its finite dimensional representations. Master functions play an essential role in the theory of KZ equations, multidimensional hypergeometric functions, and the Bethe ansatz method. The applications of master functions suggest that the number of critical points of master functions and the types of critical points are dictated by representation theory of the Lie algebra. The talk is an introduction to this area of problems.
12:30-2:30 pm	Lunch Break
2:30-3:30 pm	Speaker: Yong-Geun-Oh - Title: "Group of Hamiltonian homeomorphisms and C⁰-symplectic topology'' Abstract: In this talk, I will provide a precise definition of the group of Hamiltonian homeomorphisms which will set the stage of C⁰ Hamiltonian dynamical systems and C⁰ symplectic topology. Then I will explain how to extend various known symplectic invariants, (e.g., displacement energy and spectral invariants) to their C⁰ counterparts. If time permits, I will discuss several foundational open problems related to the group of Hamiltonian homeomorphisms.
4:00-5:00 pm	Speaker: Benson Farb - Tile: "Hidden Symmetry" Abstract: In this talk I will report on joint work with Shmuel Weinberger, addressing the question: which metrics on a Riemannian manifold have the most symmetry? Our main theorem is essentially a classification (up to finite index subgroups) of the isometry groups of the universal cover of every closed Riemannian manifold. I will try to explain this theorem and some of its corollaries. These include: new characterizations of locally symmetric (and also of arithmetic) manifolds among all closed Riemannian manifolds; a classification of 1-connected, aspherical manifolds which cover both a compact and a (noncompact) finite volume manifold; and verification of the Hopf Conjecture for manifolds with nontrivial hidden symmetry.
6:00-8:30 pm	Dinner Banquet, Gold Room North Dining Hall
Sunday, April 18, 2004
9:00-9:45 am	Coffee Time
9:45-10:45 am	Speaker: Emanuel Diaconescu - Title: "Extremal Transitions and Gromov-Witten Invariants" Abstract: Large N duality in string theory predicts a surprising relation between Gromov-Witten invariants and Chern-Simons theory. This talk explores the mathematical aspects of this correspondence from the point of view of localization on moduli spaces of maps.
11:00-12:00 noon	Speaker: Denis Auroux - Title: "Homological mirror symmetry for Fano surfaces." Abstract: The mirror of a Fano variety M is not a manifold in the usual sense, but rather a "Landau-Ginzburg model", i.e. a non-compact manifold X equipped with a complex-valued function w (the "superpotential"). In this context, the homological mirror symmetry conjecture predicts that the derived category of coherent sheaves over M is equivalent to a derived category of Lagrangian vanishing cycles associated to the critical points of the superpotential w on its mirror. In the special case where the critical points of w are non-degenerate, the existence of a rigorous definition due to Seidel makes it possible to test the homological mirror symmetry conjecture on various examples by determining both categories explicitly. In this talk, based on joint work with L. Katzarkov and D. Orlov, we will first review the necessary background, and then focus on a specific family of examples: weighted projective planes. We will show that the homological mirror conjecture holds in this case. Moreover, non-exact deformations of the symplectic structure on the Landau Ginzburg model correspond to non-commutative deformations of the weighted projective plane.