Title    name   Differential Geometry Seminar Algebraic QFT and Quantum Homotopy Invariants Park, Jaesuk (Yonsei University) 2011-04-15   In this talk, I will introduce the notions of QFT algebra and corresponding Quantum Homotopy Invariants. It will be a quantun version of the first talk.   Differential Geometry Seminar Introduction to Quantum singularity theory II Fan Huijun (Beijing University) 2011-04-07   In this talk, I will explain how to construct the quantum invariants for classical singularity theory via constructing the virtual cycle on moduli spaces of W-curves. Those invariants are closely related to the study of mirror symmetry and integrable hierarchy.   Differential Geometry Seminar Cohomology ring and quantum cohomology of Hilbert schemes Wei-Ping Li (Hong Kong University of Science and Technology) 2010-12-10   Hilbert schemes of points on surfaces are the crepant resolutions of the symmetric products of surfaces. It can be studied via the orbifold theory or as moduli spaces of stable sheaves on surfaces. I will give a brief review of the study of the cohomology ring of the Hilbert schemes of points on surfaces by the method of vertex operator algebras. I will also discuss the extremal Gromov-Witten invariants of the Hilbert schemes. The former is a joint work with Z.B. Qin and W. Q. Wang. The latter is a joint work with J. Li.   Differential Geometry Seminar Contact homology and fillings Otto Van Koert (Seoul National University) 2010-12-03   In this talk I will give an overview of contact topology and an important invariant of contact manifolds, namely contact homology. Contact homology is an invariant in the spirit of Floer homology: its chain complex is freely generated by so-called periodic Reeb orbits, which are closed orbits of a distinguished vector field. The differential is defined by counting certain holomorphic curves. Contact homology and its generalization, symplectic field theory, are able to detect the non-existence of fillings. I will describe how the algebraic structure of these theories can be used to show such a property.   Differential Geometry Seminar The Geography Problems of 4-Manifolds, Part II Park, Jongil (Seoul National University) 2010-10-28     Differential Geometry Seminar Sub-conformal and almost CR geometry Joo, Jaecheon (POSTECH) 2010-10-13   If we consider strongly-pseudo convex CR manifolds with integrable CR structure, the transformation formula of the pseudo-Hermitian scalar curvatures satisfies a very special non-linear sub-elliptic PDE, which is called the CR Yamabe equation. In 1995, R. Schoen made use of this equation for the characterization of the Heisenberg group under the non-proper action of CR automorphism group. In contrast with integrable case, the transformation formula of the pseudo-Hermitian scalar curvatures is much more complecated than the CR Yamabe equation, if the CR structure is not integrable and this complexity makes it difficult to follow the analysis of integrable case. In this talk, I will introduce a sub-class of contact sub-Riemannian manifolds for which sub-conformal transformation formula of a twisted sub-Riemannian scalar curvature becomes the sub-conformal Yamabe equation. Using the sub-conformal Yamabe equation, we will also discuss about the characterization 5 and 7-dimenisional non-integrable strongly pseudo-convex almost CR manifolds under the non-proper action of CR automorphisms by Schoen's argument.   Differential Geometry Seminar Degenerate Monge-Ampere equations and their applications Philippe Eyssidieux (University of Grenoble) 2010-10-08

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