The following talk on 19th is a pre-workshop talk. Please note that the place is "Studio Phones Room: 301B" (not in Kobe University).
To find any relationship between Mathematics and CG, which can be used to expand Mathematics, we would like to have a discussion on CG from the Mathematical point of view. For further information, Please visit Kobe Studio Seminar for Studies with Renderman.
The Gelfand-Cetlin system is a completely integrable system on a flag manifold of type A introduced by Guillemin and Sternberg. We compute potential functions and Floer cohomologies of Lagrangian fibers. We also discuss a relationship with mirror symmetry of the flag manifold. This is a joint work with Kazushi Ueda.
The Gelfand-Cetlin system is a completely integrable system on a flag manifold of type A introduced by Guillemin and Sternberg. We compute potential functions and Floer cohomologies of Lagrangian fibers. We also discuss a relationship with mirror symmetry of the flag manifold. This is a joint work with Kazushi Ueda.
For a 3-manifold M with b_1(M) = 1 fibered over S^1 and the fiberwise gradient ξ of a fiberwise Morse function on M, we introduce the notion of amidakuji-like path (AL-path) in M. An AL-path is a piecewise smooth path on M consisting of edges each of which is either a part of a critical locus of ξ or a flow line of -ξ. Counting closed AL-paths with signs gives the Lefschetz zeta function of M. The "moduli space" of AL-paths on M gives explicitly Lescop's equivariant propagator, which can be used to define Z-equivariant version of Chern-Simons perturbation theory for M.
For a 3-manifold M with b_1(M) = 1 fibered over S^1 and the fiberwise gradient ξ of a fiberwise Morse function on M, we introduce the notion of amidakuji-like path (AL-path) in M. An AL-path is a piecewise smooth path on M consisting of edges each of which is either a part of a critical locus of ξ or a flow line of -ξ. Counting closed AL-paths with signs gives the Lefschetz zeta function of M. The "moduli space" of AL-paths on M gives explicitly Lescop's equivariant propagator, which can be used to define Z-equivariant version of Chern-Simons perturbation theory for M.
In my talks, I'll explane how to construct the quantum sl(2) invariant for links and 3-manifolds. We'll recall representation theory of quantum group Uq(sl(2)) and show a construction of the quantum sl(2) invariant for links in the first talk. In the second talk, we'll show a construction of the invariant for 3-maniforlds.
In my talks, I'll explane how to construct the quantum sl(2) invariant for links and 3-manifolds. We'll recall representation theory of quantum group Uq(sl(2)) and show a construction of the quantum sl(2) invariant for links in the first talk. In the second talk, we'll show a construction of the invariant for 3-maniforlds.
Vertex operator algebras (VOA) were introduced by Borcherds and Frenkel-Lepowsky-Meurmann to prove Moonshine conjecture. In this talk I will explain modular invariance property of vertex operator algebras. In the first talk, I will recall the definition and examples of vertex operator algebras. In the second talk, I will explain Zhu's proof of modular invariance of characters of rational VOAs and how to generalize this property for non-rational VOAs.
Vertex operator algebras (VOA) were introduced by Borcherds and Frenkel-Lepowsky-Meurmann to prove Moonshine conjecture. In this talk I will explain modular invariance property of vertex operator algebras. In the first talk, I will recall the definition and examples of vertex operator algebras. In the second talk, I will explain Zhu's proof of modular invariance of characters of rational VOAs and how to generalize this property for non-rational VOAs.