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Kobe Studio Seminar for Mathematics

Workshop: Around Mathematical Physics and Geometry

Date:
2014/09/20 (-09/21)
Place:
Graduate School of Human Development and Environment, Kobe University. (No. 10 at the Campus Map)
Room:
A739
Workshop Organizers:
Yusuke Kiriu (Studio Phones)
Note:
This workshop would like to have a deep discussion on the topic hence attendance is limited to only the participants who have been contacted with us in advance. If you are a specialist in this topic and interested in our workshop, please contact to the corresponding organizer: Kosaku Nagasaka in advance.

The following talk on 19th is a pre-workshop talk. Please note that the place is "Studio Phones Room: 301B" (not in Kobe University).

Time:
09/19 15:00-, 09/20 09:30-10:30, 10:40-11:10
Discussion:
Various algorithms in CG, related to "Physics" or "Mathematics" from the viewpoint of attendees.
Moderator:
Yusuke Kiriu (Studio Phones)
Remark:

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.

Time:
09/20 11:20-12:20
Title:
The Gelfand-Cetlin system and Lagrangian intersection Floer theory
Speaker:
Yuichi Nohara (Kagawa University)
Abstract:

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.

Time:
09/20 13:40-14:40
Title:
The Gelfand-Cetlin system and Lagrangian intersection Floer theory
Speaker:
Yuichi Nohara (Kagawa University)
Abstract:

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.

Time:
09/20 15:00-16:00
Title:
Morse theory and perturbative invariants of 3-manifolds
Speaker:
Tadayuki Watanabe (Shimane University)
Abstract:

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.

Time:
09/20 16:20-17:20
Title:
Morse theory and perturbative invariants of 3-manifolds
Speaker:
Tadayuki Watanabe (Shimane University)
Abstract:

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.

Time:
09/20 17:30-
Discussion:
TBA
Time:
09/21 10:30-11:30
Title:
Quantum sl(2) invariant for links
Speaker:
Yasuyoshi Yonezawa(Nagoya University)
Abstract:

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.

Time:
09/21 13:00-14:00
Title:
Quantum sl(2) invariant for 3-manifolds
Speaker:
Yasuyoshi Yonezawa(Nagoya University)
Abstract:

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.

Time:
09/21 14:20-15:20
Title:
Modular invariance of vertex opearator algebras
Speaker:
Yusuke Arike(University of Tsukuba)
Abstract:

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.

Time:
09/21 15:40-16:40
Title:
Modular invariance of vertex opearator algebras
Speaker:
Yusuke Arike(University of Tsukuba)
Abstract:

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.