第5回国際ワークショップ 「微分幾何学と幾何解析」

開催日 平成25年3月25日(月)〜27日(水)3日間
場所 大阪市立大学 大学院理学研究科 共通研究棟 3階 数学講究室 301室

組織委員 Shu-Cheng Chang (国立台湾大学), Chang-Shou Lin (国立台湾大学, TIMS所長),
Martin Guest(早稲田大学, (兼)大阪市立大学客員教授)
河内 明夫(大阪市立大学, OCAMI所長), 大仁田義裕(大阪市立大学,代表)

主催 大阪市立大学 数学研究所 OCAM I 
国立台湾大学 台大数学科学中心 TIMS 

講演予定者 Professor Shu-Cheng Chang (National Taiwan University, Taiwan)
Professor Chen-Yu Chi (National Taiwan University, Taiwan)
Professor Hsin-Yuan Huang (National Sun Yat-sen University, Taiwan)
Professor Chiung-Ju Liu (National Taiwan University, Taiwan)
Professor Chin-Lung Wang (National Taiwan University, Taiwan)
Doctor Ting-Jung Kuo (Taida Institute for Mathematical Sciences, NTU, Taiwan)
Doctor Takanari Saotome 早乙女 飛成 (Institute of Mathematics, Academia Sinica, Taiwan)
Professor Miyuki Koiso 小磯 深幸 (Institute of Mathematics for Industry IMI, Kyushu University, Japan)
Professor Ryoichi Kobayashi 小林 亮一 (Nagoya University, Japan)
Professor Shin Nayatani 納谷 信(Nagoya University, Japan)
Professor Katrin Leschke (University of Leicester, UK)
Doctor Katsuhiro Moriya 守屋 克洋 (University of Tsukuba, Japan)
Doctor Kensuke Onda 恩田 健介(Nagoya University & OCAMI, Japan)
Mr. Hotoshi Yamanaka 山中 仁 (Ph.D. student, Osaka City University, Japan)

講演タイトル,アブストラクト abstract (in preparation)
Shu-Cheng Chang (National Taiwan University, Taiwan)
Title: The torsion flow in a closed strictly pseudoconvex CR 3-manifold
Abstract: In this talk, we define the torsion flow, a CR analogue of the Ricci flow. We first show that the torsion flow has short time existence for suitable initial conditions in a closed strictly pseudoconvex CR 3-manifold. Secondly, we give some examples for the long-time solution of the torsion flow. Finally, we derive monotonicity formulas for CR Perlman-type entropy functionals. As an application, we classify the torsion breathers. This is a jointed work with Otto van Koert and Chin-Tung Wu.
Chen-Yu Chi (National Taiwan University, Taiwan)
Title: On Toda systems of VHS type with singular sources
Abstract: We consider the Toda systems of VHS type with singular sources and provide a criterion for the existence of solutions with prescribed asymptotic behaviour near singularities when all the singular strengths are integral multiples of $n+1$, where $n$ is the number of equations in the system. We also prove the uniqueness of solution for general assignments of singular strengths. Our approach uses Simpson's theory of constructing Higgs-Hermitian-Yang-Mills metrics from stability.
Hsin-Yuan Huang (National Sun Yat-sen University, Taiwan)
Title: On the Entire Radial Solutions of the Chern-Simons SU(3) System
Abstract: In this talk, we study the entire radial solutions of the self-dual equations arising from the relativistic SU(3) Chern-Simons model proposed by Kao-Lee and Dunne. Understanding the structure of entire radial solutions is one of fundamental issues for the system of nonlinear equations. In this paper, we prove any entire radial solutions must be one of topological, non-topological and mixed type solutions, and completely classify the asymptotic behaviors at in finity of these solutions. Even for radial solutions, this classification has remained an open problem for many years. As an application of this classification, we prove that the two components u and v have intersection at most finite times. This is joint work with Chang-Shou Lin.
Chiung-Ju Liu (National Taiwan University, Taiwan)
Title: The asymptotic expansion of Tian-Yau-Zelditch on Riemann surfaces
Abstract: In this talk, we will learn about the asymptotic expansion of Tian-Yau-Zelditch on polarized Kahler manifolds and discuss its behavior on Riemann surfaces with -1 constant scalar curvature.
Chin-Lung Wang (National Taiwan University, Taiwan)
Title: Mean field equations and algebraic geometry
Abstract: In this talk I will discuss a correspondence between non-linear mean field equations on flat tori (PDE), generalized Lame equations (ODE), and certain polynomial systems (algebraic geometry). In particular this correspondence enables us to count the number of mean field solutions using algebraic geometry. Also the notion of analytic degeneracy and algebraic degeneracy match perfectly. This is a joint work with Ching-Li Chai and Chang-Shou Lin.
Ting-Jung Kuo (Taida Institute for Mathematical Sciences, NTU)
Title: Sharp estimates of the mean field equations at critical parameters
Abstract: PDF
Takanari Saotome (Institute of Mathematics, Academia Sinica, NTU)
Title: Some Estimates for a Solution to CR Yamabe Equation
Abstract: In this talk, we study some inequalities for solutions to CR Yamabe equation. This study is motivated from the study of the moduli space of the solutions to the Yamabe equation. This is a joint work with Professor Jhi-Hsin Cheng.  
Miyuki Koiso(IMI, Kyushu University, Japan)
Title: Non-convex anisotropic surface energy and zero mean curvature surfaces in the Lorentz-Minkowski space
Abstract: We study stationary surfaces of anisotropic surface energies in the euclidean three-space which are called anisotropic minimal surfaces. Usual minimal surfaces, zero mean curvature spacelike surfaces and timelike surfaces in the Lorenz-Minkowski space are regarded as anisotropic minimal surfaces for certain special axisymmetric anisotropic surface energies. In this talk, for any axisymmetric anisotropic surface energy, we show that, a surface is both a minimal surface and an anisotropic minimal surface if and only if it is a right helicoid. We also construct new examples of anisotropic cyclic minimal surfaces for certain reasonable classes of energy density. Our examples include zero mean curvature timelike surfaces and spacelike surfaces of catenoid-type and Riemann- type. This is a joint work with Atsufumi Honda (Tokyo Institute of Technology).
Ryoichi Kobayashi(Nagoya University, Japan)
Title: Hamiltonian volume minimizing property of $U(1)^n$-orbits in $CP^n$
Abstract: We will prove that any maximal dimensional $U(1)^n$-orbit in $CP^n$ is volume minimizing under Hamiltonian deformation. The idea of the proof is the following : (1) We extend a given $U(1)^n$-orbit to the moment torus fibration $\{T_t\}$ and consider its Hamiltonian deformation $\{\phi(T_t)\}$ where $\phi$ is a Hamiltonian diffeomorphism of $CP^n$. Then (2) We compare a given $U(1)^n$-orbit and its Hamiltonian deformation by looking at the large $k$-asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis $H^0(CP^n,O(k))$ obtained by Borthwick-Paul-Uribe semi-classical approximation of the $k$-Bohr-Sommerfeld tori of the Lagrangian torus fibration $\{T_t\}$ and its Hamiltonian deformation $\{\phi(T_t)\}$.
Shin Nayatani(Nagoya University, Japan)
Title: Fixed-Point Property of Infinite Groups
Abstract: I'll make a small survey on geometric approach to superrigidity and fixed-point property (fpp) of infinite groups. Starting form the fpp of individual groups, I'll discuss the fpp of random groups, and then the monstrous groups of Gromov. This talk is based on the joint work with Hiroyasu Izeki (Keio) and Takefumi Kondo (Tohoku).    
Katrin Leschke (University of Leicester, UK)
Title: Quaternionic Holomorphic Geometry: transformations of minimal surfaces
Abstract: There are various harmonic maps which are canonically associated to a minimal surface, e.g., the Gauss map of the immersion and the conformal Gauss map. Using methods from Quaternionic Holomorphic Geoemtry, we will discuss how the well-known dressing operation on harmonic maps applied to the associated harmonic maps of a minimal surface is related to transformations on the minimal surface. In particular, we will show that the simple factor dressing is connected to a generalised associated family and a family of Willmore surfaces given by the minimal surface. This is joint work with K. Moriya (University of Tsukuba).
Katsuhiro Moriya(University of Tsukuba, Japan)
Title: Surfaces with vanishing Willmore energy in Euclidean four-space
Abstract: We regard a conformal map from a Riemann surface to Euclidean four-space with vanishing Willmore energy as a higher codimensional version of a holomorphic function or a meromorphic funciton. Then we find a property of a surface with vanishing Willmore energy by a similar way to find a property of a holomorphic function or a meromorphic function.
Kensuke Onda(Nagoya University & OCAMI, Japan)
Title: Algebraic Ricci solitons on Lorentzian Lie groups
Abstract: Ricci solitons have been intensively studied. The concept of the algebraic Ricci soliton was first introduced by Lauret in Riemannian case. Algebraic Ricci soliton is useful for studying Ricci solitons on homogeneous manifolds. In this talk, we study algebraic Ricci solitons on Lorentzian Lie groups.
Hitoshi Yamanaka(Osaka City University, Japan)
Title: Hyperbolic diffeomorphisms and representation coverings
Abstract: For a given invariant hyperbolic diffeomorphism satisfying a certain convergence condition, We show a Morse theoretic analogue of a theorem of Bialynicki-Birula concerning the existence of invariant Zariski open coverings. We also discuss about the converse of the above result in case of holomorphic torus actions.


プログラム program (in preparation)

3/25(Mon) AM 9:30-10:00 Lecture Room 301 Registration and Opening
AM 10:00-10:50 Lecture Room 301 Ryoichi Kobayashi
AM 11:10-12:00 Lecture Room 301 Chin-Lung Wang
PM 13:30-14:20 Lecture Room 301 Chen-Yu Chi
PM 14:30-15:20 Lecture Room 301 Miyuki Koiso
PM 15:30- Free Discussion   
3/26(Tue) AM 9:30-10:20 Lecture Room 301 Kensuke Onda
AM 10:30-11:20 Lecture Room 301 Ting-Jung Kuo
AM 11:30-12:20 Lecture Room 301 Hsin-Yuan Huang
PM 14:00-14:50 Lecture Room 301 Chiung-Ju Liu
PM 15:00-15:40 Lecture Room 301 Hitoshi Yamanaka
PM 16:00-16:40 Lecture Room 301 Katrin Leschke
PM 16:50-17:30 Lecture Room 301 Katsuhiro Moriya
3/27(Wed) AM 9:30-10:20 Lecture Room 301 Shu-Cheng Chang
AM 10:30-11:20 Lecture Room 301 Shin Nayatani
AM 11:30-12:20 Lecture Room 301 Takanari Saotome
PM 13:40-14:30 Lecture Room 301    

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備考 : この企画は、台湾・国立台湾大学台大数学科学中心と大阪市立大学数学研究所の間の学術研究協力協定のもとでの活動の一環として行われます。

リンク等 大阪市立大学数学研究所
大阪市立大学 大学院理学研究科 数学教室
国立台湾大学台大数学科学中心 TIMS
TIMS One-Day Workshop on Differential Geometry (April 1, 2008)
第1回大阪市立大学数学研究所-台大数学科学中心 共催 国際ワークショップ 「微分幾何学と幾何解析」 (March 9-10, 2009)
第2回台大数学科学中心-大阪市立大学数学研究所 共催 国際ワークショップ 「微分幾何学と幾何解析」 (March 21-23, 2010)
第3回大阪市立大学数学研究所-台大数学科学中心 共催 国際ワークショップ 「微分幾何学と幾何解析」 (March 13-15, 2011)
第4回台大数学科学中心-大阪市立大学数学研究所 共催 国際ワークショップ 「微分幾何学と幾何解析」 (March 17-19, 2012)
関西研修センター(Kansai Kenshu Center-KKC)

補助 科学研究費基盤研究(A) 研究課題番号:21244004
(研究代表者 Martin Guest)

大仁田 義裕 : ohnita (at)

製作 のだ Last updated on 1/March/2013