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The 7th OCAMI-TIMS-Kobe-Waseda Joint International Workshop on



Differential Geometry, Geometric Analysis and Mathematical Physics


Date March 14 (Sat)- March 17 (Tue), 2015
Place Lecture Room E408, Building E, Graduate School of Science, Department of Mathematics, Osaka City University


Organizers Shu-Cheng Chang (NTU & TIMS), Chang-Shou Lin (NTU, TIMS Director),
Martin Guest (Waseda University & Visiting Professor of OCAMI),
Yoshihiro Ohnita(OCU, OCAMI Director), Masa-Hiko Saitoh (Kobe University)

Sponsors Osaka City University Advanced Mathematical Institute (OCAMI).  
National Taiwan University (NTU), Taida Institute for Mathematical Sciences (TIMS)
 
 

    
Invited speakers Professor Jason Lotay (University College London, UK)
Professor Tommaso Pacini (Scuola Normale di Pisa, Italy)
Professor Claude Warnick (University of Warwick, UK)
Professor David Kubiznak (Perimeter Institute for Theoretical Physics, Canada)
Professor Shu-Cheng Chang (National Taiwan University, Taiwan)
Professor Hsin-Yuan Huang (National Sun Yat-sen University, Taiwan)
Professor Chung-Jun Tsai(National Taiwan University, Taiwan)
Professor Mao-Pei Tsui (National Taiwan University, Taiwan)
Doctor Chih-Wei Chen (National Taiwan University, Taiwan)
Doctor Ting-Jung Kuo (Taida Institute for Mathematical Sciences, Taiwan)
Doctor Yen-Wen Fan (Taida Institute for Mathematical Sciences, Taiwan)
Professor Yasushi Homma(Waseda University, Japan)
Professor Yoshie Sugiyama(Kyushu University & Visiting Professor of OCAMI, Japan)
Professor Tsukasa Iwabuchi(Chuo University, Japan)
Professor Yoshitake Hashimoto(Tokyo City University & Visiting Professor of OCAMI, Japan)
Doctor Wenjiao Yan(Beijing Normal University, P.R. China & Tohoku University, Japan)
Doctor Yuriko Umemoto(OCAMI, Japan)
Doctor Atsuhide Mori(OCAMI, Japan)
Doctor Tohru Kajigaya(Tohoku University & OCAMI, Japan)
Mr. Keita Kunikawa(Ph.D. student, Tohoku University, Japan)
Mr. Hikaru Yamamoto(Ph.D. student, University of Tokyo, Japan)
etc.

     
Title and Abstract of Talks abstract (in preparation)
Jason Lotay (University College London, UK)
Title: Coupled flows and symplectic geometry
Abstract: The idea of coupling two geometric flows has previously been primarily motivated by analytic considerations. In the symplectic setting, we provide a geometric motivation for a new coupling of a submanifold flow with a flow of the ambient structure. We will then discuss some of its geometric and analytic properties and potential applications. This is joint work with T. Pacini (SNS, Pisa).
Tommaso Pacini (Scuola Normale di Pisa, Italy)
Title: Complexified diffeomorphism groups and the space of totally real submanifolds
Abstract: Let M be a holomorphic manifold. We will show that the space $\tau$ of totally real submanifolds in M carries a natural connection. This induces a canonical notion of geodesics in $\tau$ and a corresponding notion of whether a functional $F:\tau\rightarrow \R$ is "convex". If M is Kahler we define a canonical functional on $\tau$; it is convex if M has negative Ricci curvature. This construction is formally analogous to the notion of geodesics and to the Mabuchi functional on the space of Kahler potentials, due to Donaldson, Fujiki and Semmes. We will discuss possible applications and open problems. This work is joint with Jason Lotay, UCL.
Claude Warnick (University of Warwick, UK)
Title: Symmetries and wave equations
Abstract: From a given Lorentzian manifold, the wave equation is the simplest geometric PDE one can construct. There is a close interplay between the geometry of the manifold and properties of the solutions of the wave equation. I will discuss how symmetries, hidden and otherwise, can be exploited to understand solutions of the wave equation, and I will present recent work concerning the stability of the anti-de Sitter spacetime.
David Kubiznak (Perimeter Institute for Theoretical Physics, Canada)
Title: Dynamical symmetries in black hole spacetimes
Abstract: Starting from the well known Laplace-Runge-Lenz vector of the Kepler problem, I will introduce dynamical (hidden) symmetries as genuine phase space symmetries that stand in contract to the standard configuration space symmetries discussed by Noether's theorem. Proceeding to a relativistic description, I will demonstrate that such symmetries -- encoded in the so called Killing-Yano tensors -- play a crucial role in the study of rotating black holes described by the Kerr geometry. Even more remarkably, I will show that one such symmetry is enough to guarantee complete integrability of particle and light motion in general rotating black hole spacetimes in an arbitrary number of spacetime dimensions. Some further developments in the area of Killing-Yano tensors will also be discussed.
Shu-Cheng Chang (National Taiwan University, Taiwan)
Title: CR Subgradient Estimates and Its Applications
Abstract: In this talk, we first derive the gradient estimate for positive pseudoharmonic functions and the CR heat equation in a complete pseudohermitian manifold. Secondly, we obtain the CR matrix Li-Yau-Hamilton inequality. Finally, we will give several applications such as Liouville-type theorem as well as CR Gap theorem.
Hsin-Yuan Huang (National Sun Yat-sen University, Taiwan)
Title: On the Chern-Simons system with two Higgs particles
Abstract: In this talk, I will survey the recent developments of the system arising from the Chern-Simons Model with two Higgs Particles. Mathematically, the system is a typical skew-symmetric system. Thus, the action functional of this system is indefinite, which makes it difficult to study from the variational method. Among others, I will present my recent works on this system, including the uniqueness of the topological solutions and the radial non-topological solutions, and existence of bubbling solutions on a torus (joint work with X. Han and C.S. Lin and Y.Lee).
Chung-Jun Tsai(National Taiwan University, Taiwan)
Title: Cohomology and Hodge theory on symplectic manifolds
Abstract: In this talk, I will explain the differential cohomologies on symplectic manifolds, which are analogous to the Dolbeault theory in complex geometry. These symplectic cohomologies admit certain algebraic structure, which encodes interesting information for non-Kahler symplectic manifolds. This is a joint work with L.-S. Tseng and S.-T. Yau.
Mao-Pei Tsui (National Taiwan University, Taiwan)
Title: Generalized Lagrangian mean curvature flows in cotangent bundle
Abstract: We will show that the canonical connection on the cotangent bundle of any Riemannian manifold will induce a Generalized Lagrangian mean curvature flow. This flow preserves Lagrangian condition. It also preserves the exactness and the zero Maslov class conditions. We will also explain a long time existence and convergence result to demonstrate the stability of the zero section of the cotangent bundle of sphere. This is joint work with Knut Smoczyk and Mu-Tao Wang.
Chih-Wei Chen (National Taiwan University, Taiwan)
Title: On 3-dimensional pseudo-gradient CR Yamabe solitons with zero torsion
Abstract: It has been known from the 70’s that all closed orientable 3-manifolds admit CR structures. Among all these manifolds, we prove that only sphere and the lens spaces may admit non-trivial torsion-free pseudo-gradient CR Yamabe soliton structures. For a non-trivial complete soliton, which always admits a Riemannian metric with indefinite curvature sign, we show that it must be diffeomorphic to the Euclidean space if it is simply-connected, torsion-free and has certain bound on the Webster curvature. This is a joint work with Huai-Dong Cao and Shu-Cheng Chang.
Ting-Jung Kuo (Taida Institute for Mathematical Sciences, NTU)
Title: Existence of non-topological soluions in the SU(3) Chern-Simons model in R^2
Abstract: PDF
Yen-Wen Fan (Taida Institute for Mathematical Sciences, Taiwan)
Title: Mixed type solutions of the SU(3) Chern-Simons models on a flat two torus
Abstract: In recent years, various Cherns-Simons field theories have been developed and the relativistic self dual Abelian Chern-Simons-Higgs model was studies extensively. In our case, we are interested in the non-Abelian Chern-Simons model. First, we reviews some existence results obtained by Nolasco and Tarantello. We will show the existence and uniqueness of mixed type I solution, which has no blow up points, under non degeneracy condition. Moreover, we are able to construct mixed type II solutions which have blow up points.    
Yasushi Homma(Waseda University, Japan)
Title: Twisted Dirac operators and Generalized gradients on Rimannian spin manifolds
Abstract: Generalized gradients are the first order differential operators naturally defined on Riemannian or spin manifolds. There exist certain relations among gradients, which are called ``Weitzenb\"ock formulas'' and important in differential geometry. In this talk, we give other geometric relations among gradients. Here, we use the Dirac operator twisted with an irreducible associated vector bundle. In the simple case, twisting with the spinor bundle, we have the bundle of differential forms, and the twisted Dirac operator is just the sum of the exterior derivative and co-derivative. In general, the twisted Dirac operator is a linear combination of some gradients. So we can expect that twisting gives interesting relations among gradients. In fact, by using PRV- theorem (a deep theorem in representation theory), we have a lot of relations including new Weitzenb\”ock type formulas. We also give some applications, eigenvalue estimates for Laplace type operators, etc.
Yoshie Sugiyama(Kyushu University & Visiting Professor of OCAMI, Japan)
Title: On global existence and finite time blow-up for solutions to the Keller-Segel system coupled with the (Naiver-)Stokes fluid
Abstract: The Keller-Segel system contains several parameters which cause numerous structures such as semi-linear, quasi-linear of degenerate and singular type of PDE. In particular, the degenerate type contains the unknown function as the coefficients breaking down uniform ellipticity, which makes the problem more difficult in comparison with the other types. The Keller-Segel system itself is characterized as the parabolic- parabolic and parabolic-elliptic both of which provide us an important research theme. Indeed, we need to handle these types in accordance with the characteristic features of equations. In this talk, we consider the semi-linear Keller-Segel system coupled with the Naiver-Stokes fluid in the whole space, and prove the existence of global mild solutions with the small initial data in the scaling invariant space. Our method is based on the implicit function theorem which yields necessarily continuous dependence of solutions with respect to the initial data. As a byproduct, we show the asymptotic stability of solutions as the time goes to infinity. Since we may deal with the initial data in the weak L^p-spaces, it turns out that there exist self-similar solutions provided the initial data are small homogeneous functions. We also discuss the structures of quasi-linear Keller-Segel system of degenerate and singular type, which is different from semi-linear one.
Tsukasa Iwabuchi(Chuo University, Japan)
Title: On the large time behavior of solutions for the critical Burgers equations in the Besov spaces
Abstract: We consider the Cauchy problem for the critical Burgers equation in the Besov spaces. We show the existence of global solutions, which are bounded in time, for small initial data in the Besov spaces. We also consider the large time behavior of the solutions to show that the solution behaves like the Poisson kernel with the initial data in $L^1 (\mathbb R^n)$ and small in the Besov spaces.
Yoshitake Hashimoto(Tokyo City University & Visiting Professor of OCAMI, Japan)
Title: Conformal field theory on stable curves
Abstract: (joint work with Akihiro Tsuchiya) Conformal field theory is a quantum field theory with conformal symmetry on 2-dimensional spacetime with singularity. In this theory fields of operators constitute an "algebra" with regularization for avoiding divergence in product of operators, which is called vertex algebra. Mechanism of regularization is closely related to degeneration of Riemann surfaces. I will discuss a relation between field theory on families of Riemann surfaces with degeneration and representation theory of vertex algebras, especially tensor structure in the categories of the representations, which is related to quantum groups.
Wenjiao Yan(Beijing Normal University, P.R. China & Tohoku University, Japan)
Title: Schoen-Yau-Gromov-Lawason theory and isoparametric foliations
Abstract: Motivated by the celebrated Schoen-Yau-Gromov-Lawson surgery theory on metrics of positive scalar curvature, we construct a double manifold associated with a minimal isoparametric hypersurface in the unit sphere. The resulting double manifold carries a metric of positive scalar curvature and an isoparametric foliation as well. To investigate the topology of the double manifolds, we use K-theory and the representation of the Clifford algebra for the OT-FKM-type, and determine completely the isotropy subgroups of singular orbits for homogeneous case.
Yuriko Umemoto(OCAMI, Japan)
Title: The growth function of hyperbolic Coxeter dominoes and 2-Salem numbers
Abstract: A hyperbolic Coxeter group is defined as the group generated by reflections with respect to hyperplanes bounding a given Coxeter polytope in hyperbolic space. In this talk, I will present the growth functions and growth rates of hyperbolic Coxeter groups with respect to 4-dimensional Coxeter polytopes constructed by successive gluing of Coxeter polytopes, which we call Coxeter dominoes.
Atsuhide Mori(OCAMI, Japan)
Title: Corank one Poisson structures via contact topology
Abstract: Any contact structure of a 3-manifold can be deformed into a corank one Poisson structure. The deformation can be considered as a path of "conformally twisted" contact structures. We construct similar paths in higer dimension under a certain assumption. Particularly, deforming the standard contact structure of the 5-sphere, we obtain infinitely many examples of corank one Poisson structures which are transversely the same as the Reeb foliation of the 3-sphere. On the other hand David Martinez Torres showed that if a closed 2-form is non-degenerate along the leaves of a codimension one foliation, the foliation is transeversely the same as a taut foliation of a 3-manifold. I suspect that a foliation to which a contact structure converges would be a Poisson structure which is transversely a foliation of a 3-manifold.
Tohru Kajigaya(Tohoku University & OCAMI, Japan)
Title: A new family of Hamiltonian minimal Lagrangian submanifolds in the complex Euclidean space
Abstract: A Hamiltonian minimal (shortly, H-minimal) Lagrangian submanifold in a Kahler manifold is a critical point of the volume functional under all compactly supported Hamiltonian deformations. This gives a nice extension of the notion of minimal submanifolds. In this talk, we review the basic results for the H-minimality, H-stability and Hamiltonian volume minimizing problem. Moreover, we give a new family of non-compact, complete H-minimal submanifolds in the complex Euclidean space C^n. We show that any normal bundle of a principal orbit of the adjoint representation of a compact simple Lie group G in the Lie algebra g of G is an H-minimal Lagrangian submanifold in the tangent bundle Tg which is naturally regarded as C^n. Furthermore, we specify these orbits with this property in the class of full irreducible isoparametric submanifolds in the Euclidean space.
Keita Kunikawa(Ph.D. student, Tohoku University, Japan)
Title: A Bernstein type theorem of ancient solutions to the mean curvature flow
Abstract: Ancient solutions naturally arise as tangent flows near singularities of the mean curvature flow. I derive a curvature estimate for entire graphic solutions to the mean curvature flow. As a consequence I show a Bernstein type theorem for ancient solutions to the mean curvature flow.
Hikaru Yamamoto(Ph.D. student, University of Tokyo, Japan)
Title: Ricci-mean curvature flows in gradient shrinking Ricci solitons.
Abstract: G. Huisken studied asymptotic behavior of a mean curvature flow moving in a Euclidean space when it develops a singularity of type I, and proved that its rescaled flow converges to a self-shrinker in the Euclidean space. In this talk, we generalize this result for a Ricci-mean curvature flow moving along a Ricci flow constructed from a gradient shrinking Ricci soliton.
ETC.

 

(Provisional) Program program (in preparation)

3/14(Sat) AM 09:30-10:00 Lecture Room E408 Registration and Opening
AM 10:00-10:50 Lecture Room E408 Yasushi Homma
AM 11:10-12:00 Lecture Room E408 Shu-Cheng Chang
PM 13:30-14:20 Lecture Room E408 Chih-Wei Chen
PM 14:30-15:20 Lecture Room E408 Hikaru Yamamoto
PM 15:30-16:20 Lecture Room E408 Chung-Jun Tsai
PM 16:30-17:20 Lecture Room E408 Atsuhide Mori
PM 18:30- Dinner Party
3/15(Sun) AM 09:30-10:30 Lecture Room E408 Jason Lotay
AM 10:45-11:45 Lecture Room E408 Tommaso Pacini
PM 13:30-14:20 Lecture Room E408 Mao-Pei Tsui
PM 14:30-15:20 Lecture Room E408 Wenjiao Yan
PM 15:30-16:10 Lecture Room E408 Yuriko Umemoto
PM 16:20-17:00 Lecture Room E408 Keita Kunikawa
3/16(Mon) AM 09:30-10:20 Lecture Room E408 Claude Warnick Joint workshop with Theoretical Physics
AM 10:30-11:20 Lecture Room E408 David Kubiznak Joint workshop with Theoretical Physics
AM 11:30-12:20 Lecture Room E408 Yoshitake Hashimoto Joint workshop with Theoretical Physics
PM 14:00-14:50 Lecture Room E408 Hsin-Yuan Huang
PM 15:00-15:50 Lecture Room E408 Tsukasa Iwabuchi
PM 16:00-16:50 Lecture Room E408 Yoshie Sugiyama
3/17(Tue) AM 09:30-10:20 Lecture Room E408 Ting-Jung Kuo
AM 10:30-11:20 Lecture Room E408 Yen-Wen Fan
AM 11:30-12:10 Lecture Room E408 Tohru Kajigaya
PM 13:30-14:20 Lecture Room E408    


Suggestion to Speakers :

At the lecture room there are enough blackboards, the computer projector and the visualizer. Please prepare your talk using them.

Notice : This workshop is held as one of joint activities under the agreement of academic cooperation between TIMS and OCAMI.


    
Link Osaka City University Advanced Mathematical Institute (OCAM I)
Department of Mathematics, Osaka City Univercity
National Taiwan University Taida Institute for Mathematical Sciences (TIMS)
TIMS One-Day Workshop on Differential Geometry (April 1, 2008)
The 1st OCAMI-TIMS Joint International Workshop on Differential Geometry and Geomtric Analysis (March 9-10, 2009)
The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geomtric Analysis (March 21-23, 2010)
Poster
The 3rd OCAMI-TIMS Joint International Workshop on Differential Geometry and Geomtric Analysis (March 13-15, 2011)
The 4th TIMS-OCAMI Joint International Workshop on Differential Geometry and Geomtric Analysis (March 17-19, 2012)
Poster
The 5th OCAMI-TIMS Joint International Workshop on Differential Geometry and Geomtric Analysis (March 25-27, 2013)
The 6th TIMS-OCAMI-Waseda Joint International Workshop on Integrable Systems and Mathematical Physics (March 22-26, 2014)
Kansai Kenshu Center (KKC)

Support JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers
(Oct. 2014-Mar. 2017)
"Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI"
(Osaka City University - Kobe University - Waseda University, Principal investigator: Yoshihiro Ohnita)

Contact(e-mail)
Yoshihiro Ohnita: ohnita (at) sci.osaka-cu.ac.jp

製作 のだ Last updated on 13/March/2015