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 antide Sitter
spacetime.


David Kubiznak (Perimeter Institute for Theoretical Physics, Canada) 
Title: Dynamical symmetries in black hole spacetimes


Abstract:
Starting from the well known LaplaceRungeLenz 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 KillingYano 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 KillingYano tensors will also be discussed.


ShuCheng 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 LiYauHamilton inequality.
Finally, we will give several applications such as Liouvilletype theorem as well as CR Gap theorem.


HsinYuan Huang (National Sun Yatsen University, Taiwan) 
Title: On the ChernSimons system with two Higgs particles


Abstract:
In this talk, I will survey the recent developments of the system arising from
the ChernSimons Model with two Higgs Particles.
Mathematically, the system is a typical skewsymmetric 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 nontopological solutions, and existence of bubbling solutions on a torus
(joint work with X. Han and C.S. Lin and Y.Lee).


ChungJun 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 nonKahler symplectic manifolds.
This is a joint work with L.S. Tseng and S.T. Yau.




MaoPei 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 MuTao Wang.


ChihWei Chen (National Taiwan University, Taiwan) 
Title: On 3dimensional pseudogradient CR Yamabe solitons with zero torsion


Abstract:
It has been known from the 70’s that all closed orientable 3manifolds admit CR structures.
Among all these manifolds, we prove that only sphere and
the lens spaces may admit nontrivial torsionfree pseudogradient CR Yamabe soliton structures.
For a nontrivial 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 simplyconnected, torsionfree
and has certain bound on the Webster curvature.
This is a joint work with HuaiDong Cao and ShuCheng Chang.


TingJung Kuo (Taida Institute for Mathematical Sciences, NTU) 
Title: Existence of nontopological soluions in the SU(3) ChernSimons model in R^2 

Abstract:
PDF


YenWen Fan (Taida Institute for Mathematical Sciences, Taiwan) 
Title: Mixed type solutions of the SU(3) ChernSimons models on a flat two torus 

Abstract:
In recent years, various ChernsSimons field theories have been developed and
the relativistic self dual Abelian ChernSimonsHiggs model was studies extensively.
In our case, we are interested in the nonAbelian ChernSimons 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 coderivative. 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 blowup for solutions to the
KellerSegel system coupled with the (Naiver)Stokes fluid


Abstract:
The KellerSegel system contains several parameters which cause
numerous structures such as semilinear, quasilinear 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 KellerSegel system itself is characterized as the parabolic
parabolic and parabolicelliptic 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 semilinear KellerSegel system coupled
with the NaiverStokes 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^pspaces, it turns
out that there exist selfsimilar solutions provided the initial data are small
homogeneous functions.
We also discuss the structures of quasilinear KellerSegel system of
degenerate and singular type, which is different from semilinear 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 2dimensional 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: SchoenYauGromovLawason theory and isoparametric foliations 

Abstract:
Motivated by the celebrated SchoenYauGromovLawson 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 Ktheory and the representation of the Clifford algebra for the OTFKMtype, 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 2Salem 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 4dimensional 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 3manifold 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 5sphere, we obtain
infinitely many examples of corank one Poisson structures which are
transversely the same as the Reeb foliation of the 3sphere.
On the other hand David Martinez Torres showed that if a closed 2form is nondegenerate
along the leaves of a codimension one foliation, the foliation is transeversely
the same as a taut foliation of a 3manifold.
I suspect that a foliation to which a contact structure converges would be a
Poisson structure which is transversely a foliation of a 3manifold.


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, Hminimal) 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 Hminimality, Hstability and Hamiltonian volume minimizing problem.
Moreover, we give a new family of noncompact, complete Hminimal 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 Hminimal 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: Riccimean 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 selfshrinker in the
Euclidean space.
In this talk, we generalize this result for a Riccimean curvature flow
moving along a Ricci flow constructed from a gradient shrinking Ricci soliton.


ETC.
