Title and Abstract of Talks ：
abstract (in preparation)




ShuCheng Chang (National Taiwan University, Taiwan) 
Title: The torsion flow in a closed strictly pseudoconvex CR 3manifold 

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 3manifold. Secondly, we give some examples for the
longtime solution of the torsion flow. Finally, we derive
monotonicity formulas for CR Perlmantype entropy functionals. As an
application, we classify the torsion breathers. This is a jointed work
with Otto van Koert and ChinTung Wu.


ChenYu 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 HiggsHermitianYangMills metrics from stability.


HsinYuan Huang (National Sun Yatsen University, Taiwan) 
Title: On the Entire Radial Solutions of the ChernSimons SU(3) System 
Abstract:
In this talk, we study the entire radial solutions of the selfdual equations arising from the relativistic SU(3) ChernSimons model
proposed by KaoLee 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, nontopological 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 ChangShou Lin.




ChiungJu Liu (National Taiwan University, Taiwan) 
Title: The asymptotic expansion of TianYauZelditch on Riemann surfaces


Abstract:
In this talk, we will learn about the asymptotic expansion of TianYauZelditch on polarized Kahler manifolds
and discuss its behavior on Riemann surfaces with 1 constant scalar curvature.


ChinLung Wang (National Taiwan University, Taiwan) 
Title: Mean field equations and algebraic geometry


Abstract: In this talk I will discuss a correspondence between nonlinear 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 ChingLi Chai and ChangShou Lin.


TingJung 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 JhiHsin Cheng.


Miyuki Koiso（IMI, Kyushu University, Japan) 
Title: Nonconvex anisotropic surface energy and zero mean curvature surfaces
in the LorentzMinkowski space


Abstract: We study stationary surfaces of anisotropic surface energies in the
euclidean threespace which are called anisotropic minimal surfaces.
Usual minimal surfaces, zero mean curvature spacelike surfaces and
timelike surfaces in the LorenzMinkowski 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 catenoidtype 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
BorthwickPaulUribe semiclassical approximation of the
$k$BohrSommerfeld tori of the Lagrangian torus fibration $\{T_t\}$
and its Hamiltonian deformation $\{\phi(T_t)\}$.


Shin Nayatani（Nagoya University, Japan) 
Title: FixedPoint Property of Infinite Groups 

Abstract:
I'll make a small survey on geometric approach to superrigidity and fixedpoint 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 wellknown 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 a joint work with K. Moriya (University of Tsukuba).


Katsuhiro Moriya（University of Tsukuba, Japan) 
Title: Surfaces with vanishing Willmore energy in Euclidean fourspace 

Abstract: We regard a conformal map from a Riemann surface to Euclidean fourspace 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 BialynickiBirula concerning the existence of
invariant Zariski open coverings. We also discuss about the converse of the above result in case
of holomorphic torus actions.
