Title and Abstract of Talks ：
abstract (in preparation) 





Franz Pedit (1) 
Title: Energy quantization for harmonic 2spheres in noncompact symmetric spaces 

Abstract:
It is well known from results by Uhlenbeck, ChernWolfson and BurstallRawnsley that harmonic 2spheres in compact
symmetric spaces have quantized energies. Using the reformulation of the harmonic map equation as a family of flat
connections, we construct an energy preserving duality between harmonic maps from noncompact symmetric spaces
into their compact duals. Applying this construction to the conformal Gauss maps of Willmore 2spheres in the nsphere
provides a generalization and unifying approach to existing quantization results in special cases: Bryant for n=3;
Montiel for n=4; and Ejiri for Willmore 2spheres admitting a dual Willmore surface.


Franz Pedit (2) 
Title: Classification of homogeneous Willmore 2spheres in the nsphere 

Abstract:
The simplest surfaces in any ambient geometry are those which arise as orbits via a representation into the
symmetry group defining the geometry. For Willmore surfaces in nspace this symmetry group is the Moebius
group. We show that every Moebius homogeneous Willmore 2sphere is either a round 2sphere or is Moebius
congruent to a Veronese minimal 2sphere in a constant curvature 2msphere given by the irreducible SO(3)
representation in 2m+1.


Francis Burstrall 
Title: Integrable systems in conformal and Lie sphere geometry 

Abstract:
I shall give an overview of some geometric integrable systems that arise in conformal and Lie sphere geometry.
I shall describe isothermic surfaces and Moebiusflat submanifolds
(which include Guichard surfaces and conformally flat hypersurfaces)
in conformal geometry and their transformation theory.
Then I shall show how these are special cases of an integrable class of Lie applicable submanifolds
in a Lie sphere geometry which is, itself, novel in higher codimension.


Christoph Bohle 
Title: Differential Geometry and mcKP 

Abstract:
In my talks I want to explain how the multicomponent KP hierarchy (mcKP) can be related to differential geometry.
After briefly going through the general scheme behind this relation, I plan to focus on objects of classical differential
geometry (like multidimensional conjugate nets...) and applications to mathematical physics.


Seiichi Udagawa 
Title: Finite gap solutions for horizontal minimal surfaces of finite type in 5sphere


Abstract:
PDF


Takashi Kurose 
Title: Miura transformation and geometry of curves


Abstract:
The Miura transformation, which played an important role in the development of the theory of
integrable systems, relates the Kortewegde Vries (KdV) equation and the modified KdV equaion.
On the other hand, it is known that various integral systems naturally appear in geometry of
curves. In this talk, we shall review the cases of the KdV equation and of the modified KdV
equaion, and shall discuss geometric counterparts of the Miura transformation.


Atsushi Fujioka 
Title:
Centroaffine surfaces with parallel or recurrent cubic form relative to the induced connection


Abstract:
The cubic form of a hypersurface in the affine space is an important
invariant in affine differential geometry. In this talk, we shall give
some classification results for nondegenerate centroaffine surfaces in
terms of the cubic form and the induced connection.


Kentaro Saji 
Title: Geometric foliations of fronts 

Abstract:
In this talk, generic classification
of geometric foliations near singular points
of fronts and frontals will be discussed.
In particular, a normal form of swallowtail
will be introduced and asymptotic curves
and characteristic curves near swallowtail
will be given.


Masashi Yasumoto 
Title: Trivalent maximal surfaces in Minkowski space 

Abstract:
In this talk we introduce trivalent maximal surfaces in Minkowski
3space based on the combination of two ideas below. In particular, we see that such trivalent
maximal surfaces admit associated families and they also have variational properties and certain
singularities.
Lam investigated two types of trivalent surfaces in Euclidean 3space with vanishing mean curvature,
which are called trivalent minimal surfaces. The advantage of this discretization is that we can treat
both integrable geometric aspects of such minimal surfaces and their variational properties, which
generalize many previous works.
On the other hand, Yasumoto described quadrilateral surfaces (or, discrete surfaces) in Minkowski
3space with mean curvature identically 0, which are called discrete maximal surfaces. Unlike
the case of discrete surfaces in Euclidean 3space with vanishing mean curvature, it is shown that
discrete maximal surfaces generally have singularities, which occurs only in the case of discrete
constant mean curvature surfaces in Lorentzian spaceforms.
This talk is based on joint work with Wai Yeung Lam (Brown University).


Atsuhira Nagano 
Title: Toric K3 hypersurfaces and a Shimura variety


Abstract:
In the 19th century, elliptic modular functions appeared in the study of elliptic curves.
Special values of elliptic modular functions generate class fields over imaginary quadratic fields (Kronecker's Jugendtraum).
In this talk, the speaker will present an extension of the classical result by using K3 surfaces given by hypersurfaces
in toric 3folds. Namely, K3 surfaces are 2dimensional analogy of elliptic curves and its periods give
the moduli of K3 surfaces. Moreover, canonical models of Shimura varieties give natural extensions of Kronecker's
Jugendtraum. We will see a construction of an explicit model of a Shimura variety via techniques of periods of
toric K3 hypersurfaces.


Toru Kajigaya 
Title: On Lagrangian submanifolds with symmetries


Abstract:
Recently, Lagrangian submanifolds in a symplectic manifold M are of particular interests in several contexts,
e.g., the Lagrangian intersection theory, the Hamiltonian volume minimizing problem and the Lagrangian mean curvature flows.
In particular, homogeneous Lagrangian submanifolds, or more generally, Lagrangian submanifolds with symmetries
give nice examples of Lagrangian submanifolds with several properties (e.g., minimal, special, monotone, Hamiltonian stable etc). In this talk, I explain some known results for Lagrangian submanifolds with symmetries in a symplectic or Kahler manifold by using the notions of Hamitonian actions and moment maps. After that, I introduce the following own results:
(i) A classification result of homogeneous Lagrangian submanifolds in the complex hyperbolic spaces
(a joint work with Takahiro Hashinaga).
(ii) A HsiangLawson type theorem for minimal Lagrangian submanifolds in a Kahler manifold.


Hideo Takioka 
Title:
Infinitely many knots with the trivial $(2,1)$cable $\Gamma$polynomial


Abstract:
For coprime integers $p(>0)$ and $q$, the $(p,q)$cable $\Gamma$polynomial of a knot is
the $\Gamma$polynomial of the $(p,q)$cable knot of the knot, where the $\Gamma$polynomial
is the common zeroth coefficient polynomial of both the HOMFLYPT and Kauffman polynomials.
In this talk, we show that there exist infinitely many knots with the trivial $(2,1)$cable $\Gamma$polynomial,
that is, the $(2,1)$cable $\Gamma$polynomial of the unknot.
Moreover, we see that the knots have the trivial $\Gamma$polynomial,
the trivial first coefficient HOMFLYPT polynomial,
and the distinct Conway polynomials.


Kohei Iwaki 
Title: Exact WKB analysis and related topics


Abstract:
Exact WKB analysis, developed by Voros et.al., is an effective method for global study of
(singularly perturbed) ordinary differential equations defined on a complex domain.
After recalling fundamental facts about exact WKB analysis, I’ll talk about
relationships to other research topics, such as cluster algebras, topological recursion,
integrable systems of Painlev\’e type, etc.


Hitoshi Yamanaka 
Title: Invariant function on GKMrepresentation space


Abstract:
After recalling several notions, such as GKMrepresentations, GKMmanifolds and representation coverings,
I propose a conjecture concerning the existence of torusinvariant Morse functions on GKMmanifolds. Toward
solving the conjecture, I will examine the Hessian matrix of invariant functions on a GKMrepresentation spaces
at the origin. The result reveals a Morsetheoretic nature of the GKMconditon.


Shintaro Yanagida 
Title: Turaev's skein algebra for torus and a variant of homological mirror symmetry


Abstract: Turaev introduced skein algebras for surfaces as quantization of Goldman's
Lie algebras. Morton and Samuelson showed that the skein algebra for torus coincides with a specialization
of (the Drinfeld double of nonextended) Hall algebra of elliptic curves. We introduce a version of Hall algebra
for elliptic curves over a field with one element, and show that the skein algebra of torus is isomorphic to our
Hall algebra without specialization. We shall further explain a speculation on an extension of homological mirror
symmetry for torus.


Kentaro Mitsui 
Title: Models of torsors under elliptic curves


Abstract:
Any smooth curve of genus one over a general base field can be given as a torsor (a principal homogeneous space)
under an elliptic curve. In the case of a function field of a curve C, we may define an elliptic surface as a model of
the smooth curve, which is a fibration over the curve C. There are at most finitely many singular fibers. When the
curve C is defined over the field of complex numbers, these fibers were classified by Kodaira. We generalize his
result to the case where the curve C is defined over a general perfect field such as a finite field. We apply this
classification to study rational points on torsors over local fields.


Shintaro Akamine 
Title: Behavior of the Gaussian curvature of timelike minimal surfaces with singularities


Abstract:
A timelike minimal surface in the 3dimensional LorentzMinkowski space is a surface with a Lorentzian metric
whose mean curvature vanishes identically. The shape operator of a timelike surface is not always diagonalizable.
The diagonalizability of the shape operator of a timelike minimal surface is determined by the sign of the Gaussian
curvature away from flat points. In this talk we prove that the sign of the Gaussian curvature of any timelike minimal
surface is determined by the degeneracy and the orientations of the two null curves that generate the surface.
Moreover, we also investigate the behavior of the Gaussian curvature near singular points of a timelike minimal
surface. This talk is based on the preprint arXiv:1701.00238.


Joseph Cho 
Title: Deformation and singularities of maximal surfaces with planar curvature lines


Abstract:
Minimal surfaces with planar curvature lines in the Euclidean 3space have been studied since the late
19th century, and have connections to various different subjects of differential geometry. On the other
hand, the classification of maximal surfaces with planar curvature lines in the Minkowski 3space has
only recently been given. In this talk, we use an alternative method not only to refine the classification
of maximal surfaces with planar curvature lines, but also to show that there exists a deformation consisting
exactly of all such surfaces. Furthermore, we investigate the types of singularities that appear on maximal
surfaces with planar curvature lines.


ETC. 