研究集会

2018年10月22日，台湾師範大学 (NTNU = National Taiwan Normal University) と九大が大学間協定を結ぶのに合わせて，来日されるNTNUの3名の先生方とIMIとで，以下の mini-workshop を開催する運びとなりました．学生も含めて，ご興味のある方はご参加ください．


プログラム


13:20 - opening
Osamu Saeki (Director, IMI, KU)
Chun-Chi Lin (Chair, Dept. of Math., NTNU)

Talks
13:35 - 13:55 Hiroyuki Ochiai "Algebraic analysis and related topics"
Abstract:
In this twenty minutes talk, I will introduce my research interest such as algebraic analysis, representation theory, invariant theory, D-modules, special functions, hypergeometric systems, integrable systems, special values, zeta functions, absolute mathematics (theory of a field of one element), generating functions, combinatorial problems. I also mention my teaching subject such as actuaries and collaboration with industries such as computer graphics and materials. I hope some of them will be a possible connection/interface with your organization.

14:00 - 14:20 Mei-Heng Yueh "Computational Conformal Geometry with Applications"
Abstract:
Computational conformal geometry is an interdisciplinary field based on the theories of conformal geometry as well as computational algorithms. It has been widely applied to carry out 3D image processing tasks, such as surface remeshing, registration, rendering, and alignment. Especially when the geometry is complicated, a parameterization of the surface can be used to simplify the shape of the domain. In this talk, I will introduce my recent works on the computation of surface parameterizations, and demonstrate applications on computer graphics.

14:25 - 14:45 Hayato Waki "Ill-posed semidefinite program"
Abstract:
SemiDefinite Program (SDP) is one of the convex optimization problems, and used in the various research fields, such as combinatorial optimization, control theory, machine learning, quantum information. My recent work on SDP is related to the ill-posedness, e.g., why ill-posed SDP obtained form some applications appears and how we remove the ill-posedness. I talk a brief survey on SDP and the ill-posedness in SDP.

(break)

15:00 - 15:20 Jein-Shan Chen "Two smooth support vector machines for ε-insensitive regression"
Abstract:
In this talk, we introduce two new smooth support vector machines for ε-insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to ε-support vector regression (ε-SVR). More specifically, using the proposed smoothing functions, we employ the smoothing Newton method to solve the systems of smooth equations. The algorithm is shown to be globally and quadratically convergent without any additional conditions. Numerical comparisons among different values of parameter are also reported.

15:25 - 15:45 Chun-Chi Lin "Geometric flows of elastic curves/networks"
Abstract:
The main topic of this project is the evolution of elastic curves and networks. A typical example of a planar network is the ``Mercedes-Benz''-symbol of three curves joined at one point and with the other endpoints lying on a given boundary. Networks configurations are interesting in applications since they naturally arise in phase transitions. Evolution of networks of three or more curves under mean curvature flow has received a lot of attentions in recent years. A lot of interesting and yet unexplored mathematical questions arise when one looks at higher order flows, such as the elastic one, that is the gradient flow of the elastic energy. There are several different approaches in studying evolutions of networks. Here we use PDE approach and treat evolution of networks as evolution of joined curves with certain boundary conditions.

15:50 - 16:10 Takashi Kagaya "On geometric flows of hypersurfaces with contact angle"
Abstract:
The Brakke flow is introduced as a measure-theoretic weak solution to the mean curvature flow. By virtue of this introduction, we can deal with the motion of surface or network by its mean curvature with "intense" singularities and topological changes. In this talk, we consider the mean curvature flow in a domain and with free boundary in the boundary of the domain. For this free boundary problem, the mean curvature flow should "pop" upon tangential contact with the boundary of the domain. Therefore, it is natural to study Brakke's mean curvature flow with free boundary in order to analysis topological changes by the "popping" and I will introduce known and my works related to this problem.


18:00 Dinner at Harbor House BBQ Garden