
20080401TIMS Computational Science Software Development Workshop 2008Differential Geometry of Lagrangian submanifolds and related variational problems
Prof. Yoshihiro Ohnita ( Osaka City University, Japan & Osaka City University Advanced Mathematical Institute, Japan )2008  04  01 (Tue.)
09:00  09:50
308, Mathematics Research Center Building (ori. New Math. Bldg.)In this talk I will give a survey of my recent works and their environs on Lagrangian submanifolds in specific K\"ahler manifolds such as complex projective spaces, complex space forms and Hermitian symmmetric spaces and so on. Especially I shall discuss (1) the Hamiltonian stability problem of Lagrangian submanifolds, (2) the classification problems of homogeneous Lagrangian submanifolds, (3) the relationship between certain minimal Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres. This talk is mainly based on joint works with Amartuvshin Amarzaya(Natonal Univ. Mongolia), Hui Ma (Tsinghua Univ., Peking). 
20080401TIMS Computational Science Software Development Workshop 2008Surfaces of prescribed $p$mean curvature in the Heisenberg group
Prof. JihHsin Cheng ( Academia Sinica )2008  04  01 (Tue.)
14:00  14:50
308, Mathematics Research Center Building (ori. New Math. Bldg.)I will report on the study of the prescribed $p$% mean curvature equation in recent years. We interpreted the $p$mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve (in dimension $2$), and as a quantity in terms of calibration geometry. As a differential equation, the prescribed $p$mean curvature equation is degenerate (hyperbolic and elliptic) in dimension 2 while subelliptic in the nonsingular domain for higher dimensions. Also in dimension 2 with zero $p$mean curvature, it is a special type of scalar conservation law in the variable of the socalled characteristic angle. We analyzed the singular set and formulated an extension theorem. This allowed us to classify the entire solutions to this equation and to solve a Bernsteintype problem. As a geometric application, we proved the nonexistence of $C^{2}$ smooth hyperbolic surfaces having bounded $p$mean curvature, immersed in a pseudohermitian 3manifold. From the variational formulation of the equation, we studied the Dirichlet problem by proving the existence and the uniqueness of the ($p$)minimizers. An intriguing point is that, in dimension 2, a $C^{2}$ smooth solution from the PDE viewpoint may not be a minimizer. As an application to neurobiology, we could use such a $p$minimal surface theory as an image completion model for missing visual data in the first layer of the visual cortex. About the regularity of a $C^{1}$ smooth surface with continuous prescribed $p$mean curvature, we proved that the horizontal normal gains one more derivative by invoking the jump formulas along characteristic curves. Near a singular (or shock) curve we depicted the RankineHugoniot jump condition as characteristic incident and reflected angles being equal. In the last section we reviewed the second variation formula for a $C^{2}$ smooth $p$minimal surface in an arbitrary $3$dimensional pseudohermitian manifold. 
20080401TIMS Computational Science Software Development Workshop 2008Special solutions to Lagrangian mean curvature flow
Prof. YngIng Lee ( Department of Mathematics, National Taiwan University )2008  04  01 (Tue.)
10:00  10:50
308, Mathematics Research Center Building (ori. New Math. Bldg.)I have been interested in and working on the existence of special Lagrangian/Lagrangian minimal. There are several different approaches we have taken and obtained various results. In recent years, we took the approach of mean curvature flow. Singularities may occur in the flow. They usually model on selfsimilar solutions and translating solutions. Hence it is very important to study these solutions in studying the singularities. We have constructed many such solutions in a joint work with Joyce, and Tsui. Among our examples, there are three types that are of particular interests. One family is Lagrangian selfexpanders that are asymptotic to pair of Lagrangian planes. The Lagrangian angle can be made arbitrarily small, and these examples can serve as local model for surgery. Another family is translating solutions with arbitrarily small Lagrangian angle. Our example is rather surprising and indicates that the flow does not behave well even if under the almost calibrated assumption, which is different from the expectation in the past. Some other families of our examples give external Brakke solutions. 
20080401TIMS Computational Science Software Development Workshop 2008The LiYau Eigenvalue Estimates and CR Obata Theorem in Pseudohermitian Manifolds "
Prof. ShuCheng Chang ( Department of Mathematics, National Taiwan University )2008  04  01 (Tue.)
15:00  15:50
308, Mathematics Research Center Building (ori. New Math. Bldg.)In this talk, based on a jointed work with HungLin Chiu, we first have the CR analogue of LiYau's eigenvalue estimate on the lower bound estimate of psitive first eigenvalue of the subLaplacian in pseudohermitian $(2n+1)$manifolds. Second, we prove the CR Obata's theorem on a closed pseudohermitian manifold with vanishing torsion. The key step is a discovery of CR analogue of Bochner formula which involving the CR Paneitz operator and nonnegativity of CR Paneitz operator for any closed pseudohermitian $(2n+1)$manifold with $n>1$. 
20080401Computational Methods for microstructure of Liquid crystals and Liquid crystal flowsProf. Ping Lin ( University of Dundee, UK )

20080401TIMS Computational Science Software Development Workshop 2008Weakly reflective orbits and tangentially degenerate orbits of $s$representations
Prof. Takashi Sakai ( Tokyo Metropolitan University, Japan & Osaka City University Advanced Mathematical Institute, Japan )2008  04  01 (Tue.)
16:10  17:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)This talk is based on a joint work with Osamu Ikawa and Hiroyuki Tasaki. A linear isotropy representation of a Riemannian symmetric space is called an $s$representation. In this talk we will study some geometric properties of orbits of $s$representations as submanifolds in the Euclidean sphere. We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we give the classification of weakly reflective orbits and austere orbits of $s$representations. We observe that some wealky reflective orbits have a remarkable property, namely, they are tangentially degenerate. Furthermore these orbits provide many new examples of tangentially degenerate submanifolds which satisfy the Ferus equality. 
20080401OneDay Workshop on Differential GeometryApril 1, 2008
Room 308 , Mathematics Research Center Building (ori. New Math. Bldg.)
Website http://140.112.50.155/workshop/WorkshopNTU.pdf 
20080401Differential Geometry of Lagrangian submanifolds and related variational problemsYoshihiro Ohnita
20080401
09:00  09:50
308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080401Special solutions to Lagrangian mean curvature flowYngIng Lee
20080401
10:00 10:50
308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080401Black holes and compact Einstein manifoldsYoshitake Hashimoto 20080401
11:10  12:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080401Surfaces of prescribed $p$mean curvature in the Heisenberg groupJihHsin Cheng 20080401
14:00  14:50 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080401The LiYau Eigenvalue Estimates and CR Obata Theorem in Pseudohermitian ManifoldsShuCheng Chang 20080401
15:00  15:50 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080401Weakly reflective orbits and tangentially degenerate orbits of $s$representationsTakashi Sakai 20080401
16:10  17:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080401Computational Methods for microstructure of Liquid crystals and Liquid crystal flowsPing Lin 20080401
10:20:00  12:10:00 Computational Methods for microstructure of Liquid crystals and Liquid crystal flows405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080328Mathematical modeling and Scientifical ComputingVortex dynamics in meteorology
Prof. HungChi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008  03  28 (Fri.)
15:30  17:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080328Computational Science on MedicineModelling, Simulation and ApplicationMultiscale Modeling, Analysis and Simulation for Solid Materials
Prof. Ping Lin ( University of Dundee, UK )2008  03  28 (Fri.)
10:00  12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)Materials may be modeled by a large number of particles (or atoms) where any particle interacting with any other through a pair potential energy. The equillibrium configuration of the material is the minimizer of the total energy of the system. The computational cost is high since the number of atoms is huge. Recently much attention has been paid to the socalled quasicontinuum (QC) approximation which is a mixed atomistic/continuum model. 
20080328Multiscale Modeling, Analysis and Simulation for Solid MaterialsPing Lin 20080328
10:00:00  12:00:00 Multiscale Modeling, Analysis and Simulation for Solid Materials308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080328Vortex dynamics in meteorologyHungChi Kuo 20080328
15:30:00  17:00:00 Vortex dynamics in meteorology308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080327Seminar on Graph ColoringCircular consecutive choosability of graphs (VI)
Prof. Xuding Zhu ( Zhejiang Normal University, China )2008  03  27 (Thu.)
13:30  15:30
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080327Seminar on Graph ColoringCircular consecutive choosability of graphs (V)
Prof. Xuding Zhu ( Zhejiang Normal University, China )2008  03  27 (Thu.)
10:00  12:00
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080327Student seminar on differential geometryComparison Theorems in Riemannian Geometry2008  03  27 (Thu.)
19:00  20:30
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080327Circular consecutive choosability of graphs (V)Xuding Zhu 20080327
10:00:00  12:00:00 Circular consecutive choosability of graphs (V)405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080327Circular consecutive choosability of graphs (VI)Xuding Zhu 20080327
13:30:00  15:30:00 Circular consecutive choosability of graphs (VI)405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080327Comparison Theorems in Riemannian Geometry20080327
19:00:00  20:30:00 Comparison Theorems in Riemannian Geometry405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080326Physics and mathematics of dispersive shock waves: An introductionPhysics and mathematics of dispersive shocks: An introduction
Prof. Anatoly Kamchatnov ( Institute of Spectroscopy, Russian Academy of Science )2008  03  26 (Wed.)
15:30  17:20
405, Mathematics Research Center Building (ori. New Math. Bldg.)In this lecture, we shall introduce the Kortewegde Vries equation for description of combined action of nonlinear and dispersiveeffects. Periodic solution of this equation will be derived.Basic notions of Whitham modulation theory will be introduced.They will be illustrated by their application to a simple example of modulated linear waves. 
20080326Physics and mathematics of dispersive shocks: An introductionAnatoly Kamchatnov 20080326
15:30:00  17:20:00 Physics and mathematics of dispersive shocks: An introduction405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080325NCTS/TPE & TIMS Joint Geometry Seminar (20092010)VafaWitten theory for nonsimply laced gauge groups
Prof. Siye Wu ( National Tsing Hua University )2008  03  25 (Tue.)
14:00  15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080325NCTS/TPE & TIMS Joint Student Geometry Seminar (2008)VafaWitten theory for nonsimply laced gauge groups
Prof. Siye Wu ( National Tsing Hua University )2008  03  25 (Tue.)
14:00  15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080325VafaWitten theory for nonsimply laced gauge groupsSiye Wu 20080325
14:00:00  15:00:00 VafaWitten theory for nonsimply laced gauge groups308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080325VafaWitten theory for nonsimply laced gauge groupsSiye Wu 20080325
14:00:00  15:00:00 VafaWitten theory for nonsimply laced gauge groups308 , Mathematics Research Center Building (ori. New Math. Bldg.)