On the singularities of the Szego projection for ''0,q'' forms
Dr. Chin-Yu Hsiao ( École Polytechnique, France & Göteborgs universitet, Sweden )2008 - 10 - 07 (Tue.)
14:00 - 15:50
308, Mathematics Research Center Building (ori. New Math. Bldg.)In this work we completely study the heat equation method of Menikoff-Sjostrand and apply it to the Kohn Laplacian defined on a compact orientable connected CR manifold. We then get the full asymptotic expansion of the Szego projection for (0,q) forms. This generalizes a result of Boutet de Monvel and Sjostrand for (0,0) forms. Our mail tool is Fourier integral operators with complex valued phase functions of Melin and Sjostrand. We hope that this talk can serve as an introduction to certain micolocal techniques with applications to CR geometry and complex geometry.

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 10 - 07 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏微分方程的學生組成，主要要學習elliptic PDE的基本理論，歡迎有興趣的同學來參加。

Hidemitsu Wadade 2008-10-07
18:30:00 - 20:00:00 Golbarg-Trudinger, second order, Elliptic PDE308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Chin-Yu Hsiao 2008-10-07
14:00:00 - 15:50:00 On the singularities of the Szego projection for ''0,q'' forms308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )008 - 10 - 03 (Fri.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Online Learning with Matrix Exponentiated Gradient Updates
Dr. Hsin-Hsiung Huang ( Institute of Statistical Science , Academia Sinica )2008 - 10 - 03 (Fri.)
13:30 - 15:00
404, Freshman Classroom BuildingTsuda, Ratsch and Warmuth (2006) address the problem of learning a symmetric positive definite matrix. They offer kernelized updates which involve a calculation based on matrix logs and matrix exponentials. These updates preserve the symmetry and positive definiteness. On the other hand, Vishwanathan, Schraudolph and Smola (2006) provide an online support vector machine (SVM) that uses the stochastic meta-descent (SMD) algorithm to adapt its step size automatically. Based on their method, we derive updates that allow us to perform the step size adaptation of kernel principal component analysis (PCA). Further, the online kernel PCA is an online SVM framework to loss functions, where its gradient trace parameter is no longer a coefficient vector but an element of the RKHS.

Two-Scale Convergence and Homogenization of Periodic Structures
Prof. Jiann-Sheng Jiang ( Tung Fang Institute of Technology )2008 - 10 - 03 (Fri.)
12:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Mathematical Modeling
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 10 - 03 (Fri.)
15:30 - 17:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Jiann-Sheng Jiang 2008-10-03
12:30:00 - 14:30:00 Two-Scale Convergence and Homogenization of Periodic Structures308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hung-Chi Kuo 2008-10-03
15:30:00 - 17:30:00 Mathematical Modeling308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hsin-Hsiung Huang 2008-10-03
13:30:00 - 15:00:00 Online Learning with Matrix Exponentiated Gradient Updates404 , Freshman Classroom Building

Norden Huang 2008-10-03
09:00:00 - 11:00:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

PARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 10 - 02 (Thu.)
09:00 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Bifurcation theory and its applications on the convection problems
Prof. Chun-Hsiung Hsia ( Department of Mathematics, National Taiwan University )2008 - 10 - 02 (Thu.)
15:30 - 16:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)In the talk, we introduce the concepts and the machinery of bifurcation theory. Bifurcation theory studies the qualitative changes of the solutions for a system of equations while the control parameters of the equations vary. We will start with algebraic equations and ordinary differential equations to demonstrate basic ideas of bifurcation theory. We present different types of bifurcations including steady-state bifurcation, Hopf bifurcation and attractor bifurcation. We will conclude this talk by showing applications on the convection problems.

Chun-Hsiung Hsia 2008-10-02
15:30:00 - 16:30:00 Bifurcation theory and its applications on the convection problems308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Chang-Shou Lin 2008-10-02
09:00:00 - 12:00:00 PARTIAL DIFFERENTIAL EQUATIONS-I308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Introducing a complexity to spatial graphs
Prof. Akio Kawauchi ( Osaka City University, Japan )2008 - 10 - 01 (Wed.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)We introduce a notion which we call the warping degree for every connected spatial graph (possibly, with vertices of degree one) by defining admissible regular diagrams of the spatial graph. By definition the warping degree takes a value in non-negative integers, by which we can define a notion of a complexity among all the spatial graphs of any given connected graph.
For every connected spatial graph without vertices of degree one, this notion is used to define two kinds of notions of topological invariants. We observe that one of the notions coincides with the unknotting number for a spatial connected plane graph, in particular for a knot.

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 10 - 01 (Wed.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Akio Kawauchi 2008-10-01
14:00:00 - 15:00:00 Introducing a complexity to spatial graphs308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Norden Huang 2008-10-01
09:00:00 - 11:00:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 09 - 26 (Fri.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Data-driven Selection of Penalty in Lasso
Prof. Hung Chen ( Department of Mathematics, National Taiwan University )2008 - 09 - 26 (Fri.)
15:30 - 17:00
301, Freshman Classroom BuildingDue to rapid development in large dimensional data acquisitions such as microarray, scientists look for useful methods on predicting a quantitative measurement when number of predictors p is much greater than n, the sample size. In this talk, we will address issues arose from the data-driven selection of penalty in Lasso when n is of the same order p. In particular, we discuss orthogonal predictors and Mallows’ Cp. BIC will also be addressed.

Mathematical Modeling
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 09 - 26 (Fri.)
15:30 - 17:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Introduction to Homogenization Theory I, II
Prof. Ying-Hong Liu ( Research Center for Applied Sciences, Academia Sinica )2008 - 09 - 26 (Fri.)
12:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)With the development of the modern technique, we have ability to construct the composite material needed in the environment. Usually, these devices are weaved in the micro- or nano-scales and they satisfy the inhomogeneous electromagnetic or elastic wave equations. However, for our human sensors, we always investigate them in the long wavelength or in the low frequency limit, mathematically, that means averaged governing equations describe the bulk behaviors of the composite system in the macro-scale. Therefore, how to carry out the transformation from the inhomogeneous to homogeneous governing equations is the main issue we want to address. In this talk, we start with one-dimensional elastodynamics and then introduce the typical procedure of homogenization analysis. In addition, several examples would be addressed: Darcy’s law, heat conduction in a composite and other applications.

Ying-Hong Liu 2008-09-26
12:30:00 - 14:30:00 Introduction to Homogenization Theory I, II308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hung-Chi Kuo 2008-09-26
15:30:00 - 17:30:00 Mathematical Modeling308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hung Chen 2008-09-26
15:30:00 - 17:00:00 Data-driven Selection of Penalty in Lasso301 , Freshman Classroom Building

Norden Huang 2008-09-26
09:00:00 - 11:00:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

PARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 09 - 25 (Thu.)
09:00 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Chang-Shou Lin 2008-09-25
09:00:00 - 12:00:00 PARTIAL DIFFERENTIAL EQUATIONS-I308 , Mathematics Research Center Building (ori. New Math. Bldg.)