Hyeonbae Kang2008-03-20
14:00:00 - 15:00:00Small volume imaging308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Gunther Uhlmann2008-03-20
15:20:00 - 16:20:00Invisibility308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Reconstruction methods for inverse problems
Prof. Gen Nakamura ( Hokkaido University, Japan )2008 - 03 - 19 (Wed.)
11:20 - 12:20
308, Mathematics Research Center Building (ori. New Math. Bldg.)For the recent 10 years the several reconstruction methods have been proposed for inverse scattering problems and inverse boundary value problems. For instance they are the linear sampling method, factorization method, probe method, singular sources method, no-response test, range test and enclosure method etc. These reconstruction methods are non-iterative methods which means that they are not data fitting methods such as the least square methods or the regularized version of those. They provide how to reconstruct the unknowns directly from the given measured data. The lecture will touch the basic ideas of those methods and discuss about their convergence and relations between them.

Invisibility
Prof. Gunther Uhlmann ( Department of Atmospheric Sciences, University of Washington, USA )2008 - 03 - 19 (Wed.)
10:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)We describe construction of electromagnetic parameters that make objects invisible to electromagnetic waves.

Small volume imaging
Prof. Hyeonbae Kang ( Inha University, South Korea )2008 - 03 - 19 (Wed.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)Lecture 1. Method of Small Volume Expansions and its Applications to Medical Imaging I will explain the mathematical theory of the small volume expansions in the context of the conductivity equation, which is the simplest possible model. I then discuss how this mathematical theory can be applied to an electrical impedance tomography problem to detect small inclusions buried inside a body. Lecture 2. Mathematical Analysis for MRElastography and Applications MRElastography is a recent modality to image the internal part of body using the internal measurements of the displacement vectors. One of the advantages of the imaging method using MRE over other methods is that it can detect the stiffness parameter of the tissue, by which we can distinguish malign cancer from benign cancer. In this lecture I will explain a new method of reconstruction using MRE data. Lecture 3. New reconstruction methods for Magneto-acoustic Imaging. A new and promising technique in the medical imaging is to excite a local part of body using acoustic or ultrasonic focusing and to measure changes due to the excitation. I will explain new reconstruction methods for the Magneto-acoustic imaging and the vibration potential tomography.

Gunther Uhlmann2008-03-19
10:00:00 - 11:00:00Invisibility308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Gen Nakamura2008-03-19
11:20:00 - 12:20:00Reconstruction methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hyeonbae Kang2008-03-19
14:00:00 - 15:00:00Small volume imaging308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Ricci flow
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 03 - 18 (Tue.)
09:10 - 12:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Model Checking for ROC Regression Analysis2008 - 03 - 18 (Tue.)
13:30 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)An overview of the paper “Model Checking for ROC Regression Analysis” by Cai and Zheng (2007) is given. A possible research topic and extension is also explored in this talk.

Prof. Jenn-Nan Wang  ( Department of Mathematics, National Taiwan University )

Prof. Minking Eie  ( National Chung Cheng University )

Scientific Computing on Hemodynamics-Computational Challenges and its Application to Surgical Planning for Cardiovascular Diseases
Prof. Tony Wen-Hann Sheu ( Department of Engineering Science and Ocean Engineering, National Taiwan University )2008 - 03 - 14 (Fri.)
15:00 - 16:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Multiscale modeling, asymptotic analysis, and their applications in finance (I,II)
Prof. Chuan-Hsiang Han ( Department of Quantitative Finance, National Tsing Hua University )2008 - 03 - 14 (Fri.)
10:20 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)During the last two decades, financial mathematics has emerging as an active branch in applied mathematics. Problems arising from modern finance are often resolved from applications of various techniques including probability and statistics, differential equations, optimization and control theory, scientific computations, etc. In this talk, the evaluation of financial derivatives under an incomplete market is treated by two approaches. First, multiscale modeling in volatility processes is shown to be powerful for calibration to the term structure of implied volatility surface. In mathematical terms, an inverse problem is solved from asymptotics of a PDE by means of singular and regular perturbations. Second, we consider the usage of Monte Carlo and Quasi Monte Carlo simulations to solve high dimensional PDEs. A variance reduction method, namely the martingale control variate method is proposed to improve the convergent speed. The martingale control comprises of a low dimensional PDE obtained from the homogenization of multiple time scales. This method turns out to be general enough to solve for variational inequalities. In financial terms, a delta hedging portfolio is effective to reduce the risk of a financial derivative. In the end, some challenging problems are discussed.

Minking Eie 2008-03-14
14:30:00 - 15:20:00 New Euler sums with two branches308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Jenn-Nan Wang 2008-03-14
13:30:00 - 14:30:00 An Brief Introduction to Inverse Problems and Invisibility405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Chern-Simons-Higgs Models in Superconductivity (2)
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 03 - 13 (Thu.)
11:10 - 12:20
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Informal Discussions
Prof. Xuding Zhu ( Zhejiang Normal University, China )2008 - 03 - 13 (Thu.)
13:30 - 15:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Informal Discussions
Prof. Xuding Zhu ( Zhejiang Normal University, China )2008 - 03 - 13 (Thu.)
10:10 - 12:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Seminar on Differential Geometry
Prof. Yu-Chao Tu ( University of Utah, USA )2008 - 03 - 13 (Thu.)
19:00 - 20:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)我們希望集合一些大學部學生或碩博士生一起學Differential Geometry，從基礎的領域：manifolds, variation,curvatures, Jacobian fields,fundamental form 等，到一些進階的領域如comparison theorems,Toponogov's theorem, Homonic functions, Eigenvalue problems, heat kernels,deformation, conformality 等。目的是對 Differential Geometry 有一個基礎而多方面的認識，瞭解其在歷史上和 現在的一些重要課題。

Some topics in the study of parabolic equations
Prof. Jong-Shenq Guo ( Tamkang University )2008 - 03 - 13 (Thu.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Physics and mathematics of dispersive shocks: An introduction
Prof. Anatoly Kamchatnov ( Institute of Spectroscopy, Russian Academy of Science )2008 - 03 - 12 (Wed.)
15:30 - 17:20
405, Mathematics Research Center Building (ori. New Math. Bldg.)In this lecture, we shall study nonlinear effects by Riemann's method applied to one-dimensional compressible fluid dynamics equations. Riemann invariants will be introduced for this system. Solution of the resulted equations will be found by the hodograph method. The method will be illustrated by examples of dam problem and expansion of a gas slab.

Ricci flow
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 03 - 11 (Tue.)
09:10 - 12:10
405, Mathematics Research Center Building (ori. New Math. Bldg.)

The Strong Oka’s Lemma, bounded plurisubharmonic functions and the -Neumann problem
Prof. Mei-Chi Shaw ( University of Notre Dame, USA )2008 - 03 - 11 (Tue.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)In this talk we discuss the Cauchy-Riemann equations on pseudoconvex domains with Lipschitz domains in complex manifolds. A unified approach to the regularity of the -Neumann problem for Lipschitz domains will be given using the strong Oka’s lemma. We will also discuss the relationship between the strong Oka’s lemma,bounded plurisubharmonic exhaustion functions and their relationship with the regularity of the -Neumann problem in complex projective spaces. Applications to the nonexistence of Levi-flat hypersurfaces in complex projective spaces will be discussed.

Causality of Wave Propagation (I)
Prof. I-Liang Chern ( Department of Mathematics, National Taiwan University )2008 - 03 - 07 (Fri.)
14:00 - 15:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Jung-Chao Ban ( National Dong Hwa University (Meilun Campus) )2008 - 03 - 07 (Fri.)
10:00 - 11:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Churn-Simons-Higgs Models in Superconductivity (I)
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 03 - 06 (Thu.)
11:10 - 12:20
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Blowup rate estimate for a system of semilinear parabolic equations
Prof. Satoshi Sasayama ( Hokkaido University, Japan )2008 - 03 - 06 (Thu.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)We study the blowup rate estimate for a system of semilinear parabolic equations. The blowup rate depends on whether the two components of the solution of this system blow up simultaneously or not.

Prof. Yu-Chao Tu  ( University of Utah, USA )

Circular consecutive choosability of graphs (II)
Prof. Xuding Zhu ( Zhejiang Normal University, China )2008 - 03 - 06 (Thu.)
13:30 - 15:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)