Physics and mathematics of dispersive shocks: An introduction
Prof. Anatoly Kamchatnov ( Institute of Spectroscopy, Russian Academy of Science )2008 - 05 - 14 (Wed.)
15:00 - 17:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Ricci flow
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 05 - 13 (Tue.)
09:10 - 12:10
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Schwarzschild Geometry
Mr. Po-Yao Chang ( Department of Mathematics, National Taiwan University )2008 - 05 - 13 (Tue.)
16:10 - 17:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Golbarg-Trudinger, second order, Elliptic PDE.
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 05 - 13 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Jing Yu  ( Department of Mathematics, National Taiwan University & Taida Institute for Mathematical Sciences )

One-Dimensional Dynamics Ⅱ
Prof. Jung-Chao Ban ( National Dong Hwa University (Meilun Campus) )2008 - 05 - 12 (Mon.)
09:30 - 11:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Imaging of Multiple Targets in Rician/Rayleigh Fading Media
Prof. Albert C. Fannjiang ( University of California, Davis, USA )2008 - 05 - 09 (Fri.)
11:10 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)We consider imaging targets that are cluttered in a random medium. We assume only the phase information of the average Green function. We derive the stability condition NB > M for the time reversal imaging method where N is the number of antennas, B the number of frequencies and M the number of point targets. We demonstrate the method for a medium consisting of many randomly distributed particles.

Marriage and Divorce
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 05 - 09 (Fri.)
15:30 - 17:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Martingales, Brownian Motions, and Levy Processes.
Prof. Narn-Rueih Shieh ( Department of Mathematics, National Taiwan University )2008 - 05 - 09 (Fri.)
09:30 - 10:40
308, Mathematics Research Center Building (ori. New Math. Bldg.)In this talk, we shall talk on martingales, with view on the Doob-Meyer Decompotion. Then we talk on Brownian motion, with view on its martingale properties. Finally we introduce Levy processes via Brownian first passage times.

What are networks？
Prof. Wei-Chung Liu ( Institute of Statistical Science , Academia Sinica )2008 - 05 - 09 (Fri.)
13:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Comparison Theorems in Riemannian Geometry
Mr. Justin Yang ( Department of Mathematics, National Taiwan University )2008 - 05 - 08 (Thu.)
19:00 - 20:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Chern-Simons-Higgs Models in Superconductivity Ⅵ
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 05 - 08 (Thu.)
11:10 - 12:20
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 - 05 - 07 (Wed.)
15:30 - 17:20
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 05 - 06 (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。

Ricci flow
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 05 - 06 (Tue.)
09:10 - 12:10
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Toward the QMMP via A + B model
Prof. Chin-Lung Wang ( Department of Mathematics, National Taiwan University )2008 - 05 - 06 (Tue.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Chaos in Deterministic Continuous Systems, Poincare and Lorenz
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 05 - 02 (Fri.)
15:30 - 17:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Chiung-Jue Sung  ( National Tsing Hua University )

Lectures on Differential Geometry
Mr. Yang-Kai Lue ( Department of Mathematics, National Taiwan University )2008 - 05 - 01 (Thu.)
19:00 - 20:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Harmonic forms and Weight Poincar\'{e} inequality
Prof. Chiung-Jue Sung ( National Tsing Hua University )2008 - 05 - 01 (Thu.)
15:00 - 16:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Chiung-Jue Sung 2008-05-01
15:00:00 - 16:00:00 Harmonic forms and Weight Poincar\'{e} inequality308 , 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 - 04 - 30 (Wed.)
15:30 - 17:20
405, Mathematics Research Center Building (ori. New Math. Bldg.)In this lecture, we will shall show that the KdV hierarchy has a Hamiltonian structure and all Hamiltonians commute with each other with respect to the Poisson bracket. This leads to notion of complete integrability of the KdV hierarchy equations. After that, we shall give a few simple applications of the developed theory: (1) derivation of periodic solutions (2) new simple derivation of Whitham equations (3) cnoidal wave solution of the whole hierarchy (4) Whitham equations for higher KdV equations.

An Eigenvector Variability Plot
Prof. I-Ping Tu ( Institute of Statistical Science , Academia Sinica )2008 - 04 - 29 (Tue.)
13:30 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)Principal components analysis is perhaps the most widely used method for ex-ploring multivariate data. In this talk, we present a variability plot composed of measures on the stability of each eigenvectors over samples as a data exploration tool. We also show that this variability measure gives a good measure on the intersample variability of eigenvectors through asymptotic analysis. For distinct eigenvalues, the asymptotic behavior for this variability measure is comparable to the size of the asymptotic covariance of the eigenvector in Anderson (1963). A simulation for functional data analysis with dimension p greater than sample size n is provided. The proposed variability plot is successful to distinguish the signal components, noise components and 0 eigenvalue components. Applying this method on a gene expression data set for a gastric cancer study, many hills on the proposed variability plot are observed. When the intersample variability of eigenvectors is considered, the cuto point on informative eigenvectors should not be on the top of the hill as suggested by the proposed variability plot.

Geometric aspects of random walks on a crystal lattice
Prof. Motoko Kotani ( Tohoku University, Japan )2008 - 04 - 29 (Tue.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Ricci flow
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 04 - 29 (Tue.)
09:10 - 12:10

One-Dimensional Dynamics
Prof. Jung-Chao Ban ( National Dong Hwa University (Meilun Campus) )2008 - 04 - 28 (Mon.)
09:30 - 11:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Collapsing Bridges: Broughton and Tacoma Narrows
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 04 - 25 (Fri.)
15:30 - 17:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

2D, 3D, and Full-field Breast Ultrasound Computer-aided Diagnosis
Prof. Ruey-Feng Chang ( Department of Computer Science and Information Engineering , National Taiwan University )2008 - 04 - 25 (Fri.)
13:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)In our previous 2D CAD studies, the texture and speckle information are used to diagnose tumors and these features are classified by the neural network, support vector machine, data mining, and retrieval techniques. Recently, we dealt with 3D CAD techniques including 3D texture analysis, spiculation detection, and microcalcification identification. From these studies, using 3D techniques for CAD represents a potentially significant advantage over 2D. Vessels provide blood supply for tumor expansion and also increase the opportunity for tumor cells to enter the blood or lymph circulation. In contrast to normal vessels, tumor vasculature is highly disorganized, tortuous and dilated, with uneven diameter and excessive branching. We propose a method extracting morphological features from 3-D breast power Doppler ultrasound and a CAD system adopting these features to classify tumor. Ultrasound elastography is a newly developed technique of imaging the tissue elasticity and it has been used clinically to examine a variety of breast lesions in patients. In general, the breast cancer tissue is harder than the adjacent normal breast tissue. Recently, we have developed a CAD for color elastography from Hitachi EUB-8500. Recently, several companies such as Aloka in Japan and U-systems in USA have developed new whole breast ultrasound screening machines. We have developed a computer-aided detection system for these fully automatic screening systems. By using the full-view images, our fully automatic CAD system for whole breast screening could be used to find suspicious frames and locate the approximate positions of tumors in the US images. By the way, an automatic rib detection will be introduced in this talk.

Anomalous Dispersion and Superluminal Propagation
Ko-Shin Chen ( Department of Mathematics, National Taiwan University )2008 - 04 - 25 (Fri.)
11:00 - 12:10
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Ricci Flow
Mr. Ye-Kai Wang ( Department of Mathematics, National Taiwan University )2008 - 04 - 24 (Thu.)
13:00 - 14:00
103, Old Mathematics Building