|
課程名稱 |
流型上的分析技巧
Analysis on manifolds |
|
開課學期 |
104-1 |
|
授課對象 |
理學院 數學系 |
|
授課教師 |
馬梓銘 |
|
課號 |
MATH5011 |
|
課程識別碼 |
221 U6680 |
|
班次 |
|
|
學分 |
3 |
|
全/半年 |
半年 |
|
必/選修 |
選修 |
|
上課時間 |
星期二7,8,9(14:20~17:20) |
|
上課地點 |
普405 |
|
備註 |
總人數上限：80人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1041MATH5011 |
|
課程簡介影片 |
|
|
核心能力關聯 |
本課程尚未建立核心能力關連 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
課程概述 |
1. Elliptic differential operators, hodge decomposition and heat kernel
2. Dirac operators and Atiyah-Singer index theorem
3. Witten deformation and Morse inequality |
|
課程目標 |
n this course, we explore the relations between analytic quantities associated to
elliptic operators and topology of underlying manifolds. We will focus on two important
theorems, namely the Atiyah-Singer index theorem and the Witten's proof of Morse inequality,
using analysis of the heat kernel and asymptotic behaviour of eigenvalues respectively. |
|
課程要求 |
待補 |
|
預期每週課後學習時數 |
|
|
Office Hours |
每週二 17:20~18:20 |
|
指定閱讀 |
待補 |
|
參考書目 |
1. Berline, Getzler, and Vergne, Heat Kernels and Dirac Operators, Springer-Verlag, 1992.
2. Roe, Elliptic Operators, Topology, and Asymptotic Methods, Longman, 1988.
3. Weiping Zhang, Lectures on Chern-Weil theory and Witten deformation, World Scientific Pub. Co. Inc., 2002 |
|
評量方式
(僅供參考) |
|
|