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課程名稱 |
群表現一
Group Representations (Ⅰ) |
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開課學期 |
105-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
于 靖 |
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課號 |
MATH5105 |
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課程識別碼 |
221 U0430 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二3,4(10:20~12:10)星期四3(10:20~11:10) |
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上課地點 |
天數304天數304 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1051MATH5105_gprep |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
Contents.
We introduce group representations for finite groups, compact groups, and locally compact groups. The later includes p-adic groups, adelic groups, i.e. automorphic representations of algebraic groups over global fields. We will use algebraic tools primarily. But we will also bring in tools from harmonic analysis, Haar integrals, complex analysis, and distribution theory. We will do classification of representations for classes of groups. Will also apply representation theory to problems arising and connected with other fields of mathematics, particularly number theory and arithmetic geometry. |
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課程目標 |
Representations of groups play a central role in mathematics. Great progress had been made in the last century which lead to solutions of many key problems in mathematics. Currently, the developments of representation theory of groups involves most active frontier researches. Our goal is to introduce students this very important field. This course is suitable for advanced undergraduates as well as beginning graduate students. It connects all the basic courses, algebra and analysis. It underlines to students the fact that combining all the fundamental tools previously learnt is essential for doing modern mathematics researches. |
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課程要求 |
Prerequisite: Linear Algebra, Algebra, Analysis.
We will start with five themes: modular representations, representations of symmetric groups, computing with induced representations, compact groups and harmonic analysis, a tale of two groups. Each student should choose at least one theme among the five. We make use the Overleaf platform on the webe sites where every student can write exercises, comments, discussions directly on the site at anytime, while the professor charging this course may also look closely at the progress of students on the Overleaf site and making comments. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
J. -P. Serre, Linear representations of finite groups, Springer GTM. |
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參考書目 |
Sagan, B. Representations of the symmetric groups, Springer GTM. |
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評量方式
(僅供參考) |
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