|
課程名稱 |
多重zeta值與迭代積分
Multiple zeta values and iterated integrals |
|
開課學期 |
109-1 |
|
授課對象 |
理學院 數學系 |
|
授課教師 |
佐藤信夫 |
|
課號 |
MATH5249 |
|
課程識別碼 |
221 U8860 |
|
班次 |
|
|
學分 |
3.0 |
|
全/半年 |
半年 |
|
必/選修 |
選修 |
|
上課時間 |
星期五7,8,9(14:20~17:20) |
|
上課地點 |
天數302 |
|
備註 |
總人數上限：10人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1091MATH5249_ |
|
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 |
Introduction to the theory of multiple zeta values and iterated integrals |
|
課程目標 |
There is a class of numbers with nice arithmetic properties called period of motives. Among the periods of general motives, periods of mixed Tate motives are in a sense the most fundamental objects and multiple zeta values (MZVs in short) are simplest examples of the periods of mixed Tate motives. Despite the speciality of their appearance, MZVs generate all the periods of mixed Tate motives over Z thus forms an important class of numbers.
This introductory course is an attempt to give a thorough overview of the theory of multiple zeta values and more general iterated integrals on the projective line as well as its related topics, from various points of view, and introduce to what extent we know so far and what future perspective we have about the research in this area.
MZVs have two different aspects; the series expression and the iterated integral expression. The former half of the course mainly focuses on the series aspect where we shall discuss the topics such as conical zeta values, finite analog of MZVs, multiple Eisenstein series in relation with the original MZVs. Then in the latter half, we shall focus on the iterated integral expression of the MZVs, and see their geometric nature. The topics would include an introduction to the basics of mixed Tate motives and explain how they are related to MZVs, as well as the theory of hyperlogarithms and its applications to the Grothendieck-Teihmuller theory. We shall discuss both the nice special structures and the general theory of hyperlogarithms. Throughout the course, some of the hard theorems will be given without proof. |
|
課程要求 |
The audience will be expected to be familiar with:
NECESSARY: Complex analysis, Basics of commutative algebra,
RECOMMENDED: Elliptic modular forms, Linear differential equations |
|
預期每週課後學習時數 |
|
|
Office Hours |
|
|
指定閱讀 |
|
|
參考書目 |
Jianqiang Zhao, Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values, World Scientific, 2016
Jose Ignacio Burgos, Gil and Javier Fresan, Multiple zeta values: from numbers to motives, Clay Mathematics Proceedings
(currently available online at http://javier.fresan.perso.math.cnrs.fr/mzv.pdf) |
|
評量方式
(僅供參考) |
|
|