課程資訊
課程名稱
量子上同調入門
Introduction to Gromov-Witten theory 
開課學期
105-1 
授課對象
理學院  數學研究所  
授課教師
李元斌 
課號
MATH5034 
課程識別碼
221 U6900 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期二8,9(15:30~17:20)星期五8,9(15:30~17:20) 
上課地點
天數304天數304 
備註
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1051MATH5034_GWT1 
課程簡介影片
 
核心能力關聯
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課程大綱
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課程概述

This is a 2-semester sequence of introductory courses in Gromov--Witten theory. The course will assume only basic knowledge of algebraic geometry and algebraic topology, and spend a few weeks building necessary tools.

The format of this class will include 2 hours of lectures and 2 hours of student seminar each week. The lecture should cover the basics of Gromov--Witten theory. However, since Gromov--Witten theory requires a lot of preparatory material, it would not be productive to teach it during the regular lectures. Instead, the students will be required to present the assigned material in turns (and preferably in English, although the language will be discussed among the participants). The potential benefits of this approach are manifold. Not only do the students learn better this way, but I also get to know them better. In the future, if the students plan to apply for graduate study, I will be able to write convincing letters for them. Furthermore, this way the lectures can move at a brisk pace while the background material will be discussed in details during the student seminars.

Possible topics for the two semester sequence include

1. Moduli of curves and maps
2. Virtual fundamental cycles
3. Equivariant cohomology/intersection theory and (Virtual) localization
4. Givental's formulation
5. Relative and logarithmic Gromov--Witten theory and degeneration formula
6. Orbifold Gromov--Witten theory
7. Quasimap theory
8. Donaldson--Thomas theory and other flavors of Gromov--Witten-like theories 

課程目標
To learn the basics of Gromov--WItten theory and moduli of curves. 
課程要求
Students who are taking this class for credits are required to attend lectures and give reports on assigned topics, likely once in a month. 
預期每週課後學習時數
 
Office Hours
 
參考書目
To be assigned in class and at the website

https://sites.google.com/site/gromovwittenclass/

Those who are interested in getting some ideas of the subject in advance may consult:

1. Moduli of curves, by Harris and Morrison (ebook available upon request)
2. An invitation to quantum cohomology, by Kock and Vainsencher
3. Notes on stable maps and quantum cohomology, by Fulton and Pandharipande
4. Introduction to GWT and CTC, my notes from Grenoble Lectures in the summer 2011
5. Lectures on Donaldson--Thomas theory, by Davesh Maulik
6. Localization in Gromov--Witten theory and orbifold Gromov--Witten theory, by Melissa Liu
7. Frobenius manifolds, quantuam cohomology, and moduli spaces, by Yuri I. Manin 
指定閱讀
To be assigned in class and at the website

https://sites.google.com/site/gromovwittenclass/ 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Oral reports 
90% 
Students will be asked to report on the assigned topics, roughly once a month. 
2. 
performance during lectures 
10% 
 
 
課程進度
週次
日期
單元主題
第1週
9/13,9/16  General discussions about the class. Introduction and moduli of curves.