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課程名稱 |
Frobenius 流形專題
Topics on Frobenius Manifolds |
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開課學期 |
106-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
王金龍 |
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課號 |
MATH5082 |
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課程識別碼 |
221 U8290 |
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班次 |
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學分 |
3.0 |
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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 |
星期五2,3,4(9:10~12:10) |
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上課地點 |
天數101 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1062MATH5082_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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課程概述 |
Various constructions of Frobenius Manifolds, including (1) isomonodromic deformations, (2) Saito’s theory on singularities, (3) quantum cohomology, as well as (4) moduli space of Calabi-Yau manifolds. |
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課程目標 |
There are a few, though not many, excellent references on Frobenius manifolds. They are mainly discussing fundamental examples arising from researches in the last few decades. While these examples are very important and the constructions are highly non-trivial and technically very involved, one thing is still lacking in the development of the whole theory, namely the categorical framework of Frobenius manifolds. It is thus the purpose of this course that I try to investigate the categorical concepts when introducing these constructions. For example, the notion of analytic continuations will be introduced to connect various different objects in various different moduli points. Besides homework presentations, students are required to report on chapters in [1], [2] and [3], as well as some assigned research articles. |
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課程要求 |
修課同學需要具備微分幾何, 代數拓墣, 代數幾何的基本知識與操作能力, 並至少在其中兩項有一年以上的基礎. |
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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 |
[1] Manin: Frobenius Manifolds, Quantum Cohomology, and Moduli Sapces
[2] Hertling: Frobenius Manifolds and Moduli Spaces for Singularities
[3] Dubrovin: Geometry of 2D topological field theory, (1993), LNM 1620 |
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參考書目 |
[4] Sabbah: Isomonodromic Deformations and Frobenius Manifolds
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
作業/平時報告 |
50% |
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2. |
期末報告 |
50% |
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週次 |
日期 |
單元主題 |
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第1週 |
3/02 |
Definition of Frobenius manifolds |
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第2週 |
3/09 |
WDVV equations with Euler fields |
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第3週 |
3/16 |
Affine connections on curves with projective structures |
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第4週 |
3/23 |
Universal Torus/TCFT and their moduli/Sigma models |
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第5週 |
3/30 |
Semisimple Frobenius manifolds and canonical coordinates |
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第6週 |
4/06 |
Spring break |
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第7週 |
4/13 |
Darboux--Egoroff system |
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第8週 |
4/20 |
Isomonodromic deformations I |
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第9週 |
4/27 |
Isomonodromic deformations II |
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第10週 |
5/04 |
Monodromy groups |
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第11週 |
5/11 |
Coxeter groups and Frobenius structures |
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第12週 |
5/18 |
Explicit computations for the A_n case |
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第13週 |
5/25 |
Frobenius structure on Hurwitz spaces |
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第14週 |
6/01 |
Integrable hierachies |
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第15週 |
6/08 |
Proof of Witten's conjecture |
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第16週 |
6/15 |
Report I |
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第17週 |
6/22 |
Report II |
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