Introduction to the Minimal Model Program and SingularitiesCourse Description
This course will introduce the Minimal Model Program (MMP), including singularities in MMP and the cone theorem. We will also study 3-dimensional terminal and canonical singularities in more details. Topics will include:
• Mori’s existence theorem of rational cuves
• Singularities in MMP
• Cone theorems
• Elliptic surface singularities and 3-fold canonical singularities
• Classification of 3-fold terminal singularities
• Existence of 3-fold flips (after Shokurov)Course Objectives
The goal of this course is to provide general knowledge and skills in
birational geometry.Prerequisites
Knowledge of algebraic geometry is required:
• R. Hartshornes, Algebraic Geometry
• A. Beauville, Complex algebraic surfaces
Preliminary knowledge of the theory of deformation will be very helpful.Textbook
J. Kollar and S. Mori, Birational Geometry of Algebraic Varieties, 1998Date: Every Monday and Thursday
Sep. 4 ~ Dec. 15, 2023
Time: 10 : 20 ~ 12 : 10
Place: Room 201 (Astro-Math Building 2F, NTU)
Speaker: Sz-Sheng Wang (Academia Sinica)

臺大數學科學中心將於8月23日(星期三)舉辦一個關於代數幾何經驗傳承的特別活動，邀請過去與現在曾於中心擔任研究助理並從事相關研究的夥伴參加。活動有兩個部分：第一部分9:00 ~ 11:00由目前5位年輕的研究生報告他們最近的工作， 每一個報告包含15分鐘的pdf presentation以及5分鐘問答。第二部分11:30 ~ 14:00是午餐座談會，由6位目前任職於國內外研究機構並且於暑期造訪臺大的學者與大家分享他們的研究歷程，最後是分組座談。Part I: 9:00 - 11:00
李雙言 (NTU) p-adic norm and K-equivalence
吳博生 (NTU) New results on Lame equation with unitary monodromy
莊秉勳 (NTU) On the periods of twisted moments of the Kloosterman connection
莊家華 (NTU) Correspondence under simplicial toric flops
陳宗震 (NTU) Toric fiber product under flopsPart II: 11:30 - 14:00 經驗傳承座談會
王賜聖 (Academia Sinica)
李宗儒 (CMSA, Harvard and National Cheng-Kung U.)
范祐維 (Tsinghua U., Beijing)
許綺云 (Université de Lille and Santa Clara U.)
周祐正 (Academia Sinica)
賴冠文 (U. of Bonn and Academia Sinica)日期：2023年8月23日 (星期三)
時間：9:00 ~ 14:00
地點：Room 519 (Astro-Math Building, NTU)
主辦人：王金龍 (NTU, TIMS)、林惠雯 (NTU)

Abstract: We plan to study Calabi-Yau threefolds with Picard number up to 2 or with complex moduli up to 2 dimensions. Conjecturally, CY3 in both classes are closely related under the global mirror map, which exchanges the A side (Kahler moduli) and the B side (complex moduli). Moreover, such a global mirror correspondence should also be compatible with extremal transitions. The mirror correspondence between quintic CY and its mirror quintic is the most well studied example. The famous BCOV theory on the B side suggests fundamental identities (e.g. Yamaguchi-Yau) on the A side and eventually helps to find methods to attack the higher genus curve counting for the quintics. Such a correspondence is mostly unknown for two parameter models except for the very recent preprint by Hosono and Takagi arXiv:2103.08150v2 on abelian fibered CY3. It is our hope that a closer study on the existing literature may lead to a better understanding on the subject. In doing so, we will discuss various topics on deformations of CY3, including the Bryant-Griffiths period map and toric GKZ systems with emphasizes on 1d or 2d models. Birational geometry on CY3 also form an essential technique and it appears that a good knowledge on non-Kahler CY3 is indispensable.Topics and Speakers:Higher genus counting of quintics
    You-Cheng CHOU (AS)
    Ping-Hsuan CHUANG (NTU)
    Po-Sheng WU (NTU)
Complex moduli, period maps and VHS
    Tsung-Ju LEE (CMSA Harvard, TIMS)
    Shuang-Yen LEE (NTU)
Birational geometry of CY3
    Sz-Sheng WANG (AS)
Constructions of non-Kahler CY3
    Hsueh-Yung LIN (NTU, NCTS)

BCOV theory
Chin-Lung WANG (NTU, TIMS)Date: June 2, 6, 9, 13, 16, 2023
Time: 9:00 - 11:00, 13:00 - 15:00
Venue: Room 202, Astro-Math Building, NTU
Organizer: You-Cheng CHOU (Academi Sinica), Tsung-Ju LEE (CMSA Harvard, TIMS), Sz-Sheng WANG (Academia Sinica)

Programs:
(1) Analytic continuations of quantum cohomology under flops in higher dimensions.
(2) Recent development of Gromov—Witten theory, especially for Calabi—Yau 3-folds.Main speakers:
Ping-Hsun Chuang (NTU)
Po-Sheng Wu (NTU)
Shunag-Yen Lee (NTU)
You-Cheng Chou (Academia Sinica)
Sz-Sheng Wang (Academia Sinica)Date: July 12 (Tue), 14 (Thr), 19 (Tue), 21 (Thr), 27 (Wed), 7/28 (Thr)
Time: 9:30 - 11:30
Venue: Room 204 (TIMS discussion room) (AMB 2F)
Organizers: Chin-Lung Wang and Hui-Wen Lin (TIMS and NTU)