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)

Time: June 2 - 16, 2023
Room 202, Astronomy and Mathematics Building
Organizers:
You-Cheng Chou (Academia Sinica)
Tsung-Ju Lee (CMSA Harvard, TIMS)
Sz-Sheng Wang (Academia Sinica)

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)

Time: October 30, 2013 - December 30, 2022
Room 201 / 202, Astronomy and Mathematics Building
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
Organizers:
Chin-Lung Wang ( National Taiwan University )
Jeng-Daw Yu ( National Taiwan University )

The main goal of this program is to study the Scheme theory which is the foundation for modern algebraic geometry and the Cohomology theory which is the major technique to define numerical invariants.The audiences have to be equipped with the background on Chapter I and Chapter II (2.1~2.7) of the book “R. Hartshorne: Algebraic Geometry”.Contents:
1. Intrinsic geometry:
    1.1 Sheaves of differential: algebraic version of differential forms
    1.2 Formal schemes: they carry information about all the infinitesimal neighborhoods.
2. Cohomology theory:
    We intend to define it by using derived functors and to compute it by introducing Cech cohomology. We also show some important vanishing theorems and combine them with Serre duality to give some applications in flat family、smooth family, including Zariski’s main theorem and base change theorem of cohomology.Speakers: 陳宗震、郭婷婷、張茗遠、許嘉麟、莊家華Date: June 23 - September 1, 2022Time: Every Tuesday and Thursday, 14:00 - 16:00Venue: Room 201, Astro-Math Building, NTUOrganizer: Prof. Hui-Wen Lin (Dept. of Mathematics, NTU & TIMS)

Time: September 18, 2015- March 29, 2019 
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.) 
Organizers:
Liang-Chung Hsia ( National Taiwan Normal University )
Julie Tzu-Yueh Wang ( Academia Sinica )
Jing Yu ( National Taiwan University & Taida Institute for Mathematical Sciences )

Time: September 15, 2017 - January 12, 2018
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
Organizers:
Liang-Chung Hsia ( National Taiwan Normal University )
Julie Tzu-Yueh Wang ( Academia Sinica )
Jing Yu ( National Taiwan University & Taida Institute for Mathematical Sciences ),

Time: February 15 - June 28, 2017
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
Organizers:
Chen-Yu Chi ( National Taiwan University )
Yuan-Pin Lee ( University of Utah, USA )
Hui-Wen Lin ( National Taiwan University )
Chin-Lung Wang ( National Taiwan University )
Jeng-Daw Yu ( National Taiwan University )

Time: January 2, 2013 - December 19, 2016
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
Room 304, Mathematics Research Center Building (ori. New Math. Bldg.)
Room 430, Astronomy and Mathematics Building
Organizers: Weichung Wang ( National Taiwan University )

Time: September 14, 2009 - June 30, 2010
Room 405, Mathematics Research Center Building (ori. New Math. Bldg.) 
Room 504 , Freshman Classroom Building
Organizers:
Hung Chen ( National Taiwan University )
Chin-Tsang Chiang ( National Taiwan University )

Time: March 13, 2015 - December 7, 2016
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
Organizers:
Chen-Yu Chi ( National Taiwan University )
Hui-Wen Lin ( National Taiwan University )
Chin-Lung Wang ( National Taiwan University )

Time: 10:30 - 11:30, March 4 - June 20, 2016
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
Organizer: Jing Yu ( National Taiwan University & Taida Institute for Mathematical Sciences )

Marcos Petrúcio de Almeida Cavalcante 2015-12-03
16:00:00 - 17:00:00 R440 , Astronomy and Mathematics Building

Kazuaki Miyatani 2015-10-09
13:00:00 - 15:00:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Ching-Hung Lam 2015-10-05
13:30:00 - 15:30:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Kazuaki Miyatani 2015-09-18
13:00:00 - 15:00:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Ching-Hung Lam 2015-08-31
13:30:00 - 15:30:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Shin-Wei Liu ( National Taiwan University )
2015-06-12  09:10 - 11:00
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

Chantal David 2015-06-05
13:30:00 - 14:30:00 103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Min Ru 2015-06-05
10:30:00 - 11:30:00 101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Chih-Chung Liu 2015-06-04
15:00:00 - 16:00:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Dinesh Thakur 2015-05-29
13:30:00 - 14:30:00 103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Matt Papanikolas 2015-05-22
13:30:00 - 14:30:00 103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Stephen Lichtenbaum 2015-05-15
10:30:00 - 11:30:00 101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Yu Yasufuku 2015-05-15
14:00:00 - 15:00:00 103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Yi-Hsuan Lin 2015-04-24
10:30:00 - 11:30:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Chieh-Yu Chang 2015-04-24
13:30:00 - 14:30:00 103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Thai Hoang Le 2015-04-17
13:30:00 - 14:30:00 103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Akio Tamagawa 2015-03-27
13:30:00 - 14:30:00 103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Wentang Kuo 2015-03-20
13:30:00 - 14:30:00 103 , Mathematics Research Center Building (ori. New Math. Bldg.)