Summer Graduate School

Commutative Algebra and Related Topics

May 22, 2017 - June 02, 2017

Parent Program:	--
Location:	Okinawa Institute of Science and Technology, Japan

Organizers

Shinobu Hikami (Okinawa Institute of Science and Technology), LEAD Shihoko Ishii (Tsinghua University), Kazuhiko Kurano (Meiji University), Ken-ichi Yoshida (Nihon University)

Speaker(s)

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David Eisenbud (University of California, Berkeley)
Claudia Polini (University of Notre Dame)
Claudiu Raicu (University of Notre Dame)
Shunsuke Takagi (University of Tokyo)
Ryo Takahashi (Nagoya University)

Description

The purpose of the school will be to introduce graduate students to foundational results in commutative algebra, with particular emphasis of the diversity of the related topics with commutative algebra. Some of these topics are developing remarkably in this decade and through learning those subjects the graduate students will be stimulated toward future research.

Group Photo
Program Agenda

Text/Exercise problems:
Polini
Raicu
Takagi
Takahashi

Keywords and Mathematics Subject Classification (MSC)

Tags/Keywords

Core of ideals
multiplier ideals
category of modules
determinantal ideals
Frobenius map
modulo p reduction

Primary Mathematics Subject Classification

Secondary Mathematics Subject Classification

13Dxx - Homological methods in commutative ring theory {For noncommutative rings, see 16Exx; for general categories, see 18Gxx}

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MSRI Collegiality Statement

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Map & Directions to SLMath

Schedule, Notes/Handouts & Videos

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Calendar View

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May 22, 2017
Monday

08:00 AM - 09:00 AM		Breakfast (Seaside House)
Location Seaside House Video -- Abstract -- Supplements -- Show Detail
09:00 AM - 09:30 AM		Welcome address, Guidance of the school, Safety instructions.
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Integral closure, minimal reduction, cores (1) Claudia Polini (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The category of maximal Cohen-Macaulay modules Ryo Takahashi (Nagoya University)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Free time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Exercise
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		Dinner
Location -- Video -- Abstract -- Supplements -- Show Detail

May 23, 2017
Tuesday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Integral closure, minimal reduction, cores (2) Claudia Polini (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The category of maximal Cohen-Macaulay modules (2) Ryo Takahashi (Nagoya University)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:30 PM		Lecture by Eisenbud at Conference hall in the main campus David Eisenbud (University of California, Berkeley)
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Campus tour in OIST
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		Dinner
Location -- Video -- Abstract -- Supplements -- Show Detail

May 24, 2017
Wednesday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Integral closure, minimal reduction, cores (3) Claudia Polini (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The category of maximal Cohen-Macaulay modules (3) Ryo Takahashi (Nagoya University)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 12:45 PM		Take Group Photo
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Free time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Exercise
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		Reception
Location -- Video -- Abstract -- Supplements -- Show Detail

May 25, 2017
Thursday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Integral closure, minimal reduction, cores (4) Claudia Polini (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The category of maximal Cohen-Macaulay modules (4) Ryo Takahashi (Nagoya University)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Free time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Exercise
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		Dinner
Location -- Video -- Abstract -- Supplements -- Show Detail

May 26, 2017
Friday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Integral closure, minimal reduction, cores (5) Claudia Polini (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The category of maximal Cohen-Macaulay modules (5) Ryo Takahashi (Nagoya University)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Free time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Exercise
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		Dinner
Location -- Video -- Abstract -- Supplements -- Show Detail

May 27, 2017
Saturday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 05:45 PM		Excursion (Tour conductor: Ken-ichi Yoshida)
Location -- Video -- Abstract Nakijin Castle, or Nakijin Gusuku (Ryukyuan castle or fortress) is located in Nakijin Village, Okinawa, Japan. It was the residence of the Ryukyuan Kingdom governor and is currently in ruins. Work began on its construction in the late 13th century and it had reached its nal form by the beginning of the 15th century. The castle is strategically sited on a lone hill, well defended by natural features (river, cliffs and deep valley). The fortress includes several sacred Utaki groves, re ecting the gusuku's role as a center of religious activity. It is famous for the Hikan cherries which bloom in northern Okinawa between mid-January and early February. http://nakijinjo.jp/english/index.html Supplements -- Show Detail

May 29, 2017
Monday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Determinantal ideals (1) Claudiu Raicu (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The F-pure thresholds (1) Shunsuke Takagi (University of Tokyo)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Free time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Exercise
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		Dinner
Location -- Video -- Abstract -- Supplements -- Show Detail

May 30, 2017
Tuesday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Determinantal ideals (2) Claudiu Raicu (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The F-pure thresholds (2) Shunsuke Takagi (University of Tokyo)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Free time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Exercise
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		BBQ at Seaside
Location -- Video -- Abstract -- Supplements -- Show Detail

May 31, 2017
Wednesday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Determinantal ideals (3) Claudiu Raicu (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The F-pure thresholds (3) Shunsuke Takagi (University of Tokyo)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Free time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Exercise
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		Dinner
Location -- Video -- Abstract -- Supplements -- Show Detail

Jun 01, 2017
Thursday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Determinantal ideals (4) Claudiu Raicu (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The F-pure thresholds (4) Shunsuke Takagi (University of Tokyo)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Free time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea time
Location -- Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 05:00 PM		Exercise
Location -- Video -- Abstract -- Supplements -- Show Detail
06:00 PM - 07:00 PM		Dinner
Location -- Video -- Abstract -- Supplements -- Show Detail

Jun 02, 2017
Friday

08:00 AM - 09:00 AM		Breakfast
Location -- Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:45 AM		Lecture 1 Determinantal ideals (5) Claudiu Raicu (University of Notre Dame)
Location -- Video -- Abstract -- Supplements -- Show Detail
11:15 AM - 12:30 PM		Lecture 2 The F-pure thresholds (5) Shunsuke Takagi (University of Tokyo)
Location -- Video -- Abstract -- Supplements -- Show Detail
12:30 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail