Commutative Algebra and Related Topics
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1 Commutative Algebra and Related Topics May 22(Mon.) June 2(Fri.), 2017 This seminar is supported by the following institutions: Okinawa Institute of Science and Technology Graduate University Tancha, Onna-son, Kunigami-gun Okinawa, Japan MSRI OIST JAMS RIMS Organizers: Shihoko Ishii Kazuhiko Kurano Ken-ichi Yoshida Local organizer: Shinobu Hikami Advisor: Kei-ichi Watanabe (Tokyo Woman s Christian University) (Meiji University) (Nihon University) (OIST) (Nihon University) 1
2 Time Schedule (1st week) Location: Sea Side House Main Campus Seminar Room (1F) * Chura Hall (3F) Conference Hall May 22 (Mon.) /Seaside House 9:00 9:30 Opening ceremony 9:30 10:45 Lecture 1 (Claudia Polini, Univ. Notre Dame) Integral closure, minimal reduction, cores (1) 11:15 12:30 Lecture 2 (Ryo Takahashi, Nagoya Univ.) The category of maximal Cohen-Macaulay modules (1) 15:30 16:30 Exercise for Lecture 2 (Takahashi) Takahashi, Matsui 16:45 17:45 Exercise for Lecture 1 (Polini) Polini, Ma 15:30 16:30 Exercise for Lecture 1 (Polini) Martinez, support 16:45 17:45 Exercise for Lecture 2 (Takahashi) Araya, support 18:00 19:30 -Dinner*- Notice: Any participant and organizer can eat dinner at Chura Hall (18:00 19:30) on May 21 2
3 May 23 (Tue.) /Main Campus Sea Side House Main Campus 9:30 10:45 Lecture 1 (Claudia Polini, Univ. Notre Dame) at Conference Room Integral closure, minimal reduction, cores (2) 11:15 12:30 Lecture 2 (Ryo Takahashi, Nagoya Univ.) at Conference Room The category of maximal Cohen-Macaulay modules (2) 12:30 14:00 -Lunch - 14:00 15:30 Lecture (David Eisenbud, MSRI) at B250 The Development of a Mathematics Research Center: MSRI and its History 15:30 17:45 Campus Tour 18:00 19:30 -Dinner - Planning a random walk: Commutative Algebra in Statistics The Development MSRI opened its doors to its first programs in the fall of of a Mathematics Over the years it has grown and changed, becoming a center Research Center: known very widely among mathematicians. I will survey the MSRI and its History original motivations and the subsequent development, and give some account of the many activities in which the Institute now engages. Planning a random walk: Commutative Algebra in Statistics. I ll explain how a basic construction in commutative algebra called Groebner bases can help to measure statistical variations by random sampling. 3
4 May 24 (Wed.) /Seaside House 9:30 10:45 Lecture 1 (Claudia Polini, Univ. Notre Dame) Integral closure, minimal reduction, cores (3) 11:15 12:30 Lecture 2 (Ryo Takahashi, Nagoya Univ.) The category of maximal Cohen-Macaulay modules (3) 12:30 12:45 Photo session (we take a group photo) 12:45 14:00 -Lunch*- 15:30 16:30 Exercise for Lecture 2 (Takahashi) Takahashi, Matsui 16:45 17:45 Exercise for Lecture 1 (Polini) Polini, Ma 15:30 16:30 Exercise for Lecture 1 (Polini) Martinez, support 16:45 17:45 Exercise for Lecture 2 (Takahashi) Araya, support 18:00 19:30 Reception * 4
5 May 25 (Thu.) /Seaside House 9:30 10:45 Lecture 1 (Claudia Polini, Univ. Notre Dame) Integral closure, minimal reduction, cores (4) 11:15 12:30 Lecture 2 (Ryo Takahashi, Nagoya Univ.) The category of maximal Cohen-Macaulay modules (4) 15:30 16:30 Exercise for Lecture 2 (Takahashi) Takahashi, Araya, 16:45 17:45 Exercise for Lecture 1 (Polini) Polini, Martinez 15:30 16:30 Exercise for Lecture 1 (Polini) Ma, support 16:45 17:45 Exercise for Lecture 2 (Takahashi) Matsui, support 18:00 19:30 -Dinner*- 5
6 May 26 (Fri.) /Seaside House 9:30 10:45 Lecture 1 (Claudia Polini, Univ. Notre Dame) Integral closure, minimal reduction, cores (5) 11:15 12:30 Lecture 2 (Ryo Takahashi, Nagoya Univ.) The category of maximal Cohen-Macaulay modules (5) 15:30 16:30 Exercise for Lecture 2 (Takahashi) Takahashi, Araya 16:45 17:45 Exercise for Lecture 1 (Polini) Polini, Martinez 15:30 16:30 Exercise for Lecture 1 (Polini) Ma, support 16:45 17:45 Exercise for Lecture 2 (Takahashi) Matsui, support 18:00 19:30 -Dinner*- Please pay the Excursion fee (JPY 2,000 cash only!) to the OIST staff by 17:00, May 26 (Fri) if you want to participate our excursion. 6
7 May 27 (Sat.) 9:30 17:45 Excursion (Tour conductor: Ken-ichi Yoshida) Excursion fee: JPY 2,000 per person. Notice: Lunch is NOT included in this tour! 9:30 LV OIST seaside house 10:40 14:30 Ocean Expo Park Churaumi Aquarium (Lunch Time) 14:50 15:40 Nakijin Castle ruins 16:10 17:10 Okashigoten Confectionary Shop 17:30 AR OIST seaside house 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 final 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, reflecting 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. May 28 (Sun.) 9:00 Free Time Please eat Lunch (Dinner) at a favorite restaurant! 7
8 Time Schedule (2nd week) May 29 (Mon.) /Seaside House 9:30 10:45 Lecture 1 (Claudiu Raicu, Notre Dame) Determinantal ideals (1) 11:15 12:30 Lecture 2 (Shunsuke Takagi, Univ. Tokyo) The F-pure thresholds (1) 15:30 16:30 Exercise for Lecture 2 (Takagi) Takagi, Ejiri 16:45 17:45 Exercise for Lecture 1 (Raicu) Raicu, Jeffries 15:30 16:30 Exercise for Lecture 1 (Raicu) Boocher, support 16:45 17:45 Exercise for Lecture 2 (Takagi) Sato, support 18:00 19:30 -Dinner*- 8
9 May 30 (Tue.) /Seaside House 9:30 10:45 Lecture 1 (Claudiu Raicu, Notre Dame) Determinantal ideals (2) 11:15 12:30 Lecture 2 (Shunsuke Takagi, Univ. Tokyo) The F-pure thresholds (2) 15:30 16:30 Exercise for Lecture 2 (Takagi) Takagi, Ejiri 16:45 17:45 Exercise for Lecture 1 (Raicu) Raicu, Jeffries 15:30 16:30 Exercise for Lecture 1 (Raicu) Boocher, support 16:45 17:45 Exercise for Lecture 2 (Takagi) Sato, support 18:00 19:30 -BBQ at sea side- 9
10 May 31 (Wed.) /Seaside House 9:30 10:45 Lecture 1 (Claudiu Raicu, Notre Dame) Determinantal ideals (3) 11:15 12:30 Lecture 2 (Shunsuke Takagi, Univ. Tokyo) The F-pure thresholds (3) 15:30 16:30 Exercise for Lecture 2 (Takagi) Takagi, Sato 16:45 17:45 Exercise for Lecture 1 (Raicu) Raicu, Boocher 15:30 16:30 Exercise for Lecture 1 (Raicu) Jeffries, support 16:45 17:45 Exercise for Lecture 2 (Takagi) Ejiri, support 18:00 19:30 -Dinner*- 10
11 June 1 (Thu.) /Seaside House 9:30 10:45 Lecture 1 (Claudiu Raicu, Notre Dame) Determinantal ideals (4) 11:15 12:30 Lecture 2 (Shunsuke Takagi, Univ. Tokyo) The F-pure thresholds (4) 15:30 16:30 Exercise for Lecture 2 (Takagi) Takagi, Sato 16:45 17:45 Exercise for Lecture 1 (Raicu) Raicu, Boocher 15:30 16:30 Exercise for Lecture 1 (Raicu) Jeffries, support 16:45 17:45 Exercise for Lecture 2 (Takagi) Ejiri, support 18:00 19:30 -Dinner*- 11
12 June 2 (Fri.) /Seaside House 8:00 9:00 9:30 10:45 11:15 12:30 12:30 14:00 -Breakfast*Lecture 1 (Claudiu Raicu, Notre Dame) Determinantal ideals (5) Lecture 2 (Shunsuke Takagi, Univ. Tokyo) The F-pure thresholds (5) -Lunch*- No common dinner (You can eat dinner at your favorite restaurants in the town.) 12
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