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Existence of higher dimensional crepant resolutions and generlization of the McKay correspondence

Research Project

Project/Area Number 18K03209
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionThe University of Tokyo (2019-2023)
Nagoya University (2018)

Principal Investigator

ITO YUKARI  東京大学, カブリ数物連携宇宙研究機構, 教授 (70285089)

Co-Investigator(Kenkyū-buntansha) 石井 亮  名古屋大学, 多元数理科学研究科, 教授 (10252420)
伊山 修  東京大学, 大学院数理科学研究科, 教授 (70347532)
Project Period (FY) 2018-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2022: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2021: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordscrepant resolution / McKay correspondence / tilting theory / Austanfer-Reiten theory / dimar model / exceptional correction / クレパント特異点解消 / マッカイ対応 / 有限次元代数 / Cohen-Macaulay加群 / Tilting module / Auslander対応 / ダイマー模型 / exceptional collection / ねじれ自由類 / 特異点解消 / 非可換代数 / 特異点 / 団傾部分圏 / 非可換クレパント解消
Outline of Final Research Achievements

Ito characterizes the exceptional set of resolutions of quotient singularities of a finite group G and their corresponding irreducible representations when resolutions of singularities are obtained. Ishii investigates the Dimer models of quotient singularities and exceptional corrections on Hirzebruch surfaces. Iyama gave an invited lecture at the International Congress of Mathematicians (ICM) in 2018 and conducted research on triangulated categories, cluster categories, and AR theory. Additionally, international research meetings were held in 2018, 2020, and 2023, and in April 2023, a collection of papers related to this research project titled "McKay correspondence, tilting theory and related topics" was published as Advanced Studies in Pure Mathematics 88.

Academic Significance and Societal Importance of the Research Achievements

本研究課題の成果のうち、伊藤と石井は、2次元で知られているMcKay対応の3次元への一般化について、導来圏や新たに定義したessential representation、ダイマー模型を用いて研究をし、伊山は多元環の表現論の研究を発展させた点が数学の代数幾何学における学術的意義である。また上記の出版論文集には、サーベイも含まれ、本研究課題周辺を新たに勉強したい学生や研究者の教科書ともなる有意義な一冊である。

Report

(7 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (151 results)

All 2024 2023 2022 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (22 results) Journal Article (38 results) (of which Int'l Joint Research: 31 results,  Peer Reviewed: 35 results,  Open Access: 15 results) Presentation (82 results) (of which Int'l Joint Research: 53 results,  Invited: 76 results) Book (2 results) Remarks (4 results) Funded Workshop (3 results)

  • [Int'l Joint Research] Universidad Autnoma de Madrid (UAM)(スペイン)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Universite de Picardie Jules Verne(フランス)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Norges teknisk naturvitenskapelige(ノルウェー)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Uppsala University(スウェーデン)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] ウプサラ大学(スウェーデン)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] シュツットガルト大学(ドイツ)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] モントリオール大学(カナダ)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] ノルウェイ工科大学(ノルウェー)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] ノースカロライナ州立大学(米国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research]

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] KIAS/Incheon National University(韓国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Glasgow/Norwich(英国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Munster(ドイツ)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] UA Madrid(スペイン)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Kanzas(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research]

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] University of Bath/University of Glasgow/University of East Anglia(英国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] UAM(スペイン)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Tsinghua University(中国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] The University of Kansas/The University of Utah/North Carolina State University(米国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Universitaet Bonn/Universitaet Stuttgart(ドイツ)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research]

    • Related Report
      2018 Research-status Report
  • [Journal Article] Auslander-Reiten theory in extriangulated categories2024

    • Author(s)
      Osamu Iyama, Hiroyuki Nakaoka, Yann Palu
    • Journal Title

      Transactions of the American Mathematical Society, Series B

      Volume: 11 Issue: 8 Pages: 248-305

    • DOI

      10.1090/btran/159

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Classifying subcategories of modules over Noetherian algebras2024

    • Author(s)
      Iyama Osamu、Kimura Yuta
    • Journal Title

      Advances in Mathematics

      Volume: 446 Pages: 109631-109631

    • DOI

      10.1016/j.aim.2024.109631

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodic trivial extension algebras and fractionally Calabi-Yau algebras2024

    • Author(s)
      Aaron Chan, Erik Darpoe, Osamu Iyama, Rene Marczinzik
    • Journal Title

      Ann. Sci. Ec. Norm. Super. (4)

      Volume: -

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Triangulations of prisms and preprojective algebras of type A2024

    • Author(s)
      Osamu Iyama, Nathan Williams
    • Journal Title

      Int. Math. Res. Not. IMRN

      Volume: -

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Dimer models and group actions2023

    • Author(s)
      Ishii Akira、Nolla Alvaro、Ueda Kazushi
    • Journal Title

      Mathematische Zeitschrift

      Volume: 306 Issue: 1 Pages: 1-24

    • DOI

      10.1007/s00209-023-03394-4

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Lattice theory of torsion classes: Beyond Tau-tilting theory2023

    • Author(s)
      Demonet Laurent、Iyama Osamu、Reading Nathan、Reiten Idun、Thomas Hugh
    • Journal Title

      Transactions of the American Mathematical Society, Series B

      Volume: 10 Issue: 18 Pages: 542-612

    • DOI

      10.1090/btran/100

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Representation Theory of Geigle-Lenzing Complete Intersections2023

    • Author(s)
      Herschend Martin、Iyama Osamu、Minamoto Hiroyuki、Oppermann Steffen
    • Journal Title

      Memoirs of the American Mathematical Society

      Volume: 285 Issue: 1412 Pages: 1-141

    • DOI

      10.1090/memo/1412

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Representation theory of quivers and finite-dimensional algebras2023

    • Author(s)
      Claire Amiot, William Crawley-Boevey, Osamu Iyama, Jan Schroer
    • Journal Title

      Oberwolfach Rep.

      Volume: 20 Pages: 397-486

    • Related Report
      2023 Annual Research Report
    • Open Access / Int'l Joint Research
  • [Journal Article] Representation theory of Geigle-Lenzing complete intersections2023

    • Author(s)
      M. Herschend, O. Iyama, H. Minamoto, S. Oppermann
    • Journal Title

      Mem. Amer. Math. Soc.

      Volume: -

    • Related Report
      2022 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Lattice theory of torsion classes2023

    • Author(s)
      L. Demonet, O. Iyama, N. Reading, I. Reiten, H. Thomas
    • Journal Title

      Trans. Amer. Math. Soc. Ser. B

      Volume: -

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Auslander-Reiten theory in extriangulated categories2023

    • Author(s)
      O. Iyama, H. Nakaoka, Y. Palu
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: -

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Positive Fuss Catalan Numbers and Simple-Minded Systems in Negative Calabi-Yau Categories2022

    • Author(s)
      Iyama Osamu、Jin Haibo
    • Journal Title

      International Mathematics Research Notices

      Volume: to appear Issue: 8 Pages: 6624-6647

    • DOI

      10.1093/imrn/rnab369

    • Related Report
      2023 Annual Research Report 2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Distributive lattices and Auslander regular algebras2022

    • Author(s)
      Iyama Osamu、Marczinzik Rene
    • Journal Title

      Advances in Mathematics

      Volume: 398 Pages: 108233-108233

    • DOI

      10.1016/j.aim.2022.108233

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Representation theory of Geigle-Lenzing complete intersections2022

    • Author(s)
      M. Herschend, O. Iyama, H. Minamoto, S. Oppermann
    • Journal Title

      Mem. Amer. Math. Soc.

      Volume: to appear

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Lattice theory of torsion classes2022

    • Author(s)
      L. Demonet, O. Iyama, N. Reading, I. Reiten, H. Thomas
    • Journal Title

      Trans. Amer. Math. Soc. Ser. B

      Volume: to appear

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] G-constellations and the maximal resolution of a quotient surface singularity2020

    • Author(s)
      Ishii Akira
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 50 Issue: 3 Pages: 375-398

    • DOI

      10.32917/hmj/1607396494

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The McKay correspondence2020

    • Author(s)
      Yukari Ito
    • Journal Title

      代数幾何学シンポジウム記録

      Volume: 1 Pages: 96-105

    • NAID

      120006952787

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] Osamu Iyama2020

    • Author(s)
      Erik Darpoe
    • Journal Title

      d-Representation-finite self-injective algebras

      Volume: 362 Pages: 1-50

    • DOI

      10.1016/j.aim.2019.106932

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Quotients of triangulated categories and equivalences of Buchweitz, Orlov, and Amiot-Guo-Keller2020

    • Author(s)
      Iyama, Osamu; Zhang, Xiaojin
    • Journal Title

      Amer. J. Math.

      Volume: 142 Pages: 1641-1659

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Gorenstein modifications and Q-Gorenstein rings2020

    • Author(s)
      Dao, Hailong; Iyama, Osamu; Takahashi, Ryo; Wemyss, Michael
    • Journal Title

      J. Algebraic Geom.

      Volume: 29 Pages: 729-751

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Higher preprojective algebras, Koszul algebras, and superpotentials2020

    • Author(s)
      Grant, Joseph; Iyama, Osamu
    • Journal Title

      Compos. Math.

      Volume: 156 Issue: 12 Pages: 2588-2627

    • DOI

      10.1112/s0010437x20007538

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Gorenstein modifications and Q-Gorenstein rings2020

    • Author(s)
      H. Dao, O. Iyama, R. Takahashi, M. Wemyss
    • Journal Title

      J. Algebraic Geom

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Classifying τ -tilting modules over the Auslander algebra of K[x]/(x n)2020

    • Author(s)
      O. Iyama, X. Zhang
    • Journal Title

      J. Math. Soc. Japan

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Quotients of triangulated categories and Equivalences of Buchweitz, Orlov and Amio,Guo&Keller2020

    • Author(s)
      O. Iyama, D. Yang
    • Journal Title

      Amer. J. Math

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Higher preprojective algebras, Koszul algebras and superpotentials2020

    • Author(s)
      J. Grant, O. Iyama
    • Journal Title

      Compos. Math.

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Tilting theory for Gorenstein rings in dimension one2020

    • Author(s)
      R. Buchweitz, O. Iyama, K. Yamaura
    • Journal Title

      Forum Math. Sigma

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Extended McKay correspondence for quotient surface singularities2019

    • Author(s)
      Akira Ishii and Iku Nakamura
    • Journal Title

      Q.J.Math.

      Volume: 70 Pages: 395-408

    • NAID

      120006767378

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Weighted Projective Lines and Rational Surface Singularities2019

    • Author(s)
      O. Iyama, M. Wemyss
    • Journal Title

      Epijournal Geom. Algebrique

      Volume: 3

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Auslander?Gorenstein algebras from Serre-formal algebras via replication2019

    • Author(s)
      Chan Aaron、Iyama Osamu、Marczinzik Ren
    • Journal Title

      Advances in Mathematics

      Volume: 345 Pages: 222-262

    • DOI

      10.1016/j.aim.2019.01.010

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Tilting modules over Auslander-Gorenstein Algebra2019

    • Author(s)
      Iyama Osamu、Zhang Xiaojin
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 298 Issue: 2 Pages: 399-416

    • DOI

      10.2140/pjm.2019.298.399

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Quotients of triangulated categories and Equivaleces of Buchweitz, Orlov and Amiot-Guo-Keller2019

    • Author(s)
      Osamu Iyama, Dong Yang
    • Journal Title

      Amer. J. Math.

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Tilting Cohen-Mcauley representations2019

    • Author(s)
      Osamu Iyama
    • Journal Title

      Proceedings of the International Congress of Mathematics (ICM 2018)

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
  • [Journal Article] Extended McKay correspondence for quotient surface singularities2018

    • Author(s)
      Akira Ishii and Iku Nakamura
    • Journal Title

      The Quarterly Journal of Mathematics

      Volume: - Issue: 2 Pages: 00-00

    • DOI

      10.1093/qmath/hay047

    • NAID

      120006767378

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On steady non-commutative crepant resolutions2018

    • Author(s)
      Iyama Osamu、Nakajima Yusuke
    • Journal Title

      Journal of Noncommutative Geometry

      Volume: 12 Issue: 2 Pages: 457-471

    • DOI

      10.4171/jncg/283

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lattice structure of Weyl groups via representation theory of preprojective algebras2018

    • Author(s)
      Iyama Osamu、Reading Nathan、Reiten Idun、Thomas Hugh
    • Journal Title

      Compositio Mathematica

      Volume: 154 Issue: 6 Pages: 1269-1305

    • DOI

      10.1112/s0010437x18007078

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Noncommutative resolutions using syzygies2018

    • Author(s)
      Dao Hailong、Iyama Osamu、Iyengar Srikanth B.、Takahashi Ryo、Wemyss Michael、Yoshino Yuji
    • Journal Title

      Bulletin of the London Mathematical Society

      Volume: 51 Issue: 1 Pages: 43-48

    • DOI

      10.1112/blms.12210

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Silting reduction and Calabi--Yau reduction of triangulated categories2017

    • Author(s)
      Osamu Iyama, Dong Yang
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 印刷中 Issue: 11 Pages: 7861-7898

    • DOI

      10.1090/tran/7213

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] τ -tilting finite algebras, bricks and g-vectors2017

    • Author(s)
      Laurent Demonet, Osamu Iyama, Gustavo Jasso
    • Journal Title

      Int. Math. Res. Not.

      Volume: 1 Issue: 3 Pages: 1-41

    • DOI

      10.1093/imrn/rnx135

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Women in Science in Japan and AOWM2024

    • Author(s)
      Yukari Ito
    • Organizer
      The 2nd AASSA-WISE International Symposium on Diversity, Equity and Inclusion in STEM
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] McKay correspondence for some finite reflection groups2023

    • Author(s)
      Akira Ishii
    • Organizer
      Kinosaki Algebraic Geometry Symposium 2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Resolution of singularities and the McKay correspondence2023

    • Author(s)
      Yukari Ito
    • Organizer
      Inaugural meeting of Asian-Oceanian Women in Mathematics (AOWM)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] G-Hilbert scheme and the McKay correspondence2023

    • Author(s)
      Yukari Ito
    • Organizer
      Commutative Algebra and Algebraic Geometry seminar
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] 5 lectures on crepant resolutions and the McKay correspondence2023

    • Author(s)
      Yukari Ito
    • Organizer
      Summer school on Algebraic Geometry in Aisa
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] G-Hilbert scheme and the McKay correspondence2023

    • Author(s)
      Yukari Ito
    • Organizer
      Algebraic Geometry Seminar
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] What can we do with AOWM?2023

    • Author(s)
      Yukari Ito
    • Organizer
      10th International Congress on Industrial and Applied Mathematics (ICIAM)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] What is the G-Hilbert scheme?2023

    • Author(s)
      Yukari Ito
    • Organizer
      International workshop on Birational Geometry
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Crepant resolution of Calabi-Yau singularity2023

    • Author(s)
      Yukari Ito
    • Organizer
      Tsinghua-Tokyo workshop on Calabi-Yau
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory via g-fans in real Grothendieck groups2023

    • Author(s)
      Osamu Iyama
    • Organizer
      Algebraic Lie Theory and Representation Theory 2023
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] Singularity categories and cluster categories2023

    • Author(s)
      Osamu Iyama
    • Organizer
      Current trends in categorically approach to algebraic and symplectic geometry 2
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory via g-fans in real Grothendieck groups2023

    • Author(s)
      Osmau Iyama
    • Organizer
      MSJ-KMS Joint Meeting 2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory via g-fans in real Grothendieck groups2023

    • Author(s)
      Osamu Iyama
    • Organizer
      The 44th Japan Symposium on Commutative Algebra
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] Representation theory of non-commutative Gorenstein rings in dimension one2023

    • Author(s)
      Osamu Iyama
    • Organizer
      Representation Theory and Non-Commutative Geometry
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Semistable torsion classes and canonical decompositions in Grothendieck groups2023

    • Author(s)
      Osamu Iyama
    • Organizer
      Tokyo-Nagoya Algebra Special Seminar
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 漸化式とグラフと団代数2023

    • Author(s)
      Osamu Iyama
    • Organizer
      高校生と大学生のための金曜特別講座 (online)
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] 美しい数学の世界2023

    • Author(s)
      Yukari Ito
    • Organizer
      東京大学公開講座
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] Existence of crepant resolutions2022

    • Author(s)
      Yukari Ito
    • Organizer
      MIni-workshop on Quiver Varieties and Related Topics (Oxford)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Existence of crepant resolution and the McKay correspondence2022

    • Author(s)
      Yukari Ito
    • Organizer
      MAGIC (algebraic geometry) seminar of Imperial Collede
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The McKay correspondence2022

    • Author(s)
      Yukari Ito
    • Organizer
      8 th International Congress on Science Technology and Technology-based Innovation (STT48) (Thailand)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 初等中等教育における理数教育に望まれるジェンダーの視点2022

    • Author(s)
      伊藤 由佳理
    • Organizer
      教育数学の一側面ー高等教育における数学の多様性と普遍性 (RIMS)
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] From 3-dimensional McKay correspondence2022

    • Author(s)
      Yukari Ito
    • Organizer
      Gauge Theory, Moduli Spaces and Representation Theory (IPMU)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The McKay correspondence and the generalization2022

    • Author(s)
      Yukari Ito
    • Organizer
      K3, Enriques Surfaces, and Related Topics (Nagoya)
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Resolution of Calabi-Yau singularities and the orbifold Euler characteristics2022

    • Author(s)
      Yukari Ito
    • Organizer
      Women at the Intersection of Mathematics and Theoretical Physics Meet in Okinawa (OIST)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Singularity categories and Cluster categories2022

    • Author(s)
      Osamu Iyama
    • Organizer
      Mathematisches Forschungsinstitut Oberwolfach
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Auslander-Gorenstein rings revisited(3回講演)2022

    • Author(s)
      Osamu Iyama
    • Organizer
      Online workshop on higher dimensional homological algebras
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Singularity categories and cluster categories2022

    • Author(s)
      Osamu Iyama
    • Organizer
      Bridges between representation theory and algebraic geometry: Singularities, friezes and cluster categories
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 団代数と傾理論2022

    • Author(s)
      Osamu Iyama
    • Organizer
      東京理科大学談話会
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Quiver representations and Cohen-Macaulay representations2022

    • Author(s)
      Osamu Iyama
    • Organizer
      Algebra days in Paris in honor of Bernhard Keller
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Realizing stable categories of Cohen-Macaulay modules as cluster categories2022

    • Author(s)
      Osamu Iyama
    • Organizer
      第43回可換環論シンポジウム
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] 特異傾理論入門:Quiver表現とCohen-Macaulay表現2022

    • Author(s)
      Osamu Iyama
    • Organizer
      名古屋大学集中講義
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Complete g-fans of rank 22022

    • Author(s)
      Osamu Iyama
    • Organizer
      Flash Talks in Representation Theory Norwegian University of Science and Technology
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Fans in tilting theory: rank 2 case2022

    • Author(s)
      Osamu Iyama
    • Organizer
      Representation Theory of Quivers and Finite-Dimensional Algebras
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Singularity categories and cluster categories2022

    • Author(s)
      Osamu Iyama
    • Organizer
      Geometric and homological methods in representation theory
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Cohen-Macaulay representations, Singularity categories and Cluster categories2022

    • Author(s)
      Osamu Iyama
    • Organizer
      東京可換環論セミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] 団代数と傾理論2022

    • Author(s)
      Osamu Iyama
    • Organizer
      Encounter with mathematics, 第75回Cluster Algebras
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Exceptional collections on Σ22021

    • Author(s)
      Akira Ishii
    • Organizer
      名古屋大学代数幾何学セミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Introduction to silting theory2021

    • Author(s)
      Osamu Iyama
    • Organizer
      Network on Silting Theory
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Polytopes in silting theory2021

    • Author(s)
      Osamu Iyama
    • Organizer
      Network on Silting Theory
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Silting theory of Noetherian algebras2021

    • Author(s)
      Osamu Iyama
    • Organizer
      Network on Silting Theory
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Periodic trivial extension algebras and fractionally Calabi-Yau algebras2021

    • Author(s)
      Osamu Iyama
    • Organizer
      FD seminar
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory of contracted preprojective algebras and cluster tilting theory of cDV singularities2021

    • Author(s)
      Osamu Iyama
    • Organizer
      Braids, mutations and twists in algebra and geometry
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Wall-chamber structure in Grothendieck group and canonical decomposition2021

    • Author(s)
      Osamu Iyama
    • Organizer
      Cluster Algebras and Related Topics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 美しい数学入門 ― 特異点の謎に迫る2021

    • Author(s)
      Yukari Ito
    • Organizer
      金曜特別講座
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] The McKay correspondence2020

    • Author(s)
      Yukari Ito
    • Organizer
      城崎代数幾何学シンポジウム
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The McKay correspondence2020

    • Author(s)
      Yukari Ito
    • Organizer
      ZAG(Zoom Algebraic Geometry) Seminar
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory of contracted preprojective algebras and cDV singularities2020

    • Author(s)
      Osamu Iyama
    • Organizer
      Paris algebra seminar
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Simple-minded systems in cluster categories and generalized cluster complexes2020

    • Author(s)
      Osamu Iyama
    • Organizer
      Cluster algebras 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Contracted preprojective algebras, Coxeter groups and cDV singularities2020

    • Author(s)
      Osamu Iyama
    • Organizer
      Birthday Colloquium for Bill Crawley-Boevey
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 傾理論とその仲間たち2020

    • Author(s)
      Osamu Iyama
    • Organizer
      東京大学大学院数理科学研究科・談話会
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 傾理論と前射影代数2020

    • Author(s)
      Osamu Iyama
    • Organizer
      京都大学数学教室・集中講義
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 特異圏の傾理論2020

    • Author(s)
      Osamu Iyama
    • Organizer
      京都大学数学教室・談話会
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 自由性と単純性:K¨onig-Yang 対応を通して2020

    • Author(s)
      Osamu Iyama
    • Organizer
      第3回数理新人セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Resolution of singularities and the McKay correspondence2019

    • Author(s)
      Yukari Ito
    • Organizer
      IPMU Colloquium
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Crepant resolution and the orbifold Euler Characterisitcs2019

    • Author(s)
      Yukari Ito
    • Organizer
      Workshop: Singularities and related topics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] McKay correspondence for Calabi-Yau threefolds2019

    • Author(s)
      Yukari Ito
    • Organizer
      Mutation: Mirror Symmetry, Deformations, and Combinatorics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The McKay correspondence - a bridge between Algebra and Geometry2019

    • Author(s)
      Yukari Ito
    • Organizer
      The 10th Conference of Tsinghua Sanya Internationl Mathematics Forum-The conference on the Legacy of Elie Cartan
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Dimer models with group actions2019

    • Author(s)
      Akira Ishii
    • Organizer
      Japanese-European Symposium on Symplectic Varieties and Moduli Spaces - Fourth Edition
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Exceptional collections on the Hirzebruch surface Σ2019

    • Author(s)
      Akira Ishii
    • Organizer
      Categorical and Analytic Invariants in Algebraic Geometry VII
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Exceptional collections on the Hirzebruch surface Σ2019

    • Author(s)
      Akira Ishii
    • Organizer
      非可換代数幾何学の大域的問題とその周辺
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Cluster tilting in projective geometry2019

    • Author(s)
      Osamu Iyama
    • Organizer
      Ragnar’s Ramification in Algebra and Geometry Emerging Workshop
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory of preprojective algebras and Cohen-Macaulay modules (3 lectures)2019

    • Author(s)
      Osamu Iyama
    • Organizer
      Two weeks of silting
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory of contracted preprojective algebras2019

    • Author(s)
      Osamu Iyama
    • Organizer
      Workshop on quiver varieties and representation theory
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Radical layers of representable functors, revisited2019

    • Author(s)
      Osamu Iyama
    • Organizer
      Homological methods and Tilting theory of Finite Dimensional algebras
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Radical layers of representable functors, revisited2019

    • Author(s)
      Osamu Iyama
    • Organizer
      Seminario de Representaciones de Algebras
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Cohen-Macaulay DG modules and Calabi-Yau configurations, after H. Jin2019

    • Author(s)
      Osamu Iyama
    • Organizer
      Algebraic Representation Theory and Related Topics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Tilting theory of contracted preprojective algebras and cDV singularities2019

    • Author(s)
      Osamu Iyama
    • Organizer
      2019 Noncommutative Algebraic Geometry Shanghai Workshop
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory for Gorenstein rings in dimension one2019

    • Author(s)
      Osamu Iyama
    • Organizer
      Algebra Seminar
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory of contracted preprojective algebras and cDV singularities2019

    • Author(s)
      Osamu Iyama
    • Organizer
      第 41 回可換環論シンポ ジウム
    • Related Report
      2019 Research-status Report
  • [Presentation] Tilting modules and torsion theories revisited2019

    • Author(s)
      Osamu Iyama
    • Organizer
      第 25 回静岡代数学セミナーおよび星野光男氏の追悼 研究集会
    • Related Report
      2019 Research-status Report
  • [Presentation] Tilting theory for Gorenstein rings in dimension one2019

    • Author(s)
      Osamu Iyama
    • Organizer
      Interactions between commutative algebra, representation theory and algebraic geometry
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 特異点とマッカイ対応2018

    • Author(s)
      Yukari Ito
    • Organizer
      名古屋大学多元数理談話会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Dimer models with group actions2018

    • Author(s)
      Akira Ishii
    • Organizer
      Differential, Algebraic and Topological Methods in Complex Algebraic Geometry
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting Cohen-Macaulay representations2018

    • Author(s)
      Osamu Iyama
    • Organizer
      Higher homological algebra and cluster tilting
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Tilting theory for Gorenstein rings in dimension one2018

    • Author(s)
      Osamu Iyama
    • Organizer
      日本大学 特異点セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] Tilting Cohen-Macaulay representations2018

    • Author(s)
      Osamu Iyama
    • Organizer
      International Congress of Mathematicians 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Auslander-Reiten theory in extriangulated categories2018

    • Author(s)
      Osamu Iyama
    • Organizer
      Workshop and 18th International Conference on Representation of algeblas
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting Cohen-Macaulay representations2018

    • Author(s)
      Osamu Iyama
    • Organizer
      城崎代数幾何学シンポジウム
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Lattice theory of torsion classes beyond tau-tuktung theory2018

    • Author(s)
      Osamu Iyama
    • Organizer
      Stability Conditions and Representaion Theory of Finite-Dimesional Algebra
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tilting theory for Gorenstein rings in dimension one2018

    • Author(s)
      Osamu Iyama
    • Organizer
      代数幾何学セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Auslander algebras for Cohen-Macaulay modules2018

    • Author(s)
      Osamu Iyama
    • Organizer
      第40回可換環論シンポジウム
    • Related Report
      2018 Research-status Report
  • [Presentation] Tilting Cohen-Macaulay representations2018

    • Author(s)
      Osamu Iyama
    • Organizer
      Conference on Algebaic Representaion Theory
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Book] McKay Correspondence, Mutation and Related Topics2023

    • Author(s)
      Yukari Ito, Akira Ishii, Osamu Iyama
    • Total Pages
      533
    • Publisher
      Mathematical Society of Japan
    • ISBN
      9784864970990
    • Related Report
      2023 Annual Research Report
  • [Book] 美しい数学入門2020

    • Author(s)
      伊藤 由佳理
    • Total Pages
      176
    • Publisher
      岩波書店
    • ISBN
      9784004318422
    • Related Report
      2020 Research-status Report
  • [Remarks]

    • URL

      https://indico.ipmu.jp/event/430/

    • Related Report
      2023 Annual Research Report
  • [Remarks]

    • URL

      https://research.ipmu.jp/seminar/?conference_id=211

    • Related Report
      2020 Research-status Report
  • [Remarks]

    • URL

      https://research.ipmu.jp/seminar/?conference_id=211

    • Related Report
      2019 Research-status Report
  • [Remarks] McKay Correspondence and Noncommutative Algebra

    • URL

      https://sites.google.com/view/mckayworkshop

    • Related Report
      2018 Research-status Report
  • [Funded Workshop] McKay correspondence, Tilting theory and related topics2023

    • Related Report
      2023 Annual Research Report
  • [Funded Workshop] McKay correspondence, mutation and related topics2020

    • Related Report
      2020 Research-status Report
  • [Funded Workshop] Workshop on McKay Correspondence and Noncommutative Algebra2018

    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2025-01-30  

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