Shunya SAITO
I am Shunya Saito (齋藤 峻也 in Japanese), a postdoc at Graduate School of Mathematics, Nagoya University in Japan.
Research interests: Representaton Theory of Algebras / Algebraic Geometry / Category Theory
E-mail: m19018i [at] math.nagoya-u.ac.jp
Position: JSPS Research Fellow (PD) at Nagoya University
See CV below for more detailed information.
Links: [arXiv] [Google scholar] [ORCID] [research map]
Papers
Publications
A note on Grothendieck groups of periodic derived categories, J. Algebra 609 (2022), 552--566. [journal] [arXiv:2112.09874]
Tilting theory for periodic triangulated categories, Math. Z. 304, 47 (2023). [journal] [arXiv:2011.14096]
Preprints
The spectrum of Grothendieck monoid: classifying Serre subcategories and reconstruction theorem. [arXiv:2206.15271]
Grothendieck monoids of extriangulated categories. (joint work with Haruhisa Enomoto) [arXiv:2208.02928]
Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories. [arXiv:2304.06918]
When are KE-closed subcategories torsion-free classes? (joint work with Toshinori Kobayashi) [arXiv:2309.01044]
Notes
ヘンゼル環と Krull-Schmidt 圏 (written in japanese) [pdf]
Krull-Schmidt圏(=直既約分解の一意性が成立する加法圏)・半完全環・ヘンゼル環の関係をまとめました.とくにCohen-Macaulay表現論などでファクトにされる完備局所可換環上の加群圏はKrull-Schmidt圏になることを示しています.前提知識は少なめですが,有限次元代数の表現論への慣れは必要な気がします.DG categories [pdf]
It is a part of my master's thesis. This note contains basic materials on DG categories and aims to prove the derived Morita theorem due to Keller, which yields a triangle equivalence between a certain triangulated category and the derived category of a DG category. This note does not cover homotopical stuff on DG categories.
Talks
Upcoming talks
no schedule
Past talks
周期三角圏上の傾理論 (February 24, 2021) [slide]
Seminar Talk, Tokyo-Nagoya Algebra Seminar, OnlineTilting objects in periodic triangulated categories (June 27, 2021) [slide]
Conference Talk, Algebraic Lie Theory and Representation Theory 2021 (ALTReT 2021), OnlineTilting theory for periodic triangulated categories (September 8, 2021) [slide]
Conference Talk, The 53rd Symposium on Ring Theory and Representation Theory, Online (Yamaguchi University)周期導来圏と傾理論 (February 9, 2022) [slide]
Conference Talk, Mathsci Freshman Seminar 2022, Online (Kyushu University)The spectrum of Grothendieck monoid: a new approach to classify Serre subcategories (July 22, 2022) [slide]
Seminar Talk, Suita Representation Seminar, OnlineThe spectrum of Grothendieck monoid (September 7, 2022) [slide]
Conference Talk, The 54th Symposium on Ring Theory and Representation Theory, Saitama UniversityThe spectrum of Grothendieck monoid (March 28, 2023) [slide]
Conference Talk, 27th Conference on Algebra for Young Researchers in Japan, University of TsukubaClassifying torsionfree classes of the category of coherent sheaves and their Serre subcategories (May 26, 2023) [slide]
Seminar Talk, Sugimoto Algebra Seminar, Osaka Metropolitan UniversityClassifying Serre subcategories of the category of maximal Cohen-Macaulay modules (July 6, 2023) [slide]
Conference Talk, The 34th Commutative Algebra Seminar, Kitami Institute of TechnologyClassifying Serre subcategories of the category of maximal Cohen-Macaulay modules (August 15, 2023) [slide]
Conference Talk, The 9th China-Japan-Korea International Conference on Ring and Module Theory, Incheon National UniversityClassifying several subcategories of the category of maximal Cohen-Macaulay modules (September 6, 2023) [slide]
Conference Talk, The 55th Symposium on Ring Theory and Representation Theory, Osaka Metropolitan UniversityClassifying torsionfree classes of the category of coherent sheaves and their Serre subcategories (December 22, 2023) [slide]
Conference Talk, McKay correspondence, Tilting theory and related topics, Kavli IPMU
CV
Professional Position
Apr. 2023 - : JSPS Research Fellow (PD)
Institution: Graduate School of Mathematics, Nagoya University.
Host Researcher: Shintarou Yanagida
Apr. 2021 - Mar. 2023 : JSPS Research Fellow (DC1)
Institution: Graduate School of Mathematics, Nagoya University.
Host Researcher: Shintarou Yanagida
Education
Apr. 2021 - Mar. 2023: Doctoral course at Graduate School of Mathematics, Nagoya University.
Apr. 2019 - Mar. 2021: Master’s course at Graduate School of Mathematics, Nagoya University.
Apr. 2015 - Mar. 2019: Undergraduate course at School of Science, Nagoya University.
Degree
Doctor of Philosophy (Mathematical Science)
Graduate School of Mathematics, Nagoya University, March 2023.
Chairperson: Ryo Takahashi
Supervisor: Shintarou Yanagida
Vice chairperson: Kazuhiro Fujiwara, Sho Tanimoto, Shintarou Yanagida
Thesis: Grothendieck monoids and their applications to representation theory and algebraic geometry
Master of Mathematical Science
Graduate School of Mathematics, Nagoya University, March 2021.
Supervisor: Shintarou Yanagida
Bachelor of Science
School of Science, Nagoya University, March 2019.
Supervisor: Kazuhiro Fujiwara
Thesis: Diophantine Equations and Geometry (in Japanese)
Awards
Master’s Thesis Award, Graduate School of Mathematics, Nagoya University, March 2021.