Classifying exact categories via Wakamatsu tilting
H. Enomoto, Classifying exact categories via Wakamatsu tilting, J. Algebra 485 (2017), 1--44.
CV
Professional Position
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Apr. 2024 – : R&D Engineer at Acompany Co., Ltd. in Japan
- Apr. 2021 – Mar. 2024 : JSPS Research Fellow (PD)
- Institution: Graduate School of Science, Osaka Metropolitan University.
- Host Researcher: Yuya Mizuno
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Oct. 2020 – Mar. 2021: JSPS Research Fellow (PD)
- Institution: Graduate School of Mathematics, Nagoya University
- Host Researcher: Hiroyuki Nakaoka
- Apr. 2018 – Sep. 2020: JSPS Research Fellow (DC1)
- Institution: Graduate School of Mathematics, Nagoya University
- Host Researcher: Osamu Iyama
Education
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2018 – Sep. 2020: Doctoral course at Graduate School of Mathematics, Nagoya University.
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2016 – 2018: Master’s course at Graduate School of Mathematics, Nagoya University.
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2012 – 2016: Undergraduate course at School of Science, Nagoya University.
Degree
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Doctor of Philosophy (Mathematical Science)
- Graduate School of Mathematics, Nagoya University, September 2020.
- Supervisor: Osamu Iyama
- Thesis: Categorical Properties and Classifications of Several Subcategories of Module Categories
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Master of Mathematical Science
- Graduate School of Mathematics, Nagoya University, March 2018.
- Supervisor: Osamu Iyama
- Thesis: Relative Auslander correspondence via exact categories
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Bachelor of Science
- School of Science, Nagoya University, March 2016.
- Supervisor: Osamu Iyama
- Thesis: On categories of modules over locular categories (in Japanese)
Awards
- 12th Award for Encouragement of Alumni and Students (“Hida Award”, 飛田賞), Alumni Association of the Graduate School of Mathematics, Nagoya University, October 2023.
- Nagoya University Outstanding Graduate Student Award (学術奨励賞 (Japanese)), October 2020.
- Master’s Thesis Award, Graduate School of Mathematics, Nagoya University, March 2018.
Publications
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Classifications of exact structures and Cohen-Macaulay-finite algebras
H. Enomoto, Classifications of exact structures and Cohen-Macaulay-finite algebras, Adv. Math. 335 (2018), 838--877.
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Relations for Grothendieck groups and representation-finiteness
H. Enomoto, Relations for Grothendieck groups and representation-finiteness, J. Algebra 539 (2019), 152--176.
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Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
H. Enomoto, Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras, Comm. Algebra 49 (2021), no. 5, 2156--2189.
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Classifying substructures of extriangulated categories via Serre subcategories
H. Enomoto, Classifying substructures of extriangulated categories via Serre subcategories, Appl. Categ. Structures 29 (2021), no. 6, 1005--1018.
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ICE-closed subcategories and wide τ-tilting modules
H. Enomoto, A. Sakai, ICE-closed subcategories and wide τ-tilting modules, Math. Z. 300 (2022), no. 1, 541--577.
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Schur’s lemma for exact categories implies abelian
H. Enomoto, Schur's lemma for exact categories implies abelian, J. Algebra 584 (2021), 260--269.
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Monobrick, a uniform approach to torsion-free classes and wide subcategories
H. Enomoto, Monobrick, a uniform approach to torsion-free classes and wide subcategories, Adv. Math. 393 (2021), Paper No. 108113, 41 pp.
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The Jordan-Hölder property and Grothendieck monoids of exact categories
H. Enomoto, The Jordan-Hölder property and Grothendieck monoids of exact categories, Adv. Math. 396 (2022), Paper No. 108167.
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Rigid modules and ICE-closed subcategories in quiver representations
H. Enomoto, Rigid modules and ICE-closed subcategories in quiver representations, J. Algebra 594 (2022), 364--388.
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Intervals of s-torsion pairs in extriangulated categories with negative first extensions
T. Adachi, H. Enomoto, M. Tsukamoto, Intervals of $s$-torsion pairs in extriangulated categories with negative first extensions, Math. Proc. Cambridge Philos. Soc. 174 (2023), no. 3, 451--469.
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From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
H. Enomoto, From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories, to appear in Algebr. Represent. Theory.
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Image-extension-closed subcategories of module categories of hereditary algebras
H. Enomoto, A. Sakai, Image-extension-closed subcategories of module categories of hereditary algebras, J. Pure Appl. Algebra 227 (2023), no. 9, Paper No. 107372.
Preprints
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Grothendieck monoids of extriangulated categories
H. Enomoto, S. Saito, Grothendieck monoids of extriangulated categories, arXiv:2208.02928.
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Maximal self-orthogonal modules and a new generalization of tilting modules
H. Enomoto, Maximal self-orthogonal modules and a new generalization of tilting modules, arXiv:2301.13498.
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IE-closed subcategories of commutative rings are torsion-free classes
H. Enomoto, IE-closed subcategories of commutative rings are torsion-free classes, arXiv:2304.032608.
Talks
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On the representation theoretic realization of exact categories Permalink
Conference Talk at 22nd Conference on Algebra for Young Researchers, Okayama University, Japan
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Classification of exact structures and CM-finite Gorenstein algebras Permalink
Seminar Talk at Ring Theory and Representation Theory Seminar, Nagoya University, Japan
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Classifications of exact structures and Cohen-Macaulay finite algebras Permalink
Conference Talk at The 50th Symposium on Ring Theory and Representation Theory, University of Yamanashi, Japan
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Auslander-type correspondences for exact categories and cotilting modules Permalink
Seminar Talk at South Osaka Algebra Seminar, Osaka Prefecture University, Japan
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Exact categories in the representation theory of algebras Permalink
Conference Talk at Mathsci Freshman Seminar, Kyoto University, Japan
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Relations for Grothendieck groups and representation-finiteness Permalink
Conference Talk at 23rd Conference on Algebra for Young Researchers, Osaka University, Japan
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Classifications of exact structures and CM-finite Iwanaga-Gorenstein algebras Permalink
Conference Talk at International Conference on Representations of Algebras (ICRA 2018), Czech Technical University in Prague, Czech Republic
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Relations for Grothendieck groups and representation-finiteness
Seminar Talk at 27th Yamatokoriyama Seminar, National Institute of Technology, Nara College, Japan
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Relations for Grothendieck groups and representation-finiteness Permalink
Conference Talk at The 51st Symposium on Ring Theory and Representation Theory, Okayama University of Science, Japan
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The Jordan-Hölder property, Grothendieck monoids and Bruhat inversions Permalink
Seminar Talk at Ring Theory and Representation Theory Seminar, Nagoya University, Japan
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The Jordan-Hölder property, Grothendieck monoids and Bruhat inversions Permalink
Conference Talk at The 8th China-Japan-Korea International Conference on Ring Theory, Nagoya University, Japan
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The Jordan-Hölder property and Grothendieck monoids of exact categories Permalink
Conference Talk at MSJ Autumn Meeting 2019, Kanazawa University, Japan
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Bruhat inversions in the symmetric group and torsion-free classes over a type A quiver Permalink
Conference Talk at Representation Theory and its Combinatorial Aspects, Kyoto University, Japan
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Bruhat inversions in the symmetric group and torsion-free classes over a type A quiver Permalink
Conference Talk at Workshop on combinatorics and its related areas, Shinshu University, Japan
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Bruhat inversions in symmetric groups and representation theory of quivers of type A Permalink
Conference Talk at Mathsci Freshman Seminar 2020, Nagoya University, Japan
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Relative simples for preprojective algebras via root systems Permalink
Conference Talk at 25th Conference on Algebra for Young Researchers (canceled due to COVID-19), Nagoya University, Japan
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Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras Permalink
Seminar Talk at South Osaka Algebra Seminar, Online
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Simple objects in torsion-free classes over preprojective algebras of Dynkin type Permalink
Seminar Talk at FD Seminar, Online
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Monobricks
Seminar Talk at Ring Theory and Representation Theory Seminar, Online
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ICE-closed subcategories and wide tau-tilting modules Permalink
Conference Talk at International Conference on Representations of Algebras (ICRA 2020), Online
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ICE-closed subcategories over module categories Permalink
Seminar Talk at Kyoto Representation Theory Seminar, Online
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Computing various objects of an algebra from the poset of torsion classes Permalink
Seminar Talk at OCAMI Algebra Seminar, Online
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Some classes of subcategories of module categories: classifications and the relation between them Permalink
Conference Talk at The 53rd Symposium on Ring Theory and Representation Theory, Online (Yamaguchi University)
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Constructing the lattice of wide subcategories Permalink
Conference Talk at Flash Talks in Representation Theory at NTNU 2022, Online
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Exact-categorical properties of subcategories of abelian categories Permalink
Seminar Talk at Tokyo-Nagoya Algebra Seminar, Online
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The lattice of wide subcategories Permalink
Conference Talk at 26th Conference on Algebra for Young Researchers, Online
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From the lattice of torsion classes to wide and ICE-closed subcategories Permalink
Seminar Talk at BIREP Seminar, Online
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Combinatorics of lattices of subcategories of a module category Permalink
Conference Talk at The 67th Algebra Symposium, Kyoto University (Japan) and Zoom
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The Grothendieck monoid of an extriangulated category Permalink
Conference Talk at The 54th Symposium on Ring Theory and Representation Theory, Saitama University, Japan
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Maximal self-orthogonal modules and a new generalization of tilting modules Permalink
Seminar Talk at Paris algebra seminar, Online
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Orthogonal modules and (projectively) Wakamatsu tilting modules Permalink
Conference Talk at Orthogonal modules and homological dimensions, Online
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Maximal self-orthogonal modules and a new generalization of tilting modules Permalink
Conference Talk at 27th Conference on Algebra for Young Researchers in Japan, University of Tsukuba and Zoom
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Maximal self-orthogonal modules and a new generalization of tilting modules Permalink
Seminar Talk at South Osaka Algebra Seminar, Zoom
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Introduction to τ-tilting theory and torsion classes
Lecture Talk at Zoom, Zoom
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Lean-for-math workshop 数学系のためのLean勉強会
Workshop at Lean (Theorem Prover) workshop, Hybrid Tokyo
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Computation of the structure of module categories using FD Applet Permalink
Conference Talk at The 55th Symposium on Ring Theory and Representation Theory, Hybrid (Osaka Metropolitan University)
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On some classes of subcategories of abelian categories Permalink
Conference Talk at MSJ Autumn Meeting 2023, Tohoku, Japan
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Wakamatsu-tilting modules and self-orthogonal modules
Workshop Talk at Ring Theory and Representation Theory Workshop in Shinshu, Shinshu University, Japan