## Haruhisa ENOMOTO

About me

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About me

Study the Grothendieck monoid of an extriangulated category.

Study maximal self-orthogonal modules, a new generalization of tilting modules = projectively Wakamatsu tilting modules, and Wakamatsu tilting modules

I proved the title

Study the Morita type theorem for exact categories. The Ext-perpendicular category of cotilting modules are precisely exact category with progen & inj cogen & higher kernels.

I classify possible exact structures on a given additive category by using functor category, and give applications to CM-finite Iwanaga-Gorenstein algebras.

Rep-fin v.s. “AR seq generate relations for K_0” in exact categories.

For torsion-free classes over preprojective algebras and path algebras of Dynkin type, I classify simple objects using the root system.

Classified a possible extriangulated substructures on a given extriangulated category using functor category

Study Image-Cokernel-Extension closed subcategories of module categories using the poset of torsion classes and τ-tilting theory.

I proved the title.

Motivated by the study of simple objects of exact categories, I proposed the notion of monobricks, which enables us to study wide subcategories and torsion-free classes simultaneously.

I consider when an exact category satisfies the Jordan-Hölder property, (JHP).

Established a bijection between Image-Cokernel-Extension-closed (ICE-closed) subcats in mod kQ and rigid kQ-modules

Unify bijections of the form “Interval poset of torsion pairs is isomorphic to the poset of torsion pairs in another subcategory” in the framework of extriangulated categories.

Compute the posets of wide subcats and ICE-closed subcats from the lattice of torsion classes

Study subcategories of a module category closed under images and extensions.

Based on paper: Classifying exact categories via Wakamatsu tilting

Based on paper: Classifying exact categories via Wakamatsu tilting

Based on paper: Classifications of exact structures and Cohen-Macaulay-finite algebras

Based on papers: Classifying exact categories via Wakamatsu tilting Classifications of exact structures and Cohen-Macaulay-finite algebras

Talk to various area of young researchers.

Based on paper: Relations for Grothendieck groups and representation-finiteness

Based on paper: Classifications of exact structures and Cohen-Macaulay-finite algebras

Based on paper: Relations for Grothendieck groups and representation-finiteness

Based on paper: Relations for Grothendieck groups and representation-finiteness

Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories

Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories

Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories

Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories

Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories

Talk to various area of young researchers.

This conference was canceled due to COVID-19.

Based on paper: Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras

Based on paper: Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras

Based on paper: Monobrick, a uniform approach to torsion-free classes and wide subcategories

Based on paper: ICE-closed subcategories and wide τ-tilting modules Abstract I’ll introduce ICE-closed subcategories of an abelian length category, subcategories closed under taking Images, Cokernels and Extensions. Both torsion classes and wide subcategories of an abelian category are ICE-closed. We will see that ICE-closed subcategories are precisely torsion classes in some wide subcategories. For a finite-dimensional algebra, I’ll introduce the notion of wide τ-tilting modules, and extend Adachi-Iyama-Reiten’s bijection between support τ-tilting modules and torsion classes to a bijection between wide τ-tilting modules and ICE-closed subcategories. If time permits, I’ll talk about some results on ICE-closed subcategories over hereditary algebras and Nakayama algebras. This talk is based on a joint work with Arashi Sakai (Nagoya University). Links Slide (without handwriting), Slide (with handwriting), Talk Video (recording)

Based on paper: Rigid modules and ICE-closed subcategories in quiver representations ICE-closed subcategories and wide τ-tilting modules

Based on my paper and my SageMath program, From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories The lattice of torsion classes in SageMath

Based on my papers [1] Monobrick, a uniform approach to torsion-free classes and wide subcategories [2] Rigid modules and ICE-closed subcategories in quiver representations [3] ICE-closed subcategories and wide τ-tilting modules (joint with A. Sakai)

10-minutes flash talk, based on my paper From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories

Two talks based on my papers on exact categories.

Based on my paper From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories

Based on my preprint:

Based on my preprint:

Based on our preprint with S. Saito:

Based on my preprint:

Based on my preprint:

Based on my preprint:

Based on my preprint:

τ傾理論とねじれ類入門：分裂射影対象と広大区間の立場から

数学系のための、証明支援系Leanに関する初歩からの勉強会を、オーガナイザーの一人として開催しました。 Leanの基礎についてや、群論についての教材準備等を行いました。 詳しくは下サイトにて。

Talk (Japanese) about FD Applet Lean Theorem Prover