** Preprint **

• Periodic trivial extension algebras and fractionally Calabi-Yau algebras (with Erik Darpö, Osamu Iyama, René Marczinzik) (arXiv)

• Torsion classes of gentle algebras (with Laurent Demonet) (arXiv)

** Published / Accepted **

•
On representation-finite gendo-symmetric algebras with only one non-injective projective module (with Takuma Aihara, Takahiro Honma)

to appear in *J. Algebra*

DOI: 10.1016/j.jalgebra.2022.04.002 (arXiv)

• Irreducible representations of the symmetric groups from slash homologies of
p-complexes (with William Wong)

*Algebr. Comb.* 4, 2021, no. 1, 125--144.

DOI: 10.5802/alco.153 (arXiv)

•
On simple-minded systems and tau-periodic modules of self-injective algebras (with
Yuming Liu, Zhen Zhang)

*J. Algebra* 560, Oct 2020, 416--441

DOI: 10.1016/j.jalgebra.2020.05.024 (arXiv)

•
Coidempotent subcolagebras and short exact sequences of finitary 2-representations
(with Vanessa Miemietz)

*Nagoya Math. J.* 243, Sep 2021, 316--341

DOI: 10.1017/nmj.2020.1 (arXiv)

• Auslander-Gorenstein
algebras from Serre-formal algebras via replication (with Osamu Iyama, René
Marczinzik)

*Adv. Math.* 345, Mar 2019, 222--262

DOI: 10.1016/j.aim.2019.01.010 (arXiv)

• On
representation-finite gendo-symmetric biserial algebras (with René Marczinzik)

*Algebr. Represent. Theory* 22 (1), Feb 2019, 141--176

DOI: 10.1007/s10468-017-9760-6 (arXiv)

• Diagrams and discrete extensions
for finitary 2-representations (with Volodymyr Mazorchuk)

*Math. Proc. Cambridge Philos. Soc.* 166 (2), Mar 2019,
325--352

DOI: 10.1017/s0305004117000858 (arXiv)

• Classification of
two-term tilting complexes over Brauer graph algebras (with Takahide Adachi, Takuma
Aihara)

*Math. Z.* 290 (1), Oct 2018, pp 1--36

DOI: 10.1007/s00209-017-2006-9 (arXiv)

• Yoneda algebras of quasi-hereditary algebras, and simple-minded
systems of triangulated categories

PhD Thesis. Unviersity of Aberdeen, Scotland, UK

• Two-term
tilting complexes and simple-minded systems of self-injective Nakayama
algebras

*Algebr. Represent. Theory* 18 (1), Feb 2015, pp 183--203.

DOI: 10.1007/s10468-014-9487-6 (arXiv)

• Simple-minded
systems, configurations and mutations for representation-finite self-injective algebras
(with Steffan Koenig, Yuming Liu)

*J. Pure Appl. Algebra* 219 (6), June 2015, pp 1940–-1961.

DOI: 10.1016/j.jpaa.2014.07.018

• Some
Homological Properties of Tensor and Wreath Products of Quasi-hereditary
Algebras

*Comm. Algebra* 42 (6), 2014, 2368--2379.

DOI: 10.1080/00927872.2012.761710 (arXiv)

** Works in progress / Not for publication**

• Classification of almost-symmetric gendo-symmetric algebras (with Takuma Aihara,
Takahiro Honma, Takuya Sakurai)

• Koszulity of ADR algebras (with Takahide Adachi, Mayu Tsukamoto) - in preparation

• Generalising precluster tilting theory (with Osamu Iyama, René Marczinzik) - in
preparation

• Brauer graph algebras and surface combinatorics (with Takahide Adachi) - in
preparation

• Ext-groups and Ext-algebras of standard modules for Cubist algebras - see thesis
Ch.3,4

• Simple-minded systems on triangulated orbit categories - see thesis Ch.5,7

• Blocks with Cyclic Defect Group - 2010 CASM Part III essay
(supervised by Dr. S. Martin)

**Translations of some mathematical terminologies in representation
theory: English, Japanese, Chinese**

Additions and suggestions are welcomed!

**University of Aberdeen**:

Comments and corrections to notes below will be appreicated.

-Seminar series on highest weight categories and quasi-hereditary
algebras (Spring 2012) - organised by M. Stolorz and myself. *DISCONTINUED*

-Seminar series on étale cohomology (Fall 2011) -
organised by P. Brito and J. Taylor.

-Derived equivalences of block algebras (Fall 2010) -
lectured by Dr. SeJong Park

**University of Cambridge**:

| Lecture notes typeset for Cambridge Part III courses. Diagrams are usually
omitted.

|-**Part III 2009/2010 Lent term**:

|-Elliptic Curves (Good
condition, no picture)

|-Topics in Representation Theory (Good
condition)

|-Topics in Group Theory (not
recommended to read)

|-**Part III 2009/2010 Michealmas term**:

|-Algebraic Geometry
(PostScript, with quite a few mistakes, no picture), alternatively, see Clemens' version
note (see Link section), which is a much better enhanced version, but arranged rather
differently from the way that it was taught.

|-Algebraic Topology (Not
recommended to read)

|-Algebraic Number
Theory(Good condition, missed a a few picture) Ch3 typeset by Alex Tao

|-Lie groups, Lie Algebra and their
Representation (Good condition with no diagram/picture)

I do ** NOT** guarantee the rigourousness of the following notes. These are
some notes I typed up for myself during the course of learning different areas of Maths.
(Almost) No references to the relevant papers are given. Corrections are
appreciated!

(1) Some results on representation-finite self-injective algebras

(2) Definition and its equivalent form for cellularly stratified algebras

(3) Hecke algebras (of different adjectives) of type A

(4) Some results of Brundan-Stroppel's generalised Khovanov's arc algebra

(5) Summary on tau-tilting theory

(6) A guide to 2-representation theory