Home Maths Activities Links


• Topics in Mathematical Science VI, Autumn 2022
   ├ Course Info (Last Update: 2022-10-27)
   ├ Lecture Notes (Last Update: 2022-10-27)
   └ Homework Assignments: 1,   2,   3,   4


• Dominant Auslander-Gorenstein algebras and Koszul duality (with Osamu Iyama, René Marczinzik) (arXiv)
• 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
• 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!

Lecture Notes

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)

Some notes

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