| Project/Area Number |
19K23401
|
|---|
| Research Category |
Grant-in-Aid for Research Activity Start-up
|
| Allocation Type | Multi-year Fund |
|---|
| Review Section |
0201:Algebra, geometry, analysis, applied mathematics,and related fields
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
CHAN Aaron 名古屋大学, 高等研究院(多元), 特任助教 (50845039)
|
|---|
| Project Period (FY) |
2019-08-30 – 2023-03-31
|
| Project Status |
Completed (Fiscal Year 2022)
|
| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | gentle algebra / tilting theory / surface topology / Brauer graph algebras / Calabi-Yau algebra / Auslander algebra / Auslander correspondence / Koszul duality / Non-orientable surface / gentle algebras / categorification / cluster algebras / surface combinatorics / Calabi-Yau algebras / lamination / torsion theory / marked surface / Fukaya category / stability condition / torsion class / Tilting theory / Gentle algebras / Surface combinatorics |
|---|
| Outline of Research at the Start |
Modern algebra is about the study of manipulating a given set of rules. Representation theory is about turning such kind of systems into something we can calculate by hand, or with the help of a computer, using the so-called linear algebra. This project aims to establish a connection between representation and certain spaces associated to surfaces; the ingredient used involve classifying the so-called torsion classes of representations over gentle algebras, and the relation between gentle algebras and topological surface combinatorics.
|
| Outline of Final Research Achievements |
Over the period of the research, I have had four research projects published, as well as having four preprints finished and submitted for review. Three of these research projects are directly related to the proposed research theme. Namely, one article looks at enlargement of Brauer tree algebras via certain ring theoretical construction; one article classifies the torsion classes of gentle algebras, based on its connection with surface topology; and one article extending the connection between algebras and surface topology from the orientable setting to the non-orientable one. My other research projects revolve around understanding various homological properties of finite-dimensional algebras, providing various breakthrough in long standing questions. On top of these, I have also organised school on differential graded algebras and also school on Koszul algebras, bring together researchers across various areas.
|
| Academic Significance and Societal Importance of the Research Achievements |
The research on classifying torsion classes provide a breakthrough in understanding this type of problems. The research on non-orientable surface also bring new connection between new area of representation theory and topology.
|
