2018 Fiscal Year Research-status Report
Mutation in derived categories and lattice theory of torsion classes and wide subcategories
| Project/Area Number |
17K14160
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| Research Institution | Nagoya University |
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Principal Investigator |
DEMONET Laurent 名古屋大学, 多元数理科学研究科(国際), G30特任准教授 (70646124)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | torsion classes / lattices / gentle algebras |
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| Outline of Annual Research Achievements |
During the academic year 2018, my research work has consisted to progress on the joint project with Iyama, Reading, Reiten, and Thomas, concerning the lattice theory of torsion classes. Our understanding has improved a lot and I also started some investigation about the g-vector realization of these lattices, with Asai and Iyama.
Indeed, there are strong relations between g-vector of functorially torsion classes and so-called scattering diagrams that have taken recently a prominent role in the study of cluster algebras. We expect to insert naturally the non-functorially finite torsion classes in the picture.
On an other side, I initiated with Chan a project of classification of torsion classes for gentle algebras.
We associate to each gentle algebra a marked surface and some combinatorial datum on it, and we parameterize the torsion classes (functorially finite and non-functorially finite) by some topological object on this marked surface.
Note that this project is closed to be finished.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The project progresses following the initial research plan, except for small side details.
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| Strategy for Future Research Activity |
I will continue the project with Aaron Chan.
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| Causes of Carryover |
Certain travels were cheaper than expected originally.
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