| 研究実績の概要 |
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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