| 研究実績の概要 |
There are now a deeper understanding to differential graded module category (dg category) and silting theory. In particular the notion of perverse equivalence can be generalised to such categories. These will be similar to an application of mutation continuously. That means we can probably determine case-by-case if any equivalence given is perverse. However, it will be difficult to construct any interesting perverse equivalence, or discussing any useful combinatorics, without any extra information of the category.
In parallel to the main research theme, I am studying the p-homology of some complex of permutation modules, in collaboration with Aaron Chan in Nagoya University. We can completely determine the homology of the said complex and also hope to enrich the theory of symmetric group representations.
Up till very recently I have received news there is a group in Tokyo University of Science (TUS) is studying perverse equivalence. There seems to be some collaboration possible.
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