| Outline of Annual Research Achievements |
My research this year consisted in finishing a project about algebras of partial triangulation, and starting the general study of lattices of torsion classes and their quotients. I also started to compute this lattice in certain cases, like for algebras of partial triangulations.
My research leaded this year to the following publications : L. Demonet, P.-G. Plamondon, D. Rupel, S. Stella, P. Tumarkin. SL 2 -tilings do not exist in higher dimensions (mostly), accepted to Sem. Lotharingien de Combinatoire ; L. Demonet, Introduction to algebras of partial triangulations, accepted to Proceedings of the 49th Symposium on Ring and Representation Theory.
Moreover, the following articles are almost finished: L. Demonet, O. Iyama. Idempotent-projective Cohen-Macaulay modules and their Auslander-Reiten quiver, in preparation ; L. Demonet, O. Iyama, N. Reading, I. Reiten, H. Thomas. Lattices of torsion classes and their algebraic quotients, in preparation ; L. Demonet, O. Iyama, N. Reading, I. Reiten, H. Thomas. Exchange lattices, in preparation ; L. Demonet, O. Iyama, N. Reading, I. Reiten, H. Thomas. Brick algebras, in preparation.
I did the following talks: Orders categorifying cluster algebras structures of partial flag varieties, Algebra seminar, Bonn Universitat (May 2016) ; Algebras of partial triangulations, XVII International Conference on Representations of Algebras, Syracuse (August 2016) ; Algebras of partial triangulations, Symposium on Ring Theory and Representation Theory, Osaka (September 2016).
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