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Tokyo-Nagoya Algebra Seminar
Seminar information archive ～07/01｜Next seminar｜Future seminars 07/02～
| Organizer(s) | Noriyuki Abe, Aaron Chan, Erik Darpoe, Osamu Iyama, Tsutomu Nakamura, Hiroyuki Nakaoka, Ryo Takahashi |
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Next seminar
2022/07/06
10:30-12:00 Online
Please see the reference URL for details on the online seminar.
Nicholas Williams (The University of Tokyo)
Cyclic polytopes and higher Auslander--Reiten theory 3 (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Nicholas Williams (The University of Tokyo)
Cyclic polytopes and higher Auslander--Reiten theory 3 (English)
[ Abstract ]
This continues part 2. In the third talk, we consider the relationship between the objects from the first two talks. We explain how triangulations of even-dimensional cyclic polytopes may be interpreted in terms of tilting modules, cluster-tilting objects, or d-silting complexes. We then proceed in the d-silting framework, and show how the higher Stasheff--Tamari orders may be interpreted algebraically for even dimensions. We explain how this allows one to interpret odd-dimensional triangulations algebraically, namely, as equivalence classes of d-maximal green sequences. We briefly digress to consider the issue of equivalence of maximal green sequences itself. We then show how one can interpret the higher Stasheff--Tamari orders on equivalence classes of d-maximal green sequences. We finish by drawing out some consequences of this algebraic interpretation of the higher Stasheff--Tamari orders.
[ Reference URL ]This continues part 2. In the third talk, we consider the relationship between the objects from the first two talks. We explain how triangulations of even-dimensional cyclic polytopes may be interpreted in terms of tilting modules, cluster-tilting objects, or d-silting complexes. We then proceed in the d-silting framework, and show how the higher Stasheff--Tamari orders may be interpreted algebraically for even dimensions. We explain how this allows one to interpret odd-dimensional triangulations algebraically, namely, as equivalence classes of d-maximal green sequences. We briefly digress to consider the issue of equivalence of maximal green sequences itself. We then show how one can interpret the higher Stasheff--Tamari orders on equivalence classes of d-maximal green sequences. We finish by drawing out some consequences of this algebraic interpretation of the higher Stasheff--Tamari orders.
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
