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Thursday, December 3, 2020 — 1:00 PM EST
Title: Twisted Hopf algebras
| Speaker: | Loïc Foissy |
| Affiliation: | Université du Côte d'Opale |
| Zoom: | Contact Karen Yeats |
Abstract:
A twisted Hopf algebra is a Hopf algebra in the category of linear species. The Fock functors allow to recover "classical" Hopf algebras from twisted ones. Numerous constructions and results can be lifted to the level of twisted bialgebras, such that cofreeness, shuffle and quasi-shuffles products, etc.
Friday, December 4, 2020 — 3:30 PM EST
Title: Partial orders on the symmetric group
| Speaker: | Oliver Pechenik |
| Affiliation: | University of Waterloo |
| Zoom: | Please email Emma Watson |
Abstract:
The symmetric group of permutations is naturally a poset in at least 4 different ways, the (strong) Bruhat order and three flavors of weak order. Stanley showed in 1980 that the Bruhat order is Sperner, essentially meaning that the obvious large antichains are in fact the largest possible. The corresponding fact for weak orders was open until last year, when it was established by Gaetz and Gao.