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Online seminář z algebry - 10.6.2021 |
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Další seminář z algebry se koná 10.6.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde. Noam Zeilberger
Skew monoidal categories and the proof-theoretic anatomy of associativity (and unitality)
Abstrakt:
Based on joint work with Tarmo Uustalu and Niccolò Veltri.
The talk will survey a recent line of work, which takes a proof-theoretic approach to solving the coherence problem(s) for skew monoidal categories and related structures. I will begin by discussing the so-called Tamari order on fully-bracketed words induced by a semi-associative law (AB)C <= A(BC), and explain how a simple sequent calculus may account for some of its fascinating properties, such as the fact that the set of fully-bracketed words on n+1 letters forms a lattice Y_n under this order,as well as a remarkable formula counting the number of intervals in Y_n.
Then I will recall the definition of skew monoidal categories, and explain how a more refined sequent calculus may be used to solve two related coherence problems: deciding equality of maps and enumerating homsets in free skew monoidal categories. Closely related to recent work by Bourke and Lack, this sequent calculus may be considered as a canonical construction of the free left representable skew multicategory over aset of atoms.
Finally, I will briefly discuss variations of the sequent calculus capturing "partially skew" monoidal categories with different normality conditions.
References:
[1] https://arxiv.org/abs/1803.10080
[2] https://arxiv.org/abs/2003.05213
[3] https://arxiv.org/abs/2101.10487
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Aktualizováno Středa, 09 Červen 2021 07:49 |
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Online seminář z diferenciální geometrie - 7.6.2021 |
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Seminář z diferenciální geometrie pokračuje 7.6.2021 od 10:00 online na platformě MS Teams a v zasedací místnosti ÚMS (druhé patro).
Připojení ke schůzce ZDE. Radek Suchánek (Masaryk University):Some remarks on variational nature of Monge-Ampère equations in dimension four Abstrakt:
I will present a necessary condition for the local solvability of the strong inverse variational problem in the context of Monge-Ampère partial differential equations and first-order Lagrangians. In contrast with the previous talk by Marcus Dafinger, this condition is given by comparing differential forms on the first jet bundle and is valid only for the aforementioned PDEs. To illustrate how this approach can be applied, we will examine the linear Klein-Gordon equation, first and second heavenly equations of Plebanski, Grant equation, and Husain equation.
I will also speak about the drawbacks of the method when trying to generalize it to a system of equations. |
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Aktualizováno Čtvrtek, 03 Červen 2021 09:13 |
