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Záznam se semináře z diferenciální geometrie (habilitační přednáška) - 2.11.2020 |
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Seminář z diferenciální geometrie pokračoval 2.11.2020 od 11:00 online na platformě ZOOM
Záznam přednášky ZDE.
Veřejná habilitační přednáška: Yaroslav Bazaikin (Hradec Králové):On constructions of cohomogeneity one Spin(7)-holonomy Riemannian metrics Abstrakt:
An intrinsic property of a curved Riemannian manifold is the a priori non-commutativity of directional derivatives and, as a consequence, the dependence of the parallel translation operation on the chosen path on the Riemannian manifold. The holonomy group serves as a measure of this dependence and is a global object related to a Riemannian manifold that characterizes the deep properties of its geometry. In particular, in many important cases, the presence of a special holonomy group allows us to conclude that the Riemannian manifold is Einstein, which explains the importance of the concept of holonomy in applications to theoretical physics.
After getting familiar with the basic concepts of holonomy groups, the talk will give a survey of the author's results on constructions of examples of Spin(7)-holonomy Riemannian manifolds of cohomogeneity one, based on the geometry of 3-Sasakian manifolds. |
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Aktualizováno Pondělí, 02 Listopad 2020 15:56 |
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Online seminář z algebry - 17.12.2020 |
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Další seminář z algebry se koná 17.12.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde. Gabriele Lobbia (University of Leeds)
Distributive Laws for Relative Monads
Abstrakt:
Monads are useful tools both in mathematics (especially in universal algebra) and in computer science. An important notion is that of a distributive law between two monads, which goes back to fundamental work of Jon Beck in the late '60s. This notion describes how two monads can interact with each other, an analogue of the ring distributivity of product over sum.
In recent years, a generalisation of monads has been studied, relative monads, where we drop the endofunctor requirement. This definition relies on an extension operator instead of a multiplication. We will start by reviewing the notion of distributive law. Then we will introduce relative monads and see what the right counterpart of distributive laws is when we consider a monad and a relative monad.
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Aktualizováno Středa, 16 Prosinec 2020 11:10 |
