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Record of the differential geometry seminar (public habilitation lecture) - November 2, 11am |
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The seminar on differential geometry continued with public habilitation lecture:
November 2, 11am, online on ZOOM.
Record of the lecture is available via this LINK.
Yaroslav Bazaikin (Hradec Králové):
On constructions of cohomogeneity one Spin(7)-holonomy Riemannian metrics
Abstract:
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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Last Updated on Monday, 02 November 2020 15:59 |
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Online differential geometry seminar - November 9, 10am |
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The seminar on differential geometry will continue with this lecture:
November 9, 10am, online on MS Teams
Join via this LINK.
Andrei Dikarev (Masaryk university):
On holonomy of Weyl connections in Lorentzian signature
Abstract:
I will present my recent results about the classification of the holonomy algebras of Weyl connections in Lorentzian signature. A special attention will be paid to the construction of examples of Weyl connections with different holonomy algebras. |
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Last Updated on Friday, 30 October 2020 16:00 |
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Online algebra seminar - October 29th, 1pm |
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We will continue online on Thursday, October 29th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Jiří Rosický
Injectivity in metric-enriched categories
Abstract:
Among Banach spaces approximate injectivity is more important than injectivity. We will treat it from the point of view of enriched category theory - as enriched injectivity over complete metric spaces. |
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Last Updated on Thursday, 29 October 2020 08:48 |
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Online differential geometry seminar - October 26, 10am |
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The seminar on differential geometry will continue with this lecture:
October 26, 10am, online on MS Teams
Join via this LINK.
Keegan Flood (our new researcher, Masaryk university):
The geometry of a certain class of singular solutions to the c-projective metrizability equation
Abstract:
A nondegenerate solution to the c-projective metrizability equation is equivalent to a quasi-Kahler metric that is compatible with the c-projective class. By replacing this nondegeneracy condition on a solution to the metrizability equation with a nondegeneracy condition on its prolonged system we get a curved orbit decomposition of the underlying manifold where the open orbits inherit quasi-Kahler metrics and the closed orbits inherit CR-structures of hypersurface type. We may also examine the analogue of these considerations in the setting of projective geometry. |
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Last Updated on Thursday, 22 October 2020 08:29 |
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Online algebra seminar - October 22nd, 1pm |
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We will continue online on Thursday, October 22nd, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Christian Espindola
Categoricity in infinite quantifier theories
Abstract:
Morley's categoricity theorem states that a countable first-order theory categorical in some uncountable cardinal is categorical in all uncountable cardinals. Shelah's categoricity conjecture states that a similar eventual categoricity behavior holds for certain infinitary theories in finite quantifier languages. In this talk we will explain the main ideas of a work in progress aiming at a version of eventual categoricity for theories in infinite quantifier languages. On the categorical side this corresponds to accessible categories, where the notion of internal size is taken instead of the cardinality of the underlying model. We will start motivating this with some examples computing the categoricity spectrum of infinite quantifier theories. Then we will study also to which extent the Generalized Continuum Hypothesis can be avoided through forcing techniques and how the use of large cardinals can replace model-theoretic assumptions like directed colimits or amalgamation. Our ultimate goal is to determine whether large cardinals are really needed for these latter assumptions or whether they just follow instead from categoricity. |
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Last Updated on Wednesday, 21 October 2020 08:41 |
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