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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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Online algebra seminar - October 15th, 1pm |
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We will continue online on Thursday, October 15th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Taichi Uemura
The universal exponentiable arrow
Abstract:
Cartmell showed that the category of generalized algebraic theories is equivalent to the category of contextual categories. This implies that the theory of generalized algebraic theories is essentially algebraic. We characterize the essentially algebraic theory of generalized algebraic theories as the free category with finite limits and with an exponentiable arrow.
The main theorem and a syntactic proof are found in arXiv:2001.09940. In this talk we give a semantic proof. |
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Last Updated on Wednesday, 14 October 2020 15:27 |
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Online algebra seminar - October 8th, 1pm |
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We will continue online on Thursday, October 8th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Christina Vasilakopoulou
Oplax Hopf Algebras
Abstract:
Hopf categories were introduced by Batista, Caenepeel and Vercruysse in 2016, as a many-object generalization of Hopf algebras linked to other notions like multiplier Hopf algebras and with applications to categorical Galois theory. What is of particular interest is that the multiplication and comultiplication appear to make use of different monoidal products: Gabriella Bohm in subsequent work expressed Hopf categories as specific opmonoidal monads. In our work, we follow a different direction of generalizing Hopf monoids in a braided monoidal bicategory, that allows us to realize Hopf categories as Hopf-type objects over the same monoidal product, restoring in a sense the self-dual feature of classical Hopf algebras. In this talk, we introduce oplax bimonoids and oplax Hopf monoids in an arbitrary braided monoidal bicategory, we study their main properties and we exemplify such structures in a Span-type bicategory where they return semi-Hopf and Hopf categories.
This is a report on joint work with Mitchell Buckley, Timmy Fieremans and Joost Vercruysse.
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Last Updated on Wednesday, 07 October 2020 15:17 |
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Online algebra seminar - September 24, 1pm |
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We will continue online on Thursday, September 24, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Raffael Stenzel
Infinity-categorical comprehension schemes
Abstract:
Comprehension schemes arose as crucial notions in the early work on the foundations of set theory, and hence they found expression in a considerable variety of foundational settings for mathematics. Particularly, they have been introduced to the context of categorical logic first by Lawvere and then by Benabou in the 1970s.
In this talk we define and study a theory of comprehension schemes for fibered infinity-categories, generalizing Johnstone's respective notion for ordinary categories. This includes natural generalizations of all the fundamental instances originally defined by Benabou, and their application to Jacob's comprehension categories. Thereby, we can characterize
- numerous categorical structures arising in higher topos theory
- the notion of univalence
- internal infinity-categories
in terms of comprehension schemes, while some of the 1-categorical counterparts fail to hold in ordinary category theory. As an application, we can show that the universal cartesian fibration is represented via externalization by the "freely walking chain" in the infinity-category of small infinity-categories.
In the end, if my time management permits, we take a look at the externalization construction of internal infinity-categories from a model categorical perspective and review some examples from the literature in this light. |
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Last Updated on Tuesday, 22 September 2020 14:40 |
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