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Online seminář z diferenciální geometrie - 26.10.2020 PDF Tisk

Seminář z diferenciální geometrie pokračuje 26.10.2020 od 10:00 online na platformě MS Teams

Připojení ke schůzce ZDE.

Keegan Flood (náš nový výzkumný pracovník, Masarykova univerzita):

The geometry of a certain class of singular solutions to the c-projective metrizability equation

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.

Aktualizováno Čtvrtek, 22 Říjen 2020 08:18
Online seminář z algebry - 22.10.2020 PDF Tisk

Další seminář z algebry se koná 22.10.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Christian Espindola

Categoricity in infinite quantifier theories

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.

Aktualizováno Středa, 21 Říjen 2020 08:37