Online algebra seminar  November 19th, 1pm 


We will continue online on Thursday, November 19th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Maru Sarazola (Cornell University)
The stable homotopy hypothesis
Abstract: The homotopy hypothesis is a wellknown bridge between topology and category theory. Its most general formulation, due to Grothendieck, asserts that topological spaces should be "the same" as infinitygroupoids. In the stable version of the homotopy hypothesis, topological spaces are replaced with spectra. In this talk we will review the classical homotopy hypothesis, and then focus on the stable version. After discussing what the stable homotopy hypothesis should look like on the categorical side, we will use the Tamsamani model of higher categories to provide a proof. This is based on joint work with Moser, Ozornova, Paoli and Verdugo. 
Last Updated on Wednesday, 18 November 2020 11:31 

Online algebra seminar  November 12th, 1pm 


We will continue online on Thursday, November 12th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Marcos MazariArmida (Carnegie Mellon University)
Modeltheoretic stability and superstability in classes of modules
Abstract: Dividing lines in complete firstorder theories were introduced by Shelah in the early seventies. A dividing line is a property such that the classes satisfying such a property have some nice behaviour while those not satisfying it have a bad one. Two of the best understood dividing lines are those of stability and superstability. In this talk, I will study the notion of stability and superstability in abstract elementary classes of modules with respect to pure embeddings, i.e., classes of the form (K,≤p) where K is a class of Rmodules for a fixed ring R and ≤p is the pure submodule relation. In particular, using that the class of pgroups with pure embed dings is a stable AEC, I will present a solution to Problem 5.1 in page 181 of Abelian Groups by Laszlo Fuchs. Moreover, I will show how the notion of superstability can be used to give new characterizations of noetherian rings, puresemisimple rings, and perfect rings. 
Last Updated on Tuesday, 10 November 2020 15:14 
Online algebra seminar  Movember 5th, 1pm 


We will continue online on Thursday, November 5th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Ivan Di Liberti
Enriched Locally Generated Categories
Abstract: We introduce the notion of Mlocally generated category for a factorization system (E,M) and study its properties. We offer a GabrielUlmer duality for these categories, introducing the notion of nest. We develop this theory also from an enriched point of view. We apply this technology to Banach spaces showing that it is equivalent to the category of models of the nest of finitedimensional Banach spaces. This is a report on joint work with Jiří Rosický. 
Last Updated on Wednesday, 04 November 2020 11:05 
Record of the differential geometry seminar (public habilitation lecture)  November 2, 11am 


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 noncommutativity 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 3Sasakian manifolds. 
Last Updated on Monday, 02 November 2020 15:59 
Online differential geometry seminar  November 9, 10am 


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. 
Last Updated on Friday, 30 October 2020 16:00 

