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Online algebra seminar - April 15th, 1pm PDF Print

We will continue online on Thursday, April 15th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Mark Kamsma

Independence Relations in Abstract Elementary Categories

Abstract:
In Shelah's classification of first-order theories we classify theories using combinatorial properties. The most well-known class is that of stable theories, which are very well-behaved. Simple theories are more general, and then even more general are the NSOP_1 theories. We can characterise those classes by the existence of a certain independence relation. For example, in vector spaces such an independence relation comes from linear independence. Part of this characterisation is canonicity of the independence relation: there can be at most one nice enough independence relation in a theory.

Lieberman, Rosický and Vasey proved canonicity of stable-like independence relations in accessible categories. Inspired by this we introduce the framework of AECats (abstract elementary categories) and prove canonicity for simple-like and NSOP_1-like independence relations. This way we reconstruct part of the hierarchy that we have for first-order theories, but now in the very general category-theoretic setting.

Last Updated on Tuesday, 13 April 2021 08:34
 
Habilitation lecture: Dr. András Rontó, Ph.D. (Brno University of Technology) PDF Print

We invite you to the habilitation lecture of Dr. András Rontó, Ph.D. (Brno University of Technology), which will be held in the seminar on differential equations on Monday, April 19, 2021, at 12 via Zoom.

Link here: https://cesnet.zoom.us/j/91705657887

TITLE:
CONSTRUCTIVE ANALYSIS OF BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Last Updated on Monday, 12 April 2021 11:14
 
Online algebra seminar - April 8th, 1pm PDF Print

We will continue online on Thursday, April 8th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Michael Ching

Tangent ∞-categories and Goodwillie calculus

Abstract:
In 1984 Rosický introduced tangent categories in order to capture axiomatically some properties of the tangent bundle functor on the category of smooth manifolds and smooth maps. Starting in 2014 Cockett and Cruttwell have developed this theory in more detail to emphasize connections with cartesian differential categories and other contexts arising from computer science and logic.

In this talk I will discuss joint work with Kristine Bauer and Matthew Burke which extends the notion of tangent category to ∞-categories. To make this generalization we use a characterization by Leung of tangent categories as modules over a symmetric monoidal category of Weil-algebras and algebra homomorphisms. Our main example of a tangent ∞-category is based on Lurie's model for the tangent bundle to an ∞-category itself. Thus we show that there is a tangent structure on the ∞-category of (differentiable) ∞-categories. This tangent structure encodes all the higher derivative information in Goodwillie's calculus of functors, and sets the scene for further applications of ideas from differential geometry to higher category theory.

Last Updated on Monday, 05 April 2021 20:14
 
Online algebra seminar - April 1st, 1pm PDF Print

We will continue online on Thursday, April 1st, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Jiří Adámek

C-Varieties of Ordered and Quantitative Algebras

Abstract:
Mardare, Panangaden and Plotkin introduced c-varieties of algebras on metric spaces. These are categories of metric-enriched algebras specified by equations in a context. A context puts restrictions on the distances of variables one uses. We prove that c-varieties are precisely the monadic categories over Met for countably accessible enriched monads preserving epimorphisms.

We analogously introduce c-varieties of ordered algebras as categories specified by inequalities in a context. Which means that conditions on inequalities between variables are imposed. We prove that c-varieties precisely correspond to enriched finitary monads on Pos preserving epimorphisms.

This is joint work with Jiri Rosicky.

Last Updated on Thursday, 01 April 2021 09:42
 
Online algebra seminar - March 25th, 1pm PDF Print

We will continue online on Thursday, March 25th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Jonathan Kirby

A model-theoretic look at exponential fields

Abstract:
An exponential function is a homomorphism from the additive group of a field to its multiplicative group. The most important examples are the real and complex exponentials, and these are naturally studied analytically.
However, one can also study the algebra of exponential fields and their logical theory. It turns out that the natural ways to do this take one outside the usual finitary classical logic of model theory and into positive/coherent logic, geometric logic, or other infinitary logics, or to the more algebraic and abstract setting of accessible categories.

I will describe some of this story, focussing on the more algebraic aspects of existentially closed exponential fields.

This is joint work with Levon Haykazyan.

Last Updated on Wednesday, 24 March 2021 07:58
 
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