[Alta-Logic] My final thesis seminar

[Florian Schwarz]

Dear all,

On Tuesday, *March 31st 2026 at 2pm in MS 337* I will give my final 
seminar before my thesis defense.

A zoom link for remote participation can be found on the peripatetic 
seminar webpage: https://logic.ucalgary.ca/event/florian-schwarz-10/

*Title*: Global to local to global: differentiation and atlases in 
category theory

*Abstract*: In many different setups throughout mathematics, 
differentiation is used to analyze a globally complicated situation 
locally. Conversely, small objects are glued to form a larger object 
using atlases. Instead of studying these concepts in one specific setup 
(e.g. smooth manifolds), we use category theory to study the 
constructions without specifying what the underlying objects are. This 
talk is meant to be a broad overview over some of these constructions in 
category theory.

We study categorical constructions that allow differentiation and 
atlases, in particular tangent categories and restriction categories. We 
will define tangent categories and see that they unify different 
historical approaches to derivatives. In tangent categories many 
constructions from classical geometry still work. We will in particular 
see that dimensions, vector bundles and Lie groups work very similar to 
their classical versions.

In the second half of the talk study atlases in join restriction 
categories, instructions how to glue objects together using maps that 
are only defined on a subset of their domain. We use atlases to 
construct principal bundles, objects which locally look like the 
Cartesian product of a space and a group.

Hope to see you there!

Best regards,

Florian
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