[Alta-Logic] My final thesis seminar

[Kristine Bauer]

Reminder! :)

The final seminar is a chance for Florian to show off what he’s accomplished - it’s a celebratory talk and although all of Florian’s talks are pretty fun, this one is probably the most fun….

Kristine

Dr. Kristine Bauer
Associate Professor, Mathematics and Statistics
University of Calgary


The University of Calgary, located in the heart of Southern Alberta, both acknowledges and pays tribute to the traditional territories of the peoples of Treaty 7, which include the Blackfoot Confederacy (comprised of the Siksika, the Piikani, and the Kainai First Nations), the Tsuut’ina First Nation, and the Stoney Nakoda (including Chiniki, Bearspaw, and Goodstoney First Nations). The city of Calgary is also home to the Métis Nation within Alberta (including Nose Hill Métis District 5 and Elbow Métis District 6).

On Mar 29, 2026, at 2:18 PM, Florian Schwarz <florian.schwarz at ucalgary.ca> wrote:


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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