Hi, I am a research visitor at Tallinn University of Technology, working with Samuel Steakely and Pawel Sobocinski on string diagrams for monoidal closed categories .

I recently graduated with my PhD from the University of Calgary, where I worked on on (higher) category theory with Kristine Bauer and Robin Cockett.

In particular I am interested in tangent categories, tangent infinity categories, join-restriction categories monoidal closed categories and more recently I got interested in applied category, in particular I want to describe machine learning and power grid dynamics.

My University of Calgary profile is at https://profiles.ucalgary.ca/florian-schwarz

My thesis can be found at https://ucalgary.scholaris.ca/bitstreams/365405aa-c759-42f0-a2df-54e99a4fefe8/download

My research

My research mainly focuses on category theory, higher category theory and homotopy theory. In particular I am interested in

A graphical calculus for monoidal closed categories
Abelian functor calculus
Categorical foundations of machine learning

More details on my research can be found here.

My preprints are

The dimension of the tangent bundle and the universality of the vertical lift, https://arxiv.org/abs/2602.15807
Differential bundles as functors from free modules, https://arxiv.org/abs/2512.21147
Lie groups in tangent join restriction categories, https://arxiv.org/abs/2509.18410

My teaching/outreach

I love teaching Mathematics to interested students in a meaningful way. That is why I happily volunteered teaching multiple courses at summer schools.

As a teaching assistant I have taught tutorials for many classes. For my work as teaching assistant I received several teaching excellence awards.

As an instructor I have taught Linear Algebra I and Calculus I.

I believe that studying discipline is unnecessary if the content is presented well, that universities should respect all different learning styles and that reducing barriers to neuro-divergent students has the potential to raise many great scientists.

For my efforts in teaching I have been awarded with the

Graduate Assistant Teaching Excellence Award, for fall 2023
Faculty of Science Fred A. McKinnon Graduate Teaching Assistant Award for 2022-2023
Graduate Assistant Teaching Excellence Award, for fall 2022

My CV

This is a short version, a more extensive pdf version can be found here

Education

09/2021-04/2026: PhD in Mathematics, University of Calgary (Canada)

10/2018 - 07/2021: Mathematical Physics (Master’s degree), Julius-Maximilian-Universität Würzburg (Germany), GPA: 3.7

09/2019 – 04/2020: Exchange student, Univeristy of British Columbia, Vancouver (Canada)

04/2017 - 03/2021: Mathematics (Bachelor’s degree), Julius-Maximilian-Universität Würzburg (Germany) and Universität Augsburg (Germany) GPA: 4.0

10/2015 - 10/2018: Physics (Bachelor’s degree), Universität Augsburg, GPA: 3.6

Publications

https://arxiv.org/abs/2509.18410

https://arxiv.org/abs/2512.21147

Summer schools / Conferences

29 summer/winter/spring schools and conferences. In particular:

June 2025 Foundational methods in Computer Science, presenting on "Principal bundles in Join restriction categories" (Ottawa, Canada)
April 2025 Operads and calculus workshop (Belfast, Northern Ireland)
August 2024 Young topologist meeting 2024, presenting on "Differential bundles in tangent (infinity) categories" (Münster, Germany)
July 2024 International category theory conference (Santiago de Compostella, Spain)
June 2024 2024 CMS summer meeting, presenting on "The Lie Algebra of a group object" (Saskatoon, Canada)
April 2024 (∞,n)-Categories and their applications (Utrecht, Netherlands)
December 2023 CdE Winterakademie, taking a course on Neurodiversity (Windischleuba, Germany)
June 2023 Foundational methods in Computer Science, presenting on "Partial Monoids" (Sackville, Canada)
May 2023 CdE Pfingsakademie, teaching a course on Special Relativity (Kirchheim, Germany)
July 2022 ICM geometry and topology section, presenting on "Tangent infinity Categories" (Copenhagen, Denmark)

Awards (see my full CV for details)

I received (among others) the following awards and scholarships:

Alberta Innovates
Henrietta Weyland Graduate Scholarship
Eyes High International Doctoral Scholarship
AGES - International
Graduate Assistant Teaching Excellence Award, for fall 2023
Faculty of Science Fred A. McKinnon Graduate Teaching Assistant Award for 2022-2023
Graduate Assistant Teaching Excellence Award, for fall 2022
Studienstiftung des Deutschen Volkes (for my undergraduate and master's studies)

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