Thomas Jan Mikhail

Department of Mathematical Sciences
University of Copenhagen
Universitetsparken 5
København Ø
Denmark

email: tjm(at)math.ku.dk

I am a postdoc in the Algebra & Geometry Section and the Centre for Geometry and Topology at the University of Copenhagen. My research insterests lie mainly in category theory and type theory. Previously I was a PhD student at the Autonomous University of Barcelona under the supervision of Joachim Kock. Before my PhD I was a physicist, interested in cosmology and quantum gravity.

Curriculum Vitae

Feb. 2025Jan. 2026 Postdoc
University of Copenhagen
Apr. 2020Feb. 2025 PhD in Mathematics
Autonomous University of Barcelona
Title of thesis: Type Theory for (∞,∞)-Categories, and Decomposition Spaces
Supervisor: Joachim Kock
Oct. 2015Mar. 2019 Masters in Physics
University of Heidelberg
Title of thesis: From Instantons to Baby Universes
Supervisor: Arthur Hebecker
Sep. 2011Jun. 2015 Bachelor in Physics
University of Cyprus
Title of thesis: The Galileon Field
Supervisor: Constantinos Skordis

Publications

Free loop spaces and the Cauchy–Frobenius Lemma
Joachim Kock and Thomas Jan Mikhail
arXiv:2507.01637 (2025)

Abacus bicomodule configurations and the Bergner-Osorno-Ozornova-Rovelli-Scheimbauer equivalence
Joachim Kock and Thomas Jan Mikhail
Algebraic and Geometric Topology (to appear), arXiv:2501.16491 (2025)

A Type-Theoretic Definition of Lax (∞, ∞)-Limits
Thomas Jan Mikhail
arXiv:2412.13310 (2024)

Fuzzy simplicial sets and their application to geometric data analysis
Lukas Silvester Barth, Fatemeh Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck and Thomas Jan Mikhail
Applied Categorical Structures (to appear), arXiv:2406.11154 (2024)

Euclidean wormholes, baby universes, and their impact on particle physics and cosmology
Arthur Hebecker, Thomas Mikhail and Pablo Soler
Frontiers in Astronomy and Space Sciences (2018), arXiv: 1807.00824

Talks

06 Oct. 2025Type Theory for (∞, ∞)-Categories
Algebra/Topology Seminar, University of Copenhagen
14 May 2025 A type-theoretic definition of lax (∞, ∞)-limits
ProLog Seminar, Chalmers University of Technology
03 Mar. 2024 Type Theory for the Working Mathematician (Part 2)
Topology seminar, Autonomous University of Barcelona
12 Apr. 2024 Type Theory for the Working Mathematician (Part 1)
Topology seminar, Autonomous University of Barcelona
08 Dec. 2023 Lawvere's Fixed Point Theorem and its Applications
Foundations Day, University of Copenhagen
13 Mar. 2023 CaTT - A Type-Theoretic Definition of ω-Categories
University of San Diego (Remote talk)
16 Jan. 2023 CaTT - A Type-Theoretic Definition of ω-Categories
Topology seminar, University of Barcelona
27 Jul. 2022 Type Theory from the Category Theoretical Point of View
Max Planck Institute for Mathematics in the Sciences
14 Jul. 2022 A very brief Introduction to Homotopy Type Theory
International Congress of Mathematicians: Geometry and Topology, Sectional Workshop
University of Copenhagen
29 Oct. 2019 From Instantons to Baby Universes
Institute of Mathematics, Czech Academy of Sciences
12 Nov. 2018 Wormhole Effects
Institute for Theoretical Physics, University of Heidelberg