About me
I'm a PhD candidate in mathematics at the University of Notre Dame, working with Pavel Mnev.
Broadly speaking I am interested in Quantum Field Theory, more specifically Topological QFTs and how they relate to questions and answers ranging from pure mathematics to physics. During my Master programme at ETH Zürich I got to learn about the BV formalism and things have not been the same ever since.
Recently I have gotten very interested in the many flavours of Morse Theory and how they can be used to describe manifold invariants. In particular I am thinking about certain $A_\infty$-categories describing higher cohomological operations by counting graphs of Morse flows. Those turn out to be beautifully modelled by effective $BF$ theories.
Another scientific passion of mine are theories of gravity. My Master Thesis at ETH Zürich was about a specific model for gravity stemming from topological $BF$ theory. Through this I became familiar with Einstein–Cartan gravity and generally metric-affine gravity. At ETH I also had the pleasure of learning about Quantum Information Theory and Quantum Foundations. One of my long-term goals is to contribute to the intersection of mathematical QFT and theories of gravity.
When I'm not actively doing mathematics, you have a good chance of finding me somewhere in nature. If not, I'm probably coding, painting or playing with Turing complete cardboard.
Feel free to reach out to me about any of my research articles or notes. I try to write organically and self-contained to make them accessible and prevent myself from hiding behind "folklore". Even then, science is a team sport, so let's talk about it!
Papers and Preprints
- Gravity with torsion as deformed BF theory
Joint work with Alberto S. Cattaneo and Michele Schiavina stemming from my Master Thesis at ETH Zürich, in Classical and Quantum Gravity, Volume 41, Number 15, published 28 June, 2024, arxiv version
- Effect of torsion on neutron star structure in Einstein-Cartan gravity
Joint work with Cédric Jockel, Phys. Rev. D 110, 104022 – Published 12 November, 2024, arxiv version
Visiting positions
- Graduate Research and Teaching Assistant at the University of Zürich, visiting Prof. Alberto Cattaneo's group, September 2025 - December 2025
- Junior Research Fellow at the Institute Mittag-Leffler for the program "Cohomological Aspects of Quantum Field Theory", Januar 2025 - April 2025
Scripts, Notes and Scribbles
- How Graph Theory Links Topological Quantum Field Theory to Homotopy Transfer
Short note that I wrote for a course in discrete mathematics, slightly stretching the scope, 2023 - Mathematical Foundations of Quantum Field Theory
Script that I wrote for the corresponding lecture at ETH, 2021 - Introduction to 2-dimensional Topological Quantum Field Theory
Stemming from a semester project with the late Prof. Will J. Merry at ETH Zürich, 2021
Talks
- Reduction of 1D SUGRA, seminar talk for "Advanced Topics in Field Theory" at UZH, (announcement)
- A 1-dimensional Model for Chern–Simons Theory, 2hr seminar talk for "Advanced Topics in Field Theory" at UZH (announcement)
- Homotopy Transfer from Gauge-fixed BF Theory, Junior talk at Institute Mittag-Leffler during "Cohomological Aspects of Quantum Field Theory"
(announcement IML, announcement SMC, announcement KTH) - The Fukay-Morse Category: Enhancements and Field-Theoretic Approach, invited talk at Uppsala Universitet
(announcement) - Homotopy Transfer, Gauge-fixing and Why Some Theorems Grow on Trees, seminar talk at Notre Dame
(announcement part I, announcement part II) - Higher Massey Operations from Morse Theory [and how to model them], seminar talk at Notre Dame
(announcement)
Seminars
- During Fall 2024 and Spring 2025 I organised the Graduate Student Seminar at Notre Dame. You can find the list of talks here:
(Fall2024 / Spring2025)
Contact
Email: info[]leonmenger[]de
Github: /Leon-Menger
LinkedIn: /leonmenger
ORCID: 0000000306214977
© Leon Menger 2025
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