IMG_DD

About me

I'm a PhD candidate in mathematics at the University of Notre Dame, working with Pavel Mnev. From January 2025 to April 2025 I was a Junior Research Fellow at the Institute Mittag–Leffler. Since August 2025 I am visiting Alberto Cattaneo's group at the University of Zurich.

Broadly speaking I am interested in Quantum Field Theory. More specifically I work with 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. In particular I like thinking about certain Fukaya–Morse $A_\infty$-categories, which turn out to be beautifully modelled by effective $BF$ theories.

Another focus of mine is 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. During my stay at the University of Zurich, this project is being expanded upon, so stay tuned. 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 articles, notes or scribbles. 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

 
Visiting positions


Scripts, Notes and Scribbles

  1. 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

  2. Mathematical Foundations of Quantum Field Theory
    Script that I wrote for the corresponding lecture at ETH, 2021

  3. 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

  • BV Pushforward of Quadratically Extended BF in 4 Dimensions and its Relation to Gravity, 2hr seminar talk for "Advanced Topics in Field Theory" at UZH, (announcement)
  • Quadratically Extended BF in Dimensions 3 and Higher, 2hr seminar talk for "Advanced Topics in Field Theory" at UZH, (announcement)
  • First Quantisation Formalism for BF-like AKSZ Theories, workshop talk for "BV and its application", (announcement)
  • 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/firstnamelastname/de
ORCID: 0000000306214977
Google Scholar: Here
Github: /Leon-Menger
LinkedIn: /leonmenger

© Leon Menger 2026

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