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 certain effective quantum field 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 very 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. My long-term goal is to work at 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 as organically and self-contained as I can, 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
- 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 - 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
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 Will J. Merry at ETH Zürich, 2021
Talks
- Homotopy Transfer, Gauge-fixing and Why Some Theorems Grow on Trees
(announcement part I, announcement part II) - Higher Massey Operations from Morse Theory [and how to model them]
(announcement)
Contact
Email: info[]leonmenger[]de
Github: /Leon-Menger
LinkedIn: /leonmenger
ORCID: 0000000306214977
© Leon Menger 2024
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