[ M.Sc. Mathematical Physics ] Leipzig, DE /// DeepTech R&D · ML Engineering

Erik
Löffelholz

Mathematical Physics >>> Geometric & Differentiable ML >>> Quantum Field Theory & Holography

DeepTech R&D engineer with a background in mathematical physics. I work in geometric machine learning, differentiable physics, and graph neural networks, and I build differentiable, GPU-accelerated systems in PyTorch, from physics simulators to generative models written from scratch. The same variational and geometric ideas I study in quantum field theory tend to show up in that engineering work. Open to fully remote ML engineering, R&D, and quantitative research roles across the EU.

Focus Quantum Field Theory / AdS-CFT
Projects 13 / 10 live demos
Affiliation MPI MiS Leipzig
Status Open to remote EU roles

SK-01 Core Frameworks

PyTorch Geometric ML (PyG) Scientific ML (SciML) JAX

SK-02 Core Mathematics

Differential Geometry Partial Differential Equations (PDEs) Graph Theory Energy-Based Optimization

SK-03 Languages & Graphics

Python JavaScript / TypeScript WebGPU Three.js

SK-04 Infrastructure & Tools

Git / GitHub Linux Docker CI/CD Pipelines
01 / THEORY

Quantum Field Theory & Holography

My core work is in quantum field theory in curved backgrounds and the AdS/CFT correspondence: the Sine-Gordon model and its vertex operators in two-dimensional Euclidean Anti-de Sitter space, their holographic renormalization, anomalous dimensions, and the structure of the dual boundary theory.

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02 / SIMULATION

Differentiable Physics

I develop mesh-based differentiable physics simulators entirely in PyTorch, where mesh topology initializes particle-spring systems and physical forces come from energy-based formulations. The whole thing is differentiable, so you can optimize through the dynamics with gradients.

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03 / LEARNING

Geometric Graph ML

A parallel interest: energy-based generative modeling of geometric graphs in 3D, like branching morphologies and meshes. It combines topological reasoning, geometric invariance, and structural priors in discrete-continuous learning frameworks.

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D-01

AdS/CFT in Two Dimensions

Holographic duality between bulk fields in Euclidean AdS₂ and boundary conformal operators.

D-02

Vertex Operators & Sine-Gordon

Observables of an integrable bulk theory in hyperbolic space and their boundary duals.

D-03

Holographic Renormalization

Renormalized correlators, anomalous dimensions, and the renormalization-group flow.

D-04

Geometric & Differentiable ML

A parallel direction: energy-based modeling of geometric graphs and differentiable physics.