# Topology- and Dimensionality-Aware Learning of Physics Data

**Topology- and Dimensionality-Aware Learning of Physics Data**

*Supervisors:* Prof. Gregor Kasieczka (UHH), Prof. Armin Iske (UHH)

Observational data from particle physics live on complex manifolds in high-dimensional embedding spaces. Topological methods can be used to assign global and local properties to datasets, where persistent homology is a powerful method for doing so. A simple example is the search for resonances: The presence of a resonant feature reduces the manifold dimension by one. Measuring the local manifold dimensionality offers an entirely novel and so-far unexplored angle of analyzing physics data and searching for new phenomena. Similarly, unsupervised machine learning techniques such as autoencoders and normalizing flows suffer from non-trivial topologies.

This project at the interface of topology, physics, and machine learning will investigate how a mathematical characterization of the manifold structure of data can be used to develop new analysis techniques for collider data. For the required mathematical data nalysis, recent methods from algebraic topology and differential geometry are employed.

### Apply here!