Nils Carqueville

My work in mathematical physics often uses methods and ideas from algebra, category theory and topology -- in particular where they come together. Some background in quantum physics as well as basic algebra or category theory are useful prerequisites to work with me on a Master project. Specific topic areas include topological quantum field theory (TQFT), state sum models, topological sigma models, relations to topological phases, and applied higher category theory. You may wish to consult these introductory lecture notes on TQFT, or these lecture notes on 2-dimensional defect TQFT, and I'd be happy to give further references if you contact me.

Stefan Fredenhagen

Topics of master projects can be in the area of higher-spin gravity theories or conformal field theories. Higher-spin gravity is a generalisation of gravity where additional higher-spin gauge fields are introduced. Such models are expected to appear in a tensionless limit of string theory. For a basic introduction to the topic see e.g. here.

Conformal field theories are of wide interest in theoretical physics, ranging from condensed matter physics to string theory. In particular they occur as world-sheet theories of strings and as holographic duals of gravitational theories including higher-spin gravity and string theory. For an introduction to the topic see e.g. here.

L. Glaser

I work on Quantum Gravity, in particular on Causal set theory and non-commutative geometry (employing a spectral triple standpoint). A short, understandable (but maybe slightly outdated), intro into either can be found on my website
My work merges computer simulations with analytic work, so I am always happy to talk to students that are interested in working with simulations. Possible projects would be:

• Exploring the Ising model on particular models of causal sets
• Looking at combinatorial questions on causal sets
• Visualisations of spectral triples
• Working with simple spectral triples

My simulations generate a lot of data, and I have a side interest in trying to further explore these using Machine learning techniques, so if you are interested in this direction lets have a chat. In general I do not have fixed projects in mind, but would hope to develop ideas that are interesting to you as well as myself.

Marcus Sperling

My work delves into the fundamental aspects of quantum field theories (QFTs), focusing on symmetries and vacua. By exploring supersymmetric theories as a laboratory for QFTS, we uncover a rich dialogue between geometry, algebra, and physics. This fusion not only leverages modern mathematics to unlock precise insights into complex, strongly coupled, or even non-Lagrangian theories, but also paves new ways to illuminate mathematics through the lens of physics.

A basic understanding of quantum physics, classical field theory, algebra, group and representation theory, and geometry will greatly benefit those looking to collaborate on a Master's project with me. Our specific areas of interest include supersymmetric quantum field theories, moduli spaces of vacua, and the exploration of global symmetries and defects.

I’m open to various project ideas rather than sticking to predetermined ones. If this sparks your interest, I warmly invite you to reach out. Let’s have a conversation and discover how we can collaborate on groundbreaking research together.

Harold Steinacker

My primary area of interest is "Quantum Geometry" as an approach to quantum gravity. This involves the mathematical description of quantized spaces and geometrical structures, in analogy to Quantum Mechanics. The main focus is on those aspects which are relevant to Matrix Models, which are candidates for a theory of quantum gravity, and naturally lead to such mathematical structures. There are many challenging open research problems, which require some familiarity with basic differential geometry, and often (but not always) Lie group techniques.

Topics suitable for a Master's thesis include a somewhat numerically oriented project:

- Find the quasi-coherent states for certain examples of quantized geometry (e.g. the squased fuzzy sphere, fuzzy disk) and study their embedding in CP^N . This might lead to the development or improvement of associated software and visualization tool.