Student Projects

Summer Vacation Scholarship Projects

I had and have a strong interest in supervising Summer Vacation Scholarship projects and will be offering student projects for the summer break 2025-2026 (applications likely close in September 2025). More details can be found on a separate page.

Master and PhD Projects

I am available (and more than happy) to supervise undergraduate and graduate theses in representation theory and in fields related to more mathematical aspects of quantum condensed matter physics, quantum information theory, quantum field theory, string theory, statistical physics and data science. This includes, in particular, theoretical research in the fields of generalized symmetries, topological phases in condensed matter systems (quantum spin liquids, fractional quantum Hall systems, topological insulators,...), tensor network states, conformal field theory, entanglement and quantum computing.

The University of Melbourne has an agreement with the University of Hamburg in Germany and if you are interested it might be possible to do a PhD at both institutions at the same time under a shared supervision arrangement with certain members of the Center for Mathematical Physics.

Projects with me might centre around the following questions:

• Using generalized symmetries to study systems of physical significance

• Understanding the entanglement properties of quantum systems in quantum computing, lattice systems and QFT, especially in connection with their symmetries.

• Using algebraic and representation theoretic methods to understand the exact solvability of certain models of physics.

• Using effective field theories as well as algebraic and geometric ideas to classify topological phases in quantum spin models

• Using topological quantum field theories and conformal field theories to study topological phases and phase transitions in quantum systems

• Using various approaches to study non-equilibirum dynamics and (non-)thermalisation in quantum systems

• Why (quantum) deep learning works so well

• Studying the peculiarities of supersymmetric quantum models

• Studying the representation theory of finite and infinite dimensional Lie superalgebras

However, I am also open to supervise projects on other topics that broadly fit into my scope of research interests. In case you find the list above too schematic I have compiled a brief list with more detailed project titles.

If you would like to learn more about available projects please simply send me an email, including a transcript of your previous courses. Note: For some of the projects, some background knowledge in physics, especially quantum mechanics, is required.

Previous and current projects at the University of Melbourne

• Brae Vaughan-Hankinson (ongoing PhD project):
  Aspects of categorical symmetries

• Yuyang Zhou, Master Thesis (2023):
  The average behaviour of a multipartite entanglement measure via a random matrix theory approach

• Yuhan Gai, Master Thesis (2023):
  Generalized symmetries in one-dimensional physical systems

• Brae Vaughan-Hankinson, Master Thesis (2023):
  Categorical symmetries in quantum spin systems

• Chenyin Chen, Master Thesis (2022):
  Matrix product operator symmetry in project entangled pair state representation of string-nets

• Tyler Franke, Master Thesis (2022):
  String order in the q-deformed Affleck-Kennedy-Lieb-Tasaki model

• Caleb Smith, Master Thesis (2021):
  Quantum Groups, Symmetry-Protection, and the Generalized Haldane Phase

• Nick Evans, Master Thesis (2020):
  SU(2) Spin Chains and the sl(2)_k WZW Model

Previous projects at the University of Cologne

• Kay Herklotz, Master Thesis (2016):
  Effective Field Theory description of Topological Phases of SU(N) Quantum Spin Chains

• Jochen Peschutter, PhD Thesis (2016) [Link]:
  Quantum Superspin Systems from Conformal Field Theory

• Kasper Duivenvoorden, PhD Thesis (2013) [Link]:
  Symmetry protected topological phases of spin chains

• Nezhla Aghaei, Master Thesis (2012):
  Group isometries and D-branes in WZW models

• Harm Michalski, Diploma Thesis (2012):
  Topological phases in supersymmetric spin chains