- The group isomorphism problem, computational group theory

- Structural group theory, graphs on groups

- Weisfeiler-Leman Algorithms

• J. Brachter, E. Kaja. On groups with chordal power graph, including a classification in the case of finite simple groups , arXiv, 2022.
• J. Brachter, E. Kaja. Classification of non-solvable groups whose power graph is a cograph , accepted in the Journal of Group Theory, 2022.
• J. Brachter, P. Schweitzer. A Systematic Study of Isomorphism Invariants of Finite Groups via the Weisfeiler-Leman Dimension , 30th Annual European Symposium on Algorithms (ESA 2022), 2022.Full version (arXiv).
• M. Anders, J. Brachter, P. Schweitzer. A Characterization of Individualization-Refinement Trees, ISAAC, 2021.Full version (arXiv).
• J Brachter, P. Schweitzer. On the Weisfeiler-Leman Dimension of Finite Groups, LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, 2020.Full version (arXiv).
• Software:
  J. Brachter, S. Siccha, E. Ahrens. GaussPar, a package for GAP/HPC-GAP implementing a parallel algorithm for Gaussian elimination over finite fields, 2021.