Visit of Mercator Fellow Kevin Walker

7 July 2025

The collaborative research center welcomes Kevin Walker as Mercator Fellow. Dr. Walker’s research focuses on low-dimensional and quantum topology. His work on topological quantum field theory has had a profound influence on the development of the field and it inspires current research directions of the CRC.

Topological quantum field theories (TQFTs) are formulated in the language of higher category theory and provide, on the one hand, highly computable manifold invariants and, on the other hand, an organizing principle for many existing mathematical structures and ideas in algebra and topology – such as the classical field of knot theory. In the collaborative research center, TQFTs are of central interest in several projects, especially A1, A2, A3, and C1.

Kevin Walker's connection to the CRC builds on a prior collaboration with PI Paul Wedrich, which started with a joint paper with Scott Morrison on the construction of a 4+ε-dimensional topological quantum field theory (TQFT) from higher structures used in knot homology theory. Current collaborative work is aimed at improving methods to compute and test the sensitivity of the resulting 4-manifold invariants. In another project, Kevin Walker, Paul Wedrich and doctoral researcher Leon Goertz explore a related construction providing an example of a 3+ε-dimensional TQFT that extends only partially to dimension 4. Kevin Walker also has an ongoing collaboration with PI David Reutter on a general framework for extending TQFTs to higher dimensions and applications thereof to the construction of new non-semisimple theories.

After graduating from Princeton University, Kevin Walker earned his Ph.D. in mathematics at the University of California, Berkeley in 1989. Working at Microsoft Station Q, he was one of the mathematical pioneers of topological quantum computing, connecting research on topological quantum field theories to physics and computer science. In this direction, his research explores interactions between concepts in higher category theory and condensed matter physics, fostering a better understanding of the foundations of topological quantum computing through the lens of modern mathematical language.

During his current research visit to the CRC 1624 in Hamburg, Kevin Walker is excited to interact with his long-term collaborators as well as young researchers. He has given a colloquium talk aimed at a broader mathematical audience on Kramers-Wannier dualities and higher Morita equivalences and a specialized talk on Higher-dimensional Temperley-Lieb categories via partition relations at the Quantum Topology and Categorification (QTCat) seminar of PIs David Reutter and Paul Wedrich.

Reported by Colin Ji

Kevin Walker and David Reutter at work - captured by Leon Goertz