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Mr Jan Steinebrunner

  • College positions:

    Research Fellow

  • Subject:

Subject

Mathematics (Algebraic Topology of Manifolds)

Degree(s)

BSc and MSc in Mathematics (Freiburg); Master’s in Mathematical and Theoretical Physics (Oxford); DPhil in Mathematics (Oxford)

Research interests

My research falls in the area of Algebraic Topology and is centred around the study of moduli spaces of manifolds. These moduli spaces are fundamental objects in Topology which encode the symmetries and possible deformations of geometric objects of varying dimension. I try to connect these moduli spaces to various other areas of pure Mathematics, such as algebraic K-theory and tropical geometry, by using tools from homotopy theory, category theory, and algebra. In past I’ve particularly studied classifying spaces of (low-dimensional) bordism categories.

In some ongoing projects I also think about topological K-theory, unitary higher categories, and homological stability.

Teaching Interests

I’ve taught classes in Freiburg and Oxford on a range of topics including Calculus, Topology, Geometric Group Theory, Category Theory, and Lie Groups. I’m looking forward to giving supervisions on various topics at Caius.

Awards and prizes

Ioan and Rosemary Jones scholarship (2017-2021)

Member of the 'Studienstiftung des deutschen Volkes', (2014-17)

Bundeswettbewerb Mathematik, one of 15 winners. (2013 and 2014)

Publications

The classifying space of the one-dimensional bordism category and a cobordism model for TC of spaces. (Journal of Topology 2021, arXiv:2004.14902)

The space of traces in symmetric monoidal infinity categories. (Quarterly Journal of Mathematics 2021, arXiv:1811.11654)

Other interests

Endurance running, climbing (bouldering), science fiction.