I am a Research Associate in Mathematics at the University of Cambridge in the group of Oscar Randal-Williams. Previously, I was at the University of Copenhagen where I finished my PhD in October 2018.
Contact Information
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Research interests
Algebraic and Geometric Topology, in particular: topology of moduli spaces, manifold bundles and their characteristic classes, automorphism and embedding spaces of manifolds, mapping class groups, surgery theory, cobordism categories, and configuration spaces. My side interests include the cohomology of arithmetic groups, K-theory, and (computational) stable and unstable homotopy theory.
For further information, see my CV.
News
- Together with Mauricio Bustamante, I will give an LMS Online Graduate Lecture Series on manifold topology with a focus on exotic spheres. These lectures are kindly sponsored by the London Mathematical Society and supported as part of the ICMS/INI Online Mathematical Sciences Seminars. More information can be found here.
Preprints
- An HP2-bundle over S4 with nontrivial Â-genus (arXiv) (2020), with Alexander Kupers and Oscar Randal-Williams.
- A homological approach to pseudoisotopy theory. I (arXiv) (2020).
- Appendix to Geometric cycles and characteristic classes of manifold bundles (arXiv) (2019), by Bena Tshishiku.
Publications
- Mapping class groups of highly connected (4k+2)-manifolds (arXiv).
Selecta Mathematica, to appear. - Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic (preprint), with Oscar Randal-Williams.
Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 469-473. - A note on rational homological stability of automorphisms of manifolds (arXiv).
The Quarterly Journal of Mathematics 71 (3) (2020) 1069–1079. - Some Hermitian K-groups via geometric topology (arXiv), with Alexander Kupers.
Proceedings of the American Mathematical Society, to appear. - Characteristic numbers of manifold bundles over surfaces with highly connected fibers (arXiv), with Jens Reinhold.
Journal of the London Mathematical Society, to appear. - On characteristic classes of exotic manifold bundles (arXiv).
Mathematische Annalen, to appear. Erratum - Homological stability of topological moduli spaces (arXiv).
Geometry & Topology 23 (5) (2019) 2397–2474.
Miscellaneous
- Moduli spaces of h-cobordisms of discs (extended abstract). Oberwolfach Reports (2020), to appear.
- Pseudoisotopies of even discs, revisited (extended abstract). Oberwolfach Reports (2020), to appear.
- Weight decompositions and automorphism groups of manifolds (joint with M. Krannich) (extended abstract), by Alexander Kupers. Oberwolfach Reports (2019), to appear.
- I compiled a list of problems from the workshop on Automorphisms of Manifolds at the Hausdorff Center for Mathematics in Bonn in September 2019.
- A video of me speaking about diffeomorphism groups of discs during the workshop Four Manifolds: Confluence of High and Low Dimensions at the Fields Institute in Toronto in July 2019 can be found here.
- My thesis (University of Copenhagen, Sep 2018, winner of the SCIENCE PhD Award 2019).
Teaching and service
- In September 2020, I will give an LMS Online Graduate Lecture Series on Exotic Spheres (with Mauricio Bustamante).
- I set a part III essay on Topology of Configuration Spaces in 2020.
- In Michaelmas 2019, I was organising a seminar on aspects of work of Weiss and Williams.
Forthcoming and past talks
- Summer 2021, TBD, International Workshop on Algebraic Topology (IWoAT 2021), Beijing.
- July 2020, Moduli spaces of h-cobordisms of discs, Topologie, Oberwolfach.
- May 2020, Pseudoisotopies of discs and algebraic K-theory of the integers, Topology Seminar, Purdue.
- May 2020, The pseudoisotopy stable range, Topology Seminar, Bonn.
- Mar 2020, Pseudoisotopies of even discs and algebraic K-theory of the integers, Topology Seminar, Wayne State.
- Mar 2020, Pseudoisotopies of even discs and algebraic K-theory of the integers, Geometry & Topology Seminar, Brown.
- Mar 2020, Pseudoisotopies of even discs and algebraic K-theory of the integers, Topology Seminar, Brandeis.
- Feb 2020, Pseudoisotopies of even discs, revisited, Manifolds and Groups, Oberwolfach.
- Jan 2020, A homological approach to pseudoisotopy theory, Algebraic Topology Seminar, Warwick.
- Dec 2019, A homological approach to pseudoisotopy theory, Topology Seminar, Münster.
- Nov 2019, Diffeomorphism groups of discs, Topology Seminar, Aberdeen.
- Oct 2019, Mapping class groups, signatures, and arithmeticity, MPI Topology Seminar, Bonn.
- July 2019, Diffeomorphism groups of discs, Four Manifolds: Confluence of High and Low Dimensions, Fields Institute Toronto.
- June 2019, Rational homotopy groups of diffeomorphism groups of discs, revisited (short talk), Conference: SYM 10 years old, Copenhagen.
- Apr 2019, Mapping class groups of highly connected manifolds, Geometry Centre Seminar, Utrecht.
- Apr 2019, Mapping class groups of highly connected manifolds, Seminar in Algebra & Geometry, Stockholm.
- Mar 2019, Mapping class groups of highly connected manifolds, Topology Seminar, MIT.
- Jan 2019, Mapping class groups of highly connected manifolds, Geometry and Topology Seminar, Durham.
- Dec 2018, On the signature of bundles over surfaces, Oberseminar Differentialgeometrie, Augsburg.
- Dec 2018, Mapping class groups of highly connected manifolds, Bavarian Geometry/Topology Seminar, Augsburg.
- Dec 2018, Mapping class groups of highly connected manifolds, Workshop "Manifolds" during the programme "Homotopy harnessing higher structures", Newton Institute Cambridge.
- Nov 2018, Detecting exotic smooth structures in diffeomorphism groups, Differential Geometry and Topology Seminar, Cambridge.
- Sept 2018, Topological moduli spaces, E₂-algebras, and homological stability, Workshop Cohomological study of mapping class groups and related topics, Strasbourg.
- June 2018, On the signature of smooth bundles over surfaces, Conference "Manifolds, Groups, and Homotopy", Isle of Skye. (Slides)
- Apr 2018, Characteristic numbers of manifold bundles over surfaces with highly connected fibres, Oxford–Cambridge–Aberdeen Meeting on Manifolds, Cambridge.
- Apr 2018, Homological stability of topological moduli spaces, Topology Seminar, Purdue.
- Apr 2018, Detecting exotic smooth structures in diffeomorphism groups, Topology Seminar, Northwestern.
- Apr 2018, Topological moduli spaces, E₂-algebras, and homological stability, Geometry/Topology Seminar and Topology Seminar (joint), University of Chicago.
- Jan 2018, On characteristic classes of exotic manifold bundles, Topology Seminar, Bonn.
- Jan 2018, On characteristic classes of exotic manifold bundles, Topology Seminar, Karlsruhe.
- Jan 2018, On characteristic classes of exotic manifold bundles, Topology Seminar, Münster.
- Dec 2017, On characteristic classes of exotic manifold bundles, Topology Seminar, Copenhagen.
- July 2017, On the cohomology of moduli spaces of manifolds connect summed with an exotic sphere, Young Topologists' Meeting, Stockholm.
- Mar 2017, Homological stability of E₁-modules over E₂-algebras and twisted stability of topological moduli spaces, Topology Seminar, Aberdeen.