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
Geometric and Algebraic 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, configuration spaces, K-theory, and applications to differential geometry. My side interests include the cohomology of arithmetic groups and (computational) stable and unstable homotopy theory.
For further information, see my CV.
Preprints
- Embedding calculus for surfaces (arXiv) (2021), with Alexander Kupers.
- A homological approach to pseudoisotopy theory. I (arXiv) (2020).
Publications
- An HP2-bundle over S4 with nontrivial Â-genus (arXiv) (2020), with Alexander Kupers and Oscar Randal-Williams.
Comptes Rendus. Mathématique, to appear. - Appendix to Geometric cycles and characteristic classes of manifold bundles (arXiv), by Bena Tshishiku.
Commentarii Mathematici Helvetici, to appear. - Mapping class groups of highly connected (4k+2)-manifolds (arXiv).
Selecta Mathematica 26, 81 (2020). - 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 102 (2) (2020) 879--904. - On characteristic classes of exotic manifold bundles (arXiv).
Mathematische Annalen, 379 (2021) 1--21. 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 Lent 2021, I am organising a seminar on factorisation homology.
- I set a part III essay on Topology of Configuration Spaces in 2021.
- In September 2020, I gave an LMS Online Graduate Lecture Series on manifold topology with a focus on exotic spheres together with Mauricio Bustamante. These lectures were kindly sponsored by the London Mathematical Society and supported as part of the ICMS/INI Online Mathematical Sciences Seminars.
- 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.
- April 2021, TBD, Séminaire de l'équipe Topologie Algébrique, Université Sorbonne Paris Nord (Paris 13).
- April 2021, TBD, Building Bridges Seminar: Invariants of Embedding spaces, virtual.
- Feb 2021, Smoothing fibre bundles and diffeomorphism groups of discs, Geometry & Topology Seminar, Toronto.
- 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.