I'm a postdoc in algebraic topology at the Ludwig-Maximilians-University Munich. Before this, I was a postdoc and Marie-Curie Fellow at the University of Copenhagen. Until 2017 I was a doctoral student at the University of Oxford. My advisor was Prof. Ulrike Tillmann. My thesis on commutative K-theory is available here.
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Research interests
My research interests are in algebraic topology and its applications. A large part of my work has been on the topology of certain moduli spaces of representations, particularly spaces of commuting elements in Lie groups. Earlier in my career I did some research in theoretical particle physics.Research articles
Preprints
- Commuting varieties and the rank filtration of topological K-theory
Preprint (2024), 15 pages ▪ arXiv - A remark on the group-completion theorem
Preprint (2017) ▪ arXiv
Published or accepted articles
- A stable splitting for spaces of commuting elements in unitary groups
(with Alejandro Adem and José Manuel Gómez)
To appear in: J. London Math. Soc., Preprint (2024), 32 pages ▪ arXiv - On families of nilpotent subgroups and associated coset posets
(with Bernardo Villarreal)
J. Homotopy Relat. Struct. (2022), 17 pages ▪ journal ▪ arXiv - On the second homotopy group of spaces of commuting elements in Lie groups
(with Alejandro Adem and José Manuel Gómez)
Int. Math. Res. Not. IMRN (2021), 73 pages ▪ journal (open access) ▪ arXiv - Higher generation by abelian subgroups in Lie groups
(with Omar Antolín-Camarena and Bernardo Villarreal)
Transform. Groups (2021), 16 pages ▪ journal (open access) ▪ arXiv - Classifying spaces for commutativity of low-dimensional Lie groups
(with Omar Antolín-Camarena and Bernardo Villarreal)
Math. Proc. Cambridge Phil. Soc. 169 (2020), 433-478 ▪ journal ▪ arXiv - Commuting matrices and Atiyah's Real K-theory
(with Markus Hausmann)
J. Topol. 12 (2019), 832-853 ▪ journal ▪ arXiv - The spectrum for commutative complex K-theory
Algebr. Geom. Topol. 18 (2018), 1205-1249 ▪ journal ▪ arXiv - Variable-flavor-number scheme for final state jets in thrust
(with Piotr Pietrulewicz, Andre Hoang, Ilaria Jemos, and Vicent Mateu)
Phys. Rev. D 90, 114001 (2014) ▪ journal ▪ arXiv - Two loop soft function for secondary massive quarks
(with Andre Hoang, Ilaria Jemos, and Piotr Pietrulewicz)
Phys. Rev. D 89, 014035 (2014) ▪ journal ▪ arXiv - Secondary heavy quark production in jets through mass modes
(with Andre Hoang, Ilaria Jemos, and Piotr Pietrulewicz)
Phys. Rev. D 88, 034021 (2013) ▪ journal ▪ arXiv
Reports
- On the space of commuting pairs in a Lie group
Mathematisches Forschungsinstitut Oberwolfach. Report No. 23/2020,
doi:10.14760/OWR-2020-23
Teaching at Ludwig-Maximilians-University Munich
Supervision
- Jakob Neumaier, "Equivariant homology theories and an application to spaces of representations" (MSc, 2024)
Courses
- Reading course on rational and p-adic homotopy theory (cont.), winter term 2024/25
- Mathematical Gauge Theory 1 (Yang-Mills theory), TA, winter term 2024/25
- Topology 1, TA, winter term 2024/25
- Reading course on rational and p-adic homotopy theory, summer term 2024
- Linear Algebra 2, TA, summer term 2024
- Seminar on Spectral Sequences, winter term 2023/24
- Topology 1, TA, winter term 2023/24
- Topology 2, lecturer, summer term 2023
- Topology 1, lecturer, winter term 2022/23
- Symplectic Geometry, TA, summer term 2022
- Seminar on Representation Varieties of Surface Groups, summer term 2022
- Seminar on Vector Bundles and K-Theory, TA, winter term 2021/22
- Complex Geometry, TA, winter term 2021/22
- Mathematical Gauge Theory 2 (Seiberg-Witten-Theory), TA, winter term 2021/22
Teaching at the University of Copenhagen
Supervision
- Nicolas-Domenic Reiter, "Deformation K-theory" (MSc, 2020)
Courses
- Categories and Topology, lecturer (jointly with Jesper Grodal), winter 2020
- Homological algebra, lecturer, winter 2019
- Algebraic topology 1.5, lecturer (jointly with Thomas Wasserman), spring 2019
- Homological algebra, lecturer, winter 2018
- Algebraic topology 1.5, TA, spring 2018
- Homological algebra, TA, winter 2017
Other
A link to SPECTRA, the association for LGBTQ+ mathematicians.
The online workshop Spaces of Homomorphisms and Classifying Spaces SHCS-2021 held 7-9 September 2021, jointly organised with Omar Antolín-Camarena, Cihan Okay, and Bernardo Villarreal.
A mini-workshop on Simplicial complexes held 17-21 August 2020 at the University of Copenhagen.
From Nov-2017 until Apr-2019 I organised with Tobias Barthel the Algebra and Topology seminar in Copenhagen.