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Fakultät für Mathematik Universität Regensburg


Matthias Uschold

Universität Regensburg
93040 Regensburg

E-mail: matthias.uschold (at) mathematik.uni-regensburg.de
Office: M 205

I am a PhD student at the University of Regensburg, supervised by Prof. Dr. Clara Löh. I am a member and partially funded by the SFB 1085 "Higher Invariants".

I'm interested in: L2-Betti numbers, log-torsion growth, simplicial volume, proof assistants for the working mathematician (especially Lean)

Invited talks

06.12.2022 Homology growth of inner amenable groups in degree one” at Oberseminar Topology, Georg-August-Universität Göttingen
27.09.2022 Implementing Amenable Groups in Lean” at the workshop Recent Advances in Bounded Cohomology, University of Regensburg (Lean source code)
09.05.2022 $L^2$ -Betti numbers and computability of reals” at the International young seminar on bounded cohomology and simplicial volume
24.03.2022 Computability of $L^2$ -Betti Numbers” at the Geometry Graduate Colloquium, ETH Zürich
21.01.2022 Computability and $\ell^2$ -Betti Numbers” at Oberseminar Algebra und Geometrie, Heinrich Heine-Universität Düsseldorf


Master's thesis

I wrote my master's thesis “Computability and $\ell^2$ -Betti Numbers” (pdf) under the supervision of Prof. Dr. Clara Löh. Some of the results were implemented using the Lean Theorem Prover. The project can be found here.



Winter term 2022/23 TA for Open Covers and complexity (à la Lusternik--Schnirelmann)
Tutor for Applied Algebraic Topology
Organiser of the Online Seminar on Bounded Cohomology and Simplicial Volume (joint with Federica Bertolotti and Kevin Li)
Summer term 2022 Tutor for Geometric Group Theory
Winter term 2021/22 TA for Proof Lab: Simplicial Topology
Tutor for Algebraic Topology
Summer term 2021 Tutor for Geometrie (Lehramt Gymnasium)
Winter term 2020/21 Tutor for Analysis I
Summer term 2020 Tutor for Analysis auf Mannigfaltigkeiten (Analysis IV)
Summer term 2019 Tutor for Einführung in Wahrscheinlichkeitstheorie und Statistik
Winter term 2018/19 Tutor for Algebra
Summer term 2018 Tutor for Lineare Algebra II
Winter term 2017/18 Tutor for Lineare Algebra I

Short CV

2021 - present PhD student at the University of Regensburg
2019 - 2021 MSc in Mathematics at the University of Regensburg
Master's thesis: “Computability and $\ell^2$ -Betti Numbers
09/2019 - 01/2020 ERASMUS stay at the Université de Bordeaux
2016 - 2019 BSc in Mathematics at the University of Regensburg
Bachelor's thesis: “Chromatic Number of Groups

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Last Updated: Mar 07, 2023