Fakultät für Mathematik Universität Regensburg

Matthias Uschold

Universität Regensburg
93040 Regensburg
Germany

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

 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 “$L^2$ L2-Betti numbers and computability of reals” at the International young seminar on bounded cohomology and simplicial volume 24.03.2022 “Computability of $L^2$ L2-Betti Numbers” at the Geometry Graduate Colloquium, ETH Zürich 21.01.2022 “Computability and $\ell^2$ l2-Betti Numbers” at Oberseminar Algebra und Geometrie, Heinrich Heine-Universität Düsseldorf

Preprints

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.

Miscellaneous

Teaching

 Winter term 2022/23 TA for Open Covers and complexity (à la Lusternik--Schnirelmann) Tutor for Applied Algebraic Topology 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 $\ell^2$ l2-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”