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

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

Preprints

• Torsion homology growth and cheap rebuilding of inner-amenable groups (pdf)
  arXiv: 2212.07916 [math.GR]
• $L^2$ -Betti numbers and computability of reals (pdf)
  joint work with Clara Löh
  (Partial) Implementation in Lean
  arXiv: 2202.03159 [math.GR]

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

• Implementation of Amenable Groups in Lean, September 2022

Teaching

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: Dec 18, 2022