RESEARCH GROUP

GEOMETRY

Geometric group theory in connection with topology is my main research interest. The subject of my current research are the combinatorics of non-affine Coxeter groups within the context of my PhD studies.

Previously, I wrote my Bachelor and Master thesis on the local structure of locally compact groups and on a geometric proof of the strong Hanna Neumann conjecture.The former deals mainly with local splitting properties of these groups.

• Grundalgen der Mathematik (Ü), Wintersemester 2023/24
• Geometrie (Ü), Sommersemester 2023
• Mathematik 3 für Informatik (Ü), Wintersemester 2022/23
• Organisation der Ringvorlesung "Geschichte und Grundlagen der Mathematik", Wintersemester 2022/2023
• Geometrie (Ü), Sommersemester 2022
• Mathematische Methoden 1 (Ü) Wintersemester 2021/22
• Mathematical Foudations (Ü) Wintersemester 2021/22
• Geometrie (Ü), Sommersemester 2021
• Mathematical Foudations (Ü) Wintersemester 2020/21
• Geometrie (Ü) , Sommersemester 2020
• Mathematische Methoden 1 (Ü) Wintersemester 2019/20

2024:

• Lightning-talk at Young geometric group theory XII Conference, Bristol, United Kingdom.
• Attended: HaJe MaDre Algebra-Seminar, Dresden, Germany

2023:

• Talk: "New lower and upper bounds for reflection length in infinite non-affine Coxeter groups", MathCoRe fellows seminar, Magdeburg
• Attended: HaJe MaDre Algebra-Seminar, Halle, Germany
• Talk: "Reflection length at infinity in hyperbolic reflection groups" at Dresden Leipzig Seminar Algebra and Geometry, Universität Leipzig, Germany
• Talk: "Reflection length at infinity in hyperbolic reflection groups" at Oberseminar Algebra und Algebraische Kombinatorik, Leibniz Universität Hannover, Germany
• Lightning-talk at Young geometric group theory XI Conference, Münster, Germany.
• Attended: Young geometric group theory XI Conference, Münster, Germany.
• Organisation of "Mini-Workshop Reflection Groups in Magdeburg" together with Anna Michael in Magdeburg, Germany
• Presentation at X-MATH (eXperimental MATHematics) organized by the Heidelberg Experimental Geometry Lab (HEGL)

2022:

• Talk: "Reflection length in discrete hyperbolic reflection groups",  MathCoRe fellows seminar, Magdeburg
• Talk: "Reflection length in non-affine Coxeter groups", Geometry Graduate Colloquium, ETH Zurich
• Talk: "Reflection length in non-affine Coxeter groups" Mathematical Postgraduate Society Seminar, University of Sydney
• August and September: Visiting Researcher at University of Sydney with Anne Thomas
• Attended: Marco Burger's prime, Zürich, Switzerland
• Talk: "What is... Hilbert's ultra-parallel theorem for hyperplanes", WISST Seminar, Magdeburg
• Talk "Reflection length in hyperbolic Coxeter groups",  HaJe MaDre Algebra-Seminar, virtual

2021:

• Attended: Groups in Madrid Conference, Madrid, Spain
• Technical support for: Northern German Group Theory Colloquium, online
• Attended: Buildings 2021 Conference, Magdeburg, Germany.
• Talk: "Reflection length in hyperbolic Coxeter groups II", MathCoRe fellows seminar, Magdeburg
• Supervised: DAAD-founded internship: "Programming a geometric realisation of hyperbolic Coxeter groups".
• Attended: World of GroupCraft Conference, online
• Attended: Summer school Berlin 2021: The dual approach to Coxeter and Artin groups, Berlin, Germany
• Attended: Young geometric group theory X Conference, online
• Attended: Das Grüppchen 2021 Conference, online
• Talk: "What is... the basic construction?", WISST Seminar, Magdeburg

2020:

• Talk: "What is... a hyperbolic space?",  WISST Seminar, Magdeburg
• Talk: "Reflection length in hyperbolic Coxeter groups", MathCoRe fellows seminar, Magdeburg
• Attended: BYMAT 2020 Conference, virtual.
• Attended: Combinatorial Coworkspace Conference, Hirschegg, Austria.
• Attended: Young geometric group theory IX Conference, Saint-Jacut-de-la-mer, France.
• Talk: "What are... local groups?", WISST Seminar, Magdeburg

2019:

• Attended: Buildings 2019 Conference, Magdeburg, Germany.
• Talk: "Iwasawa’s local splitting theorem for locally compact groups", 2019, Magdeburg, Germany.

Publications

• Lotz, Marco. "Reflection length at infinity in hyperbolic reflection groups" Journal of Group Theory, 2024. https://doi.org/10.1515/jgth-2023-0073

Preprints

• Lotz, Marco. "Powers of Coxeter elements with unbounded reflection length" arXiv:2406.05218 [math.GR], 2024. https://doi.org/10.48550/arXiv.2406.05218