Geometry Marco Lotz

I am a PhD student in mathematics at Heidelberg University. Before, I was at the Otto-von-Guericke University Magdeburg. I am part of the the working groups of my advisors Petra Schwer and Thomas Kahle. Formerly, I studied at WWU Münster and completed my Masters degree under the supervision of Linus Kramer.

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 Y oung 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