Possible theses topics

I am generally interested in supervising Bachelor and Master theses in topics involving Functional Analysis or Topology, their applications in Analysis, or their interactions with Set Theory and Combinatorics. Below you can find a sample of specific topics that I would be interested in supervising. If you are interested in any of the topics listed below, or have other suggestions, I am looking forward to a chat with you.

Topics for Bachelor theses

  • Infinite-dimensional unit spheres are Lipschitz-contractible

  • Normal structure and the fixed-point property

  • Doubling metric spaces and doubling measures

  • Introduction to infinite-dimensional polyhedrality

  • Tsirelson's space and combinatorial Banach spaces

  • Discrete groups of normed spaces, constructions and properties

  • Hamel bases and cardinality of Banach spaces

  • Equivalents of the Axiom of Choice in Functional Analysis

  • Applications of Martin's axiom

  • Transfinite induction and applications

  • Equivalents of the Continuum Hypothesis in Analysis

  • Compactifications of the natural numbers

  • Constructions of point-finite tilings in normed spaces

  • Applications of Baire categories in the theory of tilings

  • Klee's construction of disjoint tilings

  • Corson's theorem on locally finite coverings

  • The mathematics of Escher's tilings

  • Penrose's aperiodic tiling of the plane

Topics for Master theses

  • The decomposition method for Lipschitz-free spaces and compact manifolds

  • Compact reduction in Lipschitz-free spaces

  • Supports in Lipschitz-free spaces and applications

  • Lipschitz-free spaces over ℝ-trees

  • Topological methods in the Calculus of the Variations (Mountain pass theorem, Linking theorem,...)

  • Eberlein compact spaces and their continuous images

  • Ultraproducts of Banach spaces and fixed-point theory

  • The fixed-point property in reflexive Banach spaces

  • Non-reflexive Banach spaces with the fixed-point property

  • Properties of polyhedral Banach spaces

  • Banach spaces of continuous functions on ordinals

  • Boundedness results for Markushevich bases

  • Equilateral sets in Banach spaces

  • Lipschitz images of positive measure sets

Supervised theses

  • The Prime Number Theorem via Complex Analysis
    Maximilian Denk, BSc thesis, Spring 2025

  • On the Lipschitz classification of Banach spaces, and Lipschitz-free spaces
    Maximilian Reibmayr, MSc thesis, Spring 2024
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