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About me

I am a Heisenberg fellow and Privatdozent at the University of Hamburg, where I am a member of the research group Mathematical Logic and Interdisciplinary Applications of Logic at the Department of Mathematics.

My fields of research are Mathematical Logic and Set Theory. My research focuses on the theory of large cardinals, infinitary combinatorics, set-theoretic definability and applications of set theory in algebra.

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News

• Brief report Large infinities and definable sets in the Proceedings of the National Academy of Sciences of the United States of America.
• DFG-Project Large cardinals, set-theoretic definability and singular cardinal combinatorics.
• Article Is Mathematics Mostly Chaos or Mostly Order? in Quanta Magazine.
• Panelist of the Sixth European Set Theory Colloquium.
• Tutorial speaker at Young Set Theory 2025.
• Member of the Editorial Board of Zeitschrift für Mathematische Logik und Grundlagen der Mathematik.

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Selected Publications

• (with Juan P. Aguilera and Joan Bagaria) Large infinities and definable sets.
  Proceedings of the National Academy of Sciences of the United States of America, Volume 123, 3 pp., 2026.
• Weak compactness cardinals for strong logics and subtlety properties of the class of ordinals.
  Journal of the London Mathematical Society, Volume 112, Issue 1, 37 pp., 2025.
• (with Joan Bagaria) Patterns of Structural Reflection in the large-cardinal hierarchy.
  Transactions of the American Mathematical Society, Volume 377, Issue 5, 3397-3447, 2024.
• (with Sandra Müller) Σ₁-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders.
  Forum of Mathematics, Sigma, Volume 11, 36 pp., 2023.
• Structural reflection, shrewd cardinals and the size of the continuum.
  Journal of Mathematical Logic, Volume 22, Issue 2, 43 pp., 2022.
• (with Saharon Shelah) Free groups and automorphism groups of infinite structures.
  Forum of Mathematics, Sigma, Volume 2, 18 pp., 2014.

Complete list of publications

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Recent Preprints

• (with Juan P. Aguilera, Joan Bagaria and Gabriel Goldberg) Large cardinals beyond HOD.
• (with Juan P. Aguilera and Joan Bagaria) Large cardinals, structural reflection, and the HOD conjecture.
• (with Peter Holy and Sandra Müller) Outward compactness.
• The complexity of non-stationary ideals.

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Current Teaching

• Lecture course: Mathematical Logic and Set Theory (Hamburg, Summer 26)
• Lecture course: Topics of Analysis (Hamburg, Winter 25/26)

• All teaching activities

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Funded research projects

• DFG-Project: Large cardinals, set-theoretic definability and singular cardinal combinatorics.
• Heisenberg Project: Definability and singular cardinals
• MSCA Project: Strong Axioms of Infinity - Frameworks, Interactions and Applications
• DFG-Project: Complexity and Definability at Higher Cardinals - Studies in Generalized Descriptive Set Theory.

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Supervision

• Ana Njegomir (PhD Thesis: Small embeddings, forcing with side conditions, and large cardinal characterizations. Bonn, 2019).
• Anna Lenz (Hamburg, since 2025).

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Profiles

• MathSciNet
• Orchid
• Google Scholar

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Contact Information