Linus Richter

I am a Research Fellow in the Department of Mathematics at the National University of Singapore. My research interests lie in both computability theory and set theory, and especially at their intersection. Currently, I am working on questions in:

• descriptive set theory
• algorithmic randomness
• interactions between computability theory and set theory

Previously, I completed a PhD in mathematics at Victoria University of Wellington (New Zealand) advised by Dan Turetsky. Before going to New Zealand, I received a Master’s degree from the University of Manchester (United Kingdom) in 2018. My Master’s thesis was supervised by Gareth Jones.

Contact

Publications

Papers

1. All Borel Group Extensions of Finite-Dimensional Real Space Are Trivial, submitted
   ∎ pdf | ↗︎ arXiv
2. (with J. Chen, B. Kjos-Hanssen, I. Koswara, F. Stephan) Languages of Words of Low Automatic Complexity Are Hard to Compute, submitted
   ∎ pdf
3. Co-analytic Counterexamples to Marstrand's Projection Theorem, submitted
   ∎ pdf | ↗︎ arXiv
4. (with N. Greenberg, S. Shelah, D. Turetsky) More on bases of uncountable free abelian groups, volume 44 of Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, p. 71-85, World Scientific, 2025
   ∎ pdf | ↗︎ published version

Theses

1. On the Definability and Complexity of Sets and Structures, PhD thesis, Victoria University of Wellington, 2024
   ∎ pdf | ↗︎ published version
2. Topics in Set Theory and Logic, Masters thesis, University of Manchester, 2018
   ∎ pdf

Talks

• Regularity Properties in Fractal Geometry, Old and New, Logic Seminar, The University of Manchester, Jun 2025
  ∎ slides pdf
• Computability, Consistency, and a Theorem on Fractals, Logic, Categories and Applications Seminar, University of Bologna, Dec 2024
  ∎ slides pdf
• On the Definability and Complexity of Sets and Structures, Colloquium Logicum 2024, PhD Colloquium, Austrian Academy of Sciences, Oct 2024
  ∎ slides pdf
• The Borel-Definable Group Cohomology of ℝⁿ Is (Hopefully) Simple, IMS Graduate Summer School in Logic, National University of Singapore, Jun 2023
  ∎ notes pdf
• On Π₁¹-recursion and Marstrand's Theorem, Victoria University of Wellington Logic Seminar
  
  1. Controlling the Construction of CA-sets, Mar 2023, ∎ notes pdf
  2. CA Counterexamples to Marstrand's Projection Theorem, Mar 2023, ∎ notes pdf
• Co-analytic Counterexamples to Marstrand's Projection Theorem
  • Penn State Logic Seminar, online, Sep 2023, ∎ slides pdf
  • National University of Singapore Logic Seminar, online, Mar 2023, ∎ slides pdf
  • Computability Theory and Applications Seminar, online, Jan 2023, ∎ slides pdf
• On (Borel) Group Extensions, University of Sydney Graduate Talks in Topology and Geometry (GT)^2, online, May 2022
  ∎ slides pdf | ∎ handwritten notes pdf
• On Homological Algebra, Group Extensions, and Descriptive Set Theory, Victoria University of Wellington SMS Graduate Seminar, May 2021
  ∎ notes pdf
• When the Search for Proofs Turns Futile, Victoria University of Wellington SMS Graduate Seminar, Nov 2020
  ∎ notes pdf
• Higher Derived Limits and Cohomology of Ordinals, Victoria University of Wellington Logic Seminar, Apr 2020
  ∎ notes pdf
• Computability, Complexity, and Some Algebra, NZMASP, Wainui, Nov 2019
  ∎ slides pdf
• More on Bases of Uncountable Free Abelian Groups, Victoria University of Wellington Logic Seminar, Aug 2019

Teaching

Below I include a few short notes I have written as additional teaching materials to students during my teaching. I include them in the hope they prove useful to some.

• ℝ³ Is a Union of Discjoint Circles Under AC
  ∎ notes pdf
• One Way to Think About: Change of Bases Matrices
  ∎ notes pdf
• One Way to Think About: Zorn's Lemma
  ∎ notes pdf