Dario Stein

Are you a motivated student looking for a project? Write me an email! I am keen on (co)supervising BSc and MSc Projects as well as Research Internships. Below are some example topics that interest me:

• Presentations of Convex Spaces
  Convex spaces are algebraic structures similar to vector spaces, which model convex subsets of Euclidean space. They are useful in the study of probabilistic computation. You will investigate some algebraic questions about convex spaces, related to free algebras and presentations.
  


• Reflections into Free Algebras
  Free algebras are the basic building blocks of algebraic structures. You will investigate algebras which can be approximated by free algebras in a certain sense, or prove why such an approximation is impossible.
  


• Uniqueness of Retrodiction:
  You will study the monoid of endo-relations on a set X, and try to classify the automorphisms of this monoid.
  

• Nominal Sets and Probability
  Nominal sets are a mathematical formalism for dealing with names such as variable names or memory locations in programming languages. It doesn't matter what these names are -- we only care whether two names are equal or not. For example, variables bindings are often considered up to α-equivalence. In this project, you'll investigate various formal similarities between fresh name generation (choosing a new variable name, or allocating a memory location), and probability.
  


• Random Variables and Isometry-Sets
  How can the notion of random variables be formalized in category theory? This project will involve sheaves over categories of sample spaces. A concrete model are Iso-Sets, a novel continuous generalization of nominal sets using isometries of Euclidean space
  


• Type Theory for Equivariance
  Group actions are a fundamental language for describing mathematical structures with symmetries. How would a type theory look where everything that typechecks is automatically equivariant?
  


• Formalization of Categorical Probability
  There are many challenges involving monoidal category theory and string diagrams in proof assistants such as Lean or Rocq
  

Supervision

• PhD Students
  Márk Széles (cosupervision with Bart Jacobs), 2023 - present


• Bachelor Students
  Gideon de Hoop (daily supervisor), Sep 2024-Jan 2025


• MFOCS Seminar
  Tjitske Koster (2022), Sergio Dominguez Cabrera (2023), Dick Blankvoort (2023), Bas van der Linden (2024)

Teaching

• Spring 25, Lecturer for Category Theory and Coalgebra, Radboud University Nijmegen
• Spring 24, Lecturer for Category Theory and Coalgebra, Radboud University Nijmegen
• Winter 2023-24, MFoCS Seminar at Radboud University Nijmegen
• Spring 23, Lecturer for Category Theory and Coalgebra, Radboud University Nijmegen
• Winter 2022-23, MFoCS Seminar at Radboud University Nijmegen
• Spring 2022, Tutor for Category Theory and Coalgebra at Radboud University Nijmegen
• Michaelmas 2020, Tutor for Categories, Proofs and Processes at University of Oxford
• Hilary 2020, Tutor for Quantum Information at University of Oxford
• Michaelmas 2019, Tutor for Principles of Programming Languages at University of Oxford.
• Hilary 2019, Tutor for Probability and Computing at University of Oxford.