About me

I am a Postdoctoral Researcher at the Interdisciplinary Hub for Security, Privacy and Data Governance (iHub) at Radboud University Nijmegen.

Here is a short overview of my CV

• DPhil in Computer Science with Sam Staton, University of Oxford, England 2021
• MASt in Pure Mathematics, Part III of the Mathematical Tripos at University of Cambridge, England 2017
• Bachelor in Mathematics, University of Hamburg, Germany

You can find my complete CV here.

Research Interests

My research interests concern the interplay of

• Category Theory
• Probability Theory
• Programming Language Semantics

These fields come together in exciting ways in categorical probability theory and probabilistic programming. Some of the mathematical tools I use are Markov categories and quasi-Borel spaces.

Other areas I'm interested in: (Bayesian) machine learning, convex analysis, functional programming with effects, type theory, quantum computation, logic, topology and algebraic geometry.

Projects

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 ideas for topics

• A Groupoid of Shapes (BSc): Two fundamental operations on an array (for example in NumPy) are reshaping and transposition, but alternating these operations can result in very complicated permutations. How can we elegantly understand such permutations using graphical reasoning and the notion of groupoid from category theory?
• Nominal Sets and Probability: What are the formal similarities between fresh name generation (choosing a new variable name, or allocating a memory location), and probability?
• Random Variables and Iso-sets: How can the formalism of random variables be captured or generalized categorically? This project will involve sheaves over categories of sample spaces. A concrete variant are Iso-sets, a continuous generalization of nominal sets using isometries of Euclidean space
• A 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?
• Causality and do-calculus: Various topics related to causal inference, causal probabilistic programming languages, and formalization
• Formalization of String Diagrams There are various tools for string diagrams, but the support in type-theoretic theorem provers (Coq/Lean) is still limited. There are various formalization challanges, e.g. Markov categories, causal inference, ...

Publications

You can find my DPhil Thesis here: Structural Foundations for Probabilistic Programming Languages

• Combs, Causality and Contractions in Atomic Markov Categories
  Dario Stein, Márk Széles
• A Categorical Treatment of Open Linear Systems
  Dario Stein, Richard Samuelson
• Graphical Quadratic Algebra
  Dario Stein, Fabio Zanasi, Richard Samuelson, Robin Piedeleu
• Towards a Compositional Framework for Convex Analysis (with Applications to Probability Theory)
  Dario Stein, Richard Samuelson, FoSSaCS 2024
• Absolute continuity, supports and idempotent splitting in categorical probability
  Tobias Fritz, Tomáš Gonda, Antonio Lorenzin, Paolo Perrone, Dario Stein
• Overdrawing Urns with Signed Probabilities
  Bart Jacobs, Dario Stein, ACT 2023
• Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic Programming
  Bart Jacobs, Dario Stein, MFPS 2023
• A Category for unifying Gaussian Probability and Nondeterminism
  Dario Stein, Richard Samuelson, CALCO 2023
• Dilations and information flow axioms in categorical probability
  Tobias Fritz, Tomáš Gonda, Nicholas Gauguin Houghton-Larsen, Paolo Perrone, Dario Stein. MSCS, 2023
• Counting and Matching
  Bart Jacobs, Dario Stein, CSL 2023
• Probabilistic Programming with Exact Conditions
  Dario Stein, Sam Staton. Invited Article, Journal of the ACM, 2023
• Compositional Semantics for Probabilistic Programs with Exact Conditioning
  Dario Stein, Sam Staton. LICS 2021 Distinguished Paper
• Probabilistic Programming Semantics for Name Generation
  Marcin Sabok, Sam Staton, Dario Stein, Michael Wolman. POPL 2021
• The Beta-Bernoulli process and Algebraic Effects
  Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, Daniel M. Roy. ICALP 2018

Teaching

• 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.

Talks

• Sep 2024, ItaCa Fest 2024, Online
• Jul 2024, SWS Seminar, RU Nijmegen
• Jun 2024, DutchCATS 2024, Leiden
• Apr 2024, FoSSaCS 2024, Luxembourg
• Nov 2023, DutchCATS 2023, Radboud Universiteit Nijmegen
• Jul 2023, ACT 2023, University of Maryland
• Jun 2023, MFPS 2023, Bloomington, Indiana
• Jun 2023, CALCO 2023, Bloomington, Indiana
• May 2023, Southern Logic Seminar, UCL
• Feb 2023, CSL 2023, University of Warsaw
• Jan 2023, Inn'formal Probability Seminar, Universität Innsbruck
• Aug 2022, Introduction to Probabilistic Programming, SWS Seminar, Radboud University Nijmegen
• Jul 2022, "A Hypergraph Category for Exact Gaussian Inference", Applied Category Theory 22 (slides, video), Strathclyde
• Jul 2022, Tutorial on Probabilistic Programming, iHub, Radboud University Nijmegen
• Jul 2021, Mathematical Foundations Seminar, Bath
• Jul 2021, VeriProP 2021
• Jun 2021, LICS 2021
• Jan 2021, Oxford Quantum Group Workshop
• Jan 2021, POPL 2021 (View on Clowdr)
• Jan 2021, LAFI. Slides
• Oct 2020, ProbProg workshop, MIT/Online
• Feb 2020, PIHOC workshop, IRIF, Paris. Slides
• Jan 2020, LAFI workshop, POPL, New Orleans. Slides
• 2019, Junior Semantics Seminar x 2, Oxford
• Jul 2018, ICALP 2018, Prague.
• 2018, Quantum Lunch, Quantum Group, Oxford

Service

• PC for ProbProg'21, LAFI'23, ACT 2023, ACT 2024
• Reviewer for Compositionality, MSCS, FSCD, ProbProg'21 PC, LICS'22, MFCS 2022, FoSSaCS 2023, ESOP 2023, FoSSaCS 2024, LICS 2024