I am a post-doc in Aalborg University. My interests are in probability, logic, quantum, and category theory, especially monads. My email address is my last name at cs dot aau dot dk.
Publications, Preprints, etc.
- Continuous Dcpos in Quantum Computing
In this paper, I show that if the unit interval of a directed-complete C*-algebra A is a continuous dcpo, then A is a product of finite-dimensional matrix algebras. Combined with previous results due to Selinger, this characterizes the directed-complete C*-algebras with continuous unit interval. I also show that if the unit interval of A has a countable base (as a dcpo) then A is isomorphic to the algebra of bounded functions on a countable set, and is therefore commutative.
- Categorical Equivalences from State-Effect Adjunctions
Accepted by QPL 2018. In an earlier paper, Bart Jacobs defined a dual adjunction between effect algebras and abstract convex sets. This paper characterizes the subcategories on which this dual adjunction is a contravariant equivalence. I then outline how to get two more adjunctions and dualities using the theory of Smith base-norm and Smith order-unit spaces, like in my PhD thesis. In an appendix I characterize the effect modules/convex effect algebras for which effect algebra morphisms are automatically effect module homomorphisms, and give counterexamples showing that the result is sharp.
- Boolean-Valued Semantics for Stochastic Lambda-Calculus with Giorgio Bacci, Dexter Kozen, Radu Mardare, Prakash Panangaden and Dana Scott
Accepted by LICS 2018.
- Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras with Mathys Rennela and Sam Staton.
Appeared in EPTCS 236. This paper relates W*-algebras to presheaves on the category of finite-dimensional matrix algebras with completely positive maps.
- Unrestricted Stone Duality for Markov Processes with Dexter Kozen, Kim Larsen, Radu Mardare and Prakash Panangaden.
This paper defines a duality for Markov processes extending Sikorski's duality for measurable spaces. Accepted for LICS 2017. The version above includes an appendix with the proofs omitted from the proceedings version.
- Riesz Modal Logic for Markov Processes with Radu Mardare and Matteo Mio.
This paper makes a connection between Riesz spaces and probabilistic modal logics for Markov processes on compact Hausdorff spaces. Accepted for LICS 2017.
- From Kleisli categories to commutative C*-algebras: Probabilistic Gelfand Duality with Bart Jacobs.
On arXiv, published in LMCS, Selected Papers of the 5th Conference on Algebra and Coalgebra in Computer Science (CALCO 2013).
An earlier version has been published by Springer in the proceedings LNCS 8089.
- Towards a Categorical Account of Conditional Probability with Bart Jacobs.
On arXiv, accepted by QPL 2013. Appeared in EPTCS 195.
- Unordered Tuples in Quantum Computation with Bas Westerbaan.
On arXiv. This paper is on how to realize certain quotient types (unordered tuples and necklaces) in C*-algebraic quantum theory. Appeared in EPTCS 195.