Previously, I was an AARMS postdoctoral fellow at Dalhousie's department of mathematics and statistics and a postdoc at the Digital Security department of the Radboud University Nijmegen. Currently, I'm programming for ProcoliX.
On May 14th 2019 I defended my Ph.D. thesis titled The Category of Von Neumann Algebras.
You can reach me via bram at westerbaan name.
Some are neither Boolean, nor quite convex.
A representation theory for ω-directed complete effect monoids.
published [ arxiv · repos · website ]
Includes the “lizard” trick.
printed supervised by Bart Jacobs [ github · arxiv · ru ]
Includes an introduction to the theory of C*-algebras and von Neumann algebras.
The title says it all.
published [ arxiv · preprint ]
A simplification and slight extension of Statman’s Hierarchy Theorem.
Featuring the metric completeness of of ω-complete effect modules.
published [ arxiv · preprint ]
We give a universal property for Paschke’s (and Stinespring’s) dilation.
published [ arxiv · preprint ]
We axiomatise the sequential product on von Neumann algebras.
unpublished [ arxiv · preprint · extended abstract ]
We interpret Selinger and Valiron’s quantum lambda calculus in the category of completely positive normal subunital maps between von Neumann algebras, and prove that the interpretation is adequate with respect to operational semantics.
unpublished [ arxiv · preprint ]
We describe the free commutative monoid on the category of von Neumann algebras
done [ arXiv ]
What would happen if one replaced subobjects S↣X by predicates X→1+1?
published [ arxiv · preprint · video · slides ]
A universal property for A ↦ √B A √B appears in a chain of adjunctions.
published [ preprint · slides ]
The step from probability measure to integral gets a universal property with the aid of ω-complete effect algebras and ω-complete effect modules.
unpublished [ preprint ]
A universal property for A ↦ √B A √B appears in a chain of adjunctions.
published [ arxiv · preprint ]
The category of positive unital linear maps between C*-algebras is the Kleisli category of a comonad on the subcategory of unital *-homomorphisms between C*-algebras.
published [ preprint · slides ]
Convex sets appear as state spaces of computation in an effectus, and form an effectus.
Our take on when an adjunction can be lifted to coalgebras, with many examples.
published [ preprint · slides ]
Study of a generalisation of the removal of ε-transitions from a non-deterministic automaton.
done supervised by prof. A.C.M. van Rooij [ arxiv ]
Simultaneous study of measure and integral using lattices and uniform spaces.