Jim de Groot

Most of my life I've lived in Amsterdam. I studied maths at the University of Amsterdam. After my master's there I moved to Australia to do a PhD under the supervision of Dirk Pattinson.

Roughly, I am interested in categorical dualities in logic. Here are some more specific questions I sometimes think about.

  • In our recent paper Dirk and I proposed the idea of dialgebraic logic, which provide a coalgebra-like framework for modal logics. All examples we gave are modal extensions of intuitionistic logics. I'm wondering if there are more logical paradigms that fit the framework of dialgebraic logic.
  • Yosida duality is a duality for compact Hausdorff spaces with certain Riesz spaces. I'm curious if there is a natural description of the Yosida dual of the Vietoris functor and whether this gives rise to an interesting modal logic. (The Vietoris functor is of course well-known from its appearance in modal logic over a classical base.)
  • More to come

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