Profile Information

京都大学白眉センター / JSTさきがけ兼任
D.Phil.(University of Oxford)

I am a D.Phil. student in the Quantum Group of Oxford University Computing Laboratory. My supervisors are Samson Abramsky and Bob Coecke.

I have been working mainly on categorical dualities (esp., Stone-type dualities) and their applications to other areas including mathematical logic (esp., algebraic, topological, and categorical logic), the semantics of programming languages (esp., domain theory), and quantum physics and information (esp., foundations in terms of duality and symmetry). I am recently developing Categorical Universal Logic, which is meant to unify topos-theoretical and categorical quantum concepts of Space from a logical perspective.

At the same time, I have serious interests in (both analytic and continental) philosophy. For instance, pointfree geometry (locale theory, topos theory, etc.) seems to be closely related to philosophical conceptions of Space by Brentano-Husserl (Phenomenology), Whitehead (Process Philosophy), Wittgenstein (arithmetical vs. geometrical space), and so fourth. A bit more detailed discussion on this can be found in my paper on Wittgenstein's conception of space, which is available below.

I want to understand diverse nuances of the notion of duality from both mathematical and philosophical perspectives. My slogan is that categorical duality arises between the ontological and the epistemological. Indeed, there is plenty of evidence supporting the slogan: Hilbert's duality between points (or prime ideals or varieties) and properties (or function algebras); Abramsky's duality between denotations and observable properties of computational processes; the state-observable duality in quantum physics; and of course the classic Stone duality between syntax and semantics.

In more informal terms, I am concerned with the interactive relationships between our world views and mathematical theories. I always wish to place my mathematical research in a wider context of the human knowledge of the world (I do not necessarily mean this real world by "world").

Please note that not all of my papers are listed here. Most of my conference papers are listed in my DBLP entry. If you are interested in any paper that is not uploaded here, please send me an e-mail.