I am interested in the broad idea of composition: how parts interact to form a whole. My favourite tools are those of category theory, with a particular emphasis on monoidal (higher) categories and related structures. My favourite game is to break categories down into their smallest components, finding the fundamental blocks that make them up and the rules to compose them. In more technical terms, I am interested in presenting monoidal categories in terms of generators and relations.
At the moment, my research focuses on the fundamental structures of concurrency. Concurrent processes form monoidal categories (that is, with both a sequential and parallel composition operation) whose presentations reveal how these processes interact and how they access, use and share resources (computational, physical etc.). From simple algebraic rules we can study key properties like nondeterminism, mutual exclusion or deadlock.
I have also worked on categorical accounts of how graphs, compose. Using finitely presented PROPs it is possible to formulate a convincing syntax for open graphs whose models can shed light on various essential graph-theoretic notions: decompositions, factorizations, vertex-colorings, flows etc.
Finally, I am interested in the coherence problem for higher algebraic structures called (symmetric) Frobenius pseudomonoids: they are a fully weak generalization of Frobenius algebras in the context of (symmetric) monoidal weak 2-categories. Since the theory of Frobenius algebras turns out to be central to the presentation of categories of open graphs, a clear theory of Frobenius pseudomonoids is required to give a presentation of the fully weak symmetric monoidal 2-categorical structure naturally present in these categories.
In my master's thesis I applied similar categorical tools and methods to represent polysemy and, more broadly, various forms of ambiguity in models of meaning in linguistics. I tried to clarify how meaning emerges out of composing discourse fragments (from words to sentences, sentences to text) and how we resolve ambiguity by refering to a broader context (from text to sentences, sentences to words).
After a degree at HEC Paris I studied mathematics at Université Pierre et Marie Curie (Paris VI) and completed a masters degree in computer science at the University of Oxford.
Open System Categorical Quantum Semantics in Natural Language Processing
Robin Piedeleu‚ Dimitri Kartsaklis‚ Bob Coecke and Mehrnoosh Sadrzadeh
In CoRR. Vol. abs/1502.00831. 2015.
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