I am interested in the broad idea of composition: how parts make up a whole. My favourite tool to study this phenomenon is the mathematical field of category theory, with a particular emphasis on monoidal (higher) categories and related structures.
At the moment, my research focuses on giving an algebraic account 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.
I am also studying 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 to investigate the mathematical structure of contextuality and 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).
Teaching Assistant for Categories, Proofs and Processes.
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. My MSc. thesis explored models of lexical ambiguity in compositional distributional semantics.
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.