I am interested in higher category theory as an interface for logic, algebra, and geometry. More specifically, I am interested in studying algebraic theories and proof systems as geometric objects, in their categorical embodiment (as categories with duals, with structure, Lawvere theories, PROs...), and under the assumption that a higher category should be seen as a combinatorial description of a directed topological space. String diagrams (and ribbons, tubes...) are both an influence, and a major component of this approach.
My current case study is the theory of qubits, seen as a theory of interacting algebras associated with the GHZ and W quantum states, as suggested in a paper by Bob Coecke and Aleks Kissinger. Through the associated diagrammatic calculus, I aim at reaching a topological classification of multipartite qubit entanglement.
I have started my DPhil in Computer Science at Oxford University in 2013, under the supervision of Bob Coecke.
Previously, I have been studying Mathematics at the University of Pavia, as a student of Collegio Ghislieri. My master's thesis, that I wrote as an exchange student at the University of Utrecht under the supervision of Benno van den Berg, was awarded the AILA Prize for the best master's thesis in logic defended at an Italian university in the year 2013. In July 2014, I was awarded a Best Graduate Student prize by the University of Pavia for finishing top of my class in the Mathematics MSc course.
A Topological Perspective on Interacting Algebraic Theories
In Ross Duncan and Chris Heunen, editors, Proceedings 13th International Conference on Quantum Physics and Logic‚ Glasgow‚ Scotland‚ 6−10 June 2016. Vol. 236 of Electronic Proceedings in Theoretical Computer Science. Pages 70−86. Open Publishing Association. 2017.
A Diagrammatic Axiomatisation for Qubit Entanglement
In Proceedings of the 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science. Pages 573–584. IEEE Computer Society. 2015.
Nonstandard functional interpretations and categorical models
Amar Hadzihasanovic and Benno van den Berg
In Notre Dame J. Formal Logic. 2014.