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 compositionally, in their categorical embodiments (in particular, polygraphs: freely generated higher categories), and under the assumption that a higher category should be seen as a combinatorial description of a directed space. String diagrams are both an influence, and a major component of this approach.
A special case study is the theory of qubits, seen as a theory of interacting algebras, for which I developed a complete diagrammatic axiomatisation: the ZW calculus.
- My DPhil thesis The algebra of entanglement and the geometry of composition is now available on the arXiv.
- September 2017. I will be giving contributed talks A combinatorial-topological shape category for polygraphs (extended abstract) at HDRA 2017, and Developments on the ZW calculus (abstract) at STRING 2017.
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.
Nonstandard functional interpretations and categorical models
Amar Hadzihasanovic and Benno van den Berg
In Notre Dame J. Formal Logic. Vol. 58. No. 3. Pages 343–380. 2017.
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.