# Nicola Pinzani

## Interests

I am interested in applying methods from category theory to understand causality and contextuality in the spacetime of quantum processes. In particular, I am interested in providing categorical semantics to causally exotic scenarios. Starting from time travel and cyclic causal structures, I am now investigating the operational nature of indefinite causality. The set-up and outcomes of an experiment presuppose the existence of causally stable surroundings, where the notions of cause and consequence take their familiar form independently of the specific processes being performed. Without these assumptions, how can we ensure that a mathematical model of quantum theory in the presence of dynamic spacetimes is even empirically testable?

Together with my supervisor Stefano Gogioso, I have worked on understanding the order-theoretic structure that describes measurement contexts in more complicated (definite and indefinite) causal scenarios. This has allowed us to generalize the sheaf-theoretic framework by Abramsky and Brandenburger to describe the idea of assigning causal data to contexts. The sheaf-theroetic formalisation allows us to understand quantum theory and other generalised contextual theory, in their operational formulation, as a way of consistently associating data to an open cover of these topologies of contexts, where the structure of the topology is informed by the causal structure of the underlying protocols.

## Biography

I grew up as a pure mathematician at the University of St Andrews, with some research experience in analysis and combinatorics. I graduated from Oxford with an MSc from the Mathematical Institute, where I became interested in studying quantum foundations using categorical tools. Nevertheless, I remain of the opinion that Proust understands time better than most physicists.

## Education:

**DPhil in Computer Science** (2018-2023)*Institution*: University of Oxford, St Hugh's College*Thesis*: `The Topology and Geometry of Causality'*Supervisor*: Dr Stefano Gogioso, Prof Bob Coecke and Prof Jonathan Barrett

**MSc in Mathematics and Foundations of Computer Science** (2017-2018)*Institution*: University of Oxford, St Catherine's College*Thesis*: `Categorical Semantics for Time Travel'*Supervisor*: Dr Stefano Gogioso and Prof Bob Coecke

**MMath in Mathematics** (2013-2017)*Institution*: University of St Andrews*Thesis*: ‘A Spectral Theory of Expansion and Expander Graphs’*Supervisor*: Prof Peter Cameron

## Teaching:

**Michaelmas 2021: Tutor at the William-Exeter Exchange Programme, **Exeter College, University of Oxford

**Michaelmas 2021: Tutor at the Sarah Lawrence Exchange ****Programme, **Wadham College, University of Oxford

**Mathematical Institute, Oxford:**

Hilary 2021: Teaching assistant for 'Algebraic Number Theory'

**Department of Computer Science, Oxford:**

2020-Present: Teaching assistant for the course on Quantum Computing for the MSc programme in software engineering.

Michaelmas 2021: Tutor for `Quantum Information'

Michaelmas 2020: Tutor for `Categories Proofs and Processes'

Michaelmas 2020: Tutor for `Quantum Processes and Computation'

Michaelmas 2019: Tutor for `Categories Proofs and Processes'

Trinity 2019: Teaching Assistant for `Introduction to Quantum Information'

## Selected Pubblications:

- S. Gogioso, N. Pinzani, ‘The Topology and Geometry of Causality’ available at https:// arxiv.org/abs/2206.08911, arXiv (2022)
- S. Gogioso, N. Pinzani, ‘On the Sheaf Theoretic Structure of Definite Causality’ in
*Proceedings 17th International Conference on Quantum Physics and Logic*(2021). EPTCS 343 - N. Pinzani, S. Gogioso, ‘Giving Operational Meaning to the Superposition of Causal Orders’ in
*Proceedings 17th International Conference on Quantum Physics and Logic*(2020). EPTCS 340 - N. Pinzani, S. Gogioso and B. Coecke, ‘Categorical Semantics for Time Travel’ in
*Proocedings**34th Annual ACM/IEEE Symposium on Logic in Computer LICS*(2019) - B. Adam-Day, C. Ashcroft, L. Olsen, N. Pinzani, A. Rizzoli, J. Rowe, ‘On the Average Box Dimensions of Graphs of Typical Continuous Function’ in
*Acta Mathematica Hungarica*, 156: 26 (2018)