Paolo Perrone
- Occupation: Mathematician and math teacher
- Position: Research Associate
- Institution: University of Oxford
- Group leader: Sam Staton
- Some coworkers and coauthors: Carmen Constantin, Tobias Fritz, Tomáš Gonda, Sharwin Rezagholi, Eigil Rischel, Brandon Shapiro, Walter Tholen
Research Interests
- Category Theory
- Probability and Information Theory
- Complexity and Networks
- Theoretical Computer Science
- Geometry and Topology
Curriculum Vitae
Short CV:
- Born in Italy in 1989
- Bachelor degree in Physics, University of Milan-Bicocca, Italy, in 2011
- Master's degree in Physics, University of Milan, Italy, in 2013
- PhD in Mathematics, Max Planck Institute for Mathematics in the Sciences and University of Leipzig, Germany, in 2018
- Currently researcher at the University of Oxford, England
Full academic CV:
Articles
Published:
- T. Fritz and P. Perrone, Stochastic Order on Metric Spaces and the Ordered Kantorovich Monad, Advances in Mathematics 366, 2020. Available here.
- T. Fritz and P. Perrone, Monads, partial evaluations, and rewriting. Proceedings of MFPS 36, ENTCS, 2020. Available here.
- T. Fritz and P. Perrone, A Probability Monad as the Colimit of Spaces of Finite Samples, Theory and Applications of Categories 34, 2019. Available here.
- T. Fritz and P. Perrone, Bimonoidal Structure of Probability Monads. Proceedings of MFPS 34, ENTCS, 2018. Available here.
- P. Perrone and N. Ay, Hierarchical Quantification of Synergy in Channels, Front. Robot. AI, 08 January 2016. Available here.
Submitted:
- P. Perrone and W. Tholen, Kan extensions are partial colimits, 2021. Available here.
- T. Fritz, T. Gonda, P. Perrone and E. Rischel, Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability, 2020. Available here.
- C. Constantin, T. Fritz, P. Perrone and B. Shapiro, Partial Evaluations and the Compositional Structure of the Bar Construction, 2020. Available here.
- T. Fritz, P. Perrone, and S. Rezagholi, Probability, valuations, hyperspace: Three monads on Top and the support as a morphism, 2019. Available here.
Lecture notes, conference papers and other material:
- P. Perrone, Notes on Category Theory with examples from basic mathematics, 2019. Lecture notes. Available here.
- P. Perrone, Categorical Probability and Stochastic Dominance in Metric Spaces, 2018. PhD thesis, University of Leipzig. Full text here, abstract here.
- T. Fritz and P. Perrone, A Criterion for Kan Extensions of Lax Monoidal Functors, 2018. Available here.
- P. Perrone and N. Ay, Iterative Scaling Algorithm for Channels, 2016. Available here.
- P. Perrone and N. Ay, Decomposition of Markov Kernels. Proceedings of WUPES 10, 2015. Available here.
- P. Perrone, Dual Connections and Holonomy, 2015. Available here.
Teaching
Current:
(No teaching in the current semester.)Past lectures and seminars:
- Applied Category Theory Adjoint School 2020, based at MIT (moved online), together with Carmen Constantin and Eliana Lorch. More information here.
- Reading seminar, Categories and gauge theory, at MIT.
- Course, Applied Linear Algebra, at the York University of Toronto. Fall semester 2019. For notes and other teaching material see the Moodle page (students only).
- Course, Category theory and applications, at the Max Planck Institute of Leipzig. Summer semester 2019. Lecture notes here.
- Teaching assistant at the Applied Category Theory Adjoint School, based at the University of Oxford. March-July 2019. For notes and other teaching material see the shared folder (students only).
- Reading seminar on Applied Category Theory at the Max Planck Institute of Leipzig. Summer semester 2018.
- "LikBez" seminar at the Max Planck Institute of Leipzig. Years 2017 and 2018.
- Student seminar on Geometric Group Theory at the University of Leipzig. Summer semester 2017.
- Student seminar on Characteristic Classes at the University of Leipzig. Summer semester 2015.
Events
Upcoming and current events:
- Categorical probability and the de Finetti theorem, Invited talk, New York Category Seminar, City University (CUNY), New York NY (USA), 17th March 2021, 23h UTC. Held online. Speaker: Tobias Fritz (joint work).
Past events:
- Partial evaluations: the results so far. Invited talk, Seminario de categorías UNAM, Universidad Nacional Autónoma de México, Mexico City (Mexico), February 2021. Held online. Main page here, video here.
- Partial evaluations for monads and 2-monads. Invited talk, Seminário de Teoria das Categorias, University of Coimbra (Portugal), February 2021. Held online.
- Kan extensions are partial colimits. Invited talk, Masaryk University Algebra Seminar, Masaryk University, Brno (Czech Republic), February 2021. Held online. Main page here, video here.
- An introduction to monads. Invited lecture, Applied Compositional Thinking for Engineers (ACT4E), ETH Zürich (Switzerland), January 2021. Held online. Main page here, video here.
- Markov categories: randomness and information flow. Oxford Quantum Group Workshop 2021, University of Oxford (UK), January 2021. Held online.
- Colimits as algebraic operations. Invited talk, ItaCaFest. Online seminar, Italy, September 2020. Link and abstract here, video here.
- Compositional structure of partial evaluations. MIT Categories Seminar. Massachusetts Institute of Technology, Cambridge, MA (USA), September 2020. Held online. Speaker: Brandon Shapiro (joint work). Main page here, video here.
- Distribution functors, second-order stochastic dominance and the Blackwell-Sherman-Stein Theorem in Categorical Probability. Keynote talk at the Applied Category Theory Conference, based at MIT, Cambridge, MA (USA), July 2020. Held online. Speaker: Tomáš Gonda (joint work). Main page here, video here.
- Monads and comonads. Tutorial talk, Applied Category Theory Conference, based at MIT, Cambridge, MA (USA), July 2020. Held online. Main page here, video here.
- Applied Category Theory Adjoint School, Massachusetts Institute of Technology, Cambridge, MA (USA), June-July 2020. Held online. Link here.
- Monads, partial evaluations, and rewriting. Principles of Programming and Verification seminar, Boston University, Boston, MA (USA), June 2020. Held online. Link here.
- Kan extensions are partial colimits. MIT Categories Seminar. Massachusetts Institute of Technology, Cambridge, MA (USA), June 2020. Held online. Main page here, video here.
- Probability monads and stochastic dominance, Categorical Probability and Statistics Workshop, University of Ottawa, ON (Canada), June 2020. Held online. Main page here, video here.
- What is a probability monad? Tutorial talk, Categorical Probability and Statistics Workshop, University of Ottawa, ON (Canada), June 2020. Held online. Main page here, video here.
- Monads, partial evaluations, and rewriting. Mathematical Foundations of Programming Semantics 36, Paris (France), June 2020. Held online. Main page here, video here.
- The support as a morphism from probability to possibility. TallCat Seminar. Tallinn Institute of Technology (TalTech), Tallinn (Estonia), May 2020. Speaker: Sharwin Rezagholi (joint work). Held online.
- Stochastic orders and Kantorovich duality. Metric geometry seminar. Max Planck Institute for Mathematics in the Science, Leipzig (Germany), April 2020. Held online.
- Composing partial evaluations. MIT Categories Seminar. Massachusetts Institute of Technology, Cambridge, MA (USA), March 2020. Held online. Main page here, video here.
- The compositional structure of partial evaluations. Invited talk, University of Ottawa, ON (Canada), November 2019.
- Partial evaluations, the bar construction, and second-order stochastic dominance. Project at the Applied Category Theory Adjoint School, University of Oxford (UK), July 2019. Link here.
- The support is a morphism of monads. Applied Category Theory 2019, University of Oxford (UK), July 2019. Link here.
- Categorical Probability: Results and Challenges. 4th Symposium on Compositional Structures, Chapman University, CA (USA), May 2019. Speaker: Tobias Fritz (joint work). Link here.
- The support is a morphism of monads. 3rd Symposium on Compositional Structures, University of Oxford (UK), March 2019. Speaker: Sharwin Rezagholi (joint work). Link here.
- Towards probability theory without measure theory. Invited talk, MIT Categories Seminar. Massachusetts Institute of Technology, Cambridge, MA (USA), February 2019. Speaker: Tobias Fritz (joint work). Main page here, video here.
- Monads, Partial Evaluations, and Martingales. Invited talk, MIT Categories Seminar. Massachusetts Institute of Technology, Cambridge, MA (USA), October 2018. Link and abstract here.
- Monads, Partial Evaluations, and Rewriting. 1st Symposium on Compositional Structures, University of Birmingham (United Kingdom), September 2018. Link and slides here.
- On the Operational Meaning of the Bar Construction. Category Theory 2018, University of Azores, Ponta Delgada (Portugal), July 2018. Abstract and slides here.
- Bimonoidal Structure of Probability Monads. Mathematical Foundations of Programming Semantics 34, Halifax, NS (Canada), June 2018. Abstract and paper here.
- A Kantorovich Monad for Ordered Spaces. 26th Foundational Methods in Computer Science Workshop, Mount Allison University, Sackville, NB (Canada), May-June 2018. Abstract and slides here.
- The Wasserstein Monad in Categorical Probability. Category Theory 2017, Vancouver, BC (Canada), July 2017. Abstract and slides here.
- A Conceptual Viewpoint on Information Decomposition. Invited talk, Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada), November 2016. Abstract and video here.
- Decomposition of Markov Kernels. 10th Workshop on Uncertainty Processing, Monínec (Czech Republic), September 2015. Link and abstract here.
- Synergy as a Linear Operator. Guided Self Organization 2014, Freiburg (Germany), December 2014. Link here.

Contact
- Email: paolo.perrone at cs.ox.ac.uk
- Address:
University of Oxford
Department of Computer Science
Wolfson Building, Parks Road
Oxford, OX1 3QD, U.K. - Office: Wolfson Building 331
(Currently in home office.)