- Category Theory, Applied Category Theory
- Probability and Information Theory
- Complexity and Networks
- Theoretical Computer Science
- Born in Bergamo, 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, University of Leipzig, Germany, in 2018
- Currently researcher at the MPI MIS, Leipzig, Germany
Full academic CV (PDF format):
- 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.
- T. Fritz and P. Perrone, Stochastic Order on Metric Spaces and the Ordered Kantorovich Monad, 2018. Available here.
Other preprints and conference papers:
- T. Fritz and P. Perrone, Monads, partial evaluations, and rewriting. Notes for the Applied Category Theory School 2019. Available 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.
- Course, Category theory and applications, at the MPI MIS. Summer semester 2019. More information available soon.
- 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).
Past lectures and seminars:
- Reading seminar on Applied Category Theory at the MPI MIS. Summer semester 2018.
- "LikBez" seminar at the MPI MIS. 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.
- The support is a morphism of monads. 3rd Symposium on Compositional Structures, University of Oxford (United Kingdom), 27-28th March 2019. Speaker: Sharwin Rezagholi. Link here.
- Partial evaluations, the bar construction, and second-order stochastic dominance. Project at the Applied Category Theory Adjoint School, University of Oxford (United Kingdom), 22-26th July 2019. 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. Abstract 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.