Paolo Perrone

- Occupation: Mathematician and math teacher
- Position: Postdoctoral Associate
- Institution: Massachusetts Institute of Technology (MIT)
- Group leader: David Spivak
- Some coworkers and coauthors: Carmen Constantin, Tobias Fritz, Tomáš Gonda, Sharwin Rezagholi, Eigil Rischel, Brandon Shapiro, Walter Tholen

## Research Interests

- Category Theory, Applied 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 MIT, Cambridge, MA (U.S.A.)

### 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:

- 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.

*For further material about past courses please contact me directly*.

## Events

### Upcoming and current events:

- Further MIT Categories Seminar talks, currently held online.

### Past events:

*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 (United Kingdom), July 2019. Link here.*The support is a morphism of monads*. Applied Category Theory 2019, University of Oxford (United Kingdom), 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 (United Kingdom), 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:**pperrone, at mit dot edu**Address:**

MIT, Department of Mathematics

77 Massachusetts Avenue

Cambridge, MA 02139, U.S.A.**Office:**Building 2, Room 180