Research Interests

  • Category Theory, Applied Category Theory
  • Probability and Information Theory
  • Complexity and Networks
  • Theoretical Computer Science
My doctoral thesis is available at this link.

Curriculum Vitae

Short CV:

Full academic CV:

Articles

Published:

Submitted:

  • T. Fritz, P. Perrone, and S. Rezagholi, Probability, valuations, hyperspace: Three monads on Top and the support as a morphism, 2019. Available here.
  • T. Fritz and P. Perrone, Stochastic Order on Metric Spaces and the Ordered Kantorovich Monad, 2018. Available here.

PhD Thesis:

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.
See also my arXiv page.

Teaching

Current:

Past lectures and seminars:

  • Course, Category theory and applications, at the Max Planck Institute of Leipzig. Summer semester 2019. Course page here, 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:

  • Conference talk, Categorical Probability and Statistics Workshop, University of Ottawa, ON (Canada), June 5-8, 2020. Link here.
  • Applied Category Theory Adjoint School, Massachusetts Institute of Technology, Cambridge, MA (USA), June 29-July 3, 2020. Link here.

Past events:

  • 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. Link here.
  • The support is a morphism of monads. 3rd Symposium on Compositional Structures, University of Oxford (United Kingdom), March 2019. Speaker: Sharwin Rezagholi. 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.

Contact

  • Email: pperrone, at yorku dot ca
  • Address:
    York University, Math Department
    4700 Keele Street
    Toronto, ON M3J 1P3, Canada
  • Office: Ross Building, N605
  • Phone: +1 (416) 736 5250
  • Fax: +1 (416) 736 5757
  • Office hours (for students):
    Wednesdays, 1:30 PM - 3:00 PM,
    or by (email) appointment

Social