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 (PDF format):

Articles

Published:

  • P. Perrone and N. Ay, Hierarchical Quantification of Synergy in Channels, Front. Robot. AI, 08 January 2016. Available here.

Submitted:

  • T. Fritz and P. Perrone, Stochastic Order on Metric Spaces and the Ordered Kantorovich Monad, 2018. Available here.
  • T. Fritz and P. Perrone, A Probability Monad as the Colimit of Finite Powers, 2017. Available here.

Conference papers:

  • T. Fritz and P. Perrone, Bimonoidal Structure of Probability Monads. Proceedings of MFPS 34, ENTCS, 2018. Available here.
  • P. Perrone and N. Ay, Decomposition of Markov Kernels. Proceedings of WUPES 10, 2015. Available here.

PhD Thesis (accepted):

Other preprints:

  • 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, Dual Connections and Holonomy, 2015. Available here.
See also my arXiv page.

Talks

Conference talks:

  • 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.
  • 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.

Invited talks:

  • Monads, Partial Evaluations, and Martingales, MIT Categories Seminar. Massachusetts Institute of Technology, Cambridge, MA (USA), October 2018. Link and abstract here.
  • A Conceptual Viewpoint on Information Decomposition. Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada), November 2016. Abstract and video here.

Lectures and Seminars

  • Organizer of reading seminar on Applied Category Theory at the MPI MIS. Summer semester 2018.
  • Co-organizer of the LikBez seminar at the MPI MIS. Summer semesters 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.

Contact

  • Email: my last name, at mis.mpg.de
  • Address:
    Max Planck Institute for Mathematics in the Sciences
    Inselstrasse 22
    04103 Leipzig, Germany
  • Office: A3 08
  • Phone: +49 341 9959 531
  • Fax: +49 341 9959 658

Social