Mario Román

Research Associate.
Department of Computer Science, University of Oxford.
Room 309, Wolfson Building, Parks Road.
Oxford, OX1 3QD.
mromang08@gmail.com

My research is in category theory, functional programming, foundations for probabilistic programming, formal languages, and mathematical notation.

• ArXiv, GitHub, Résumé, CV.

• A Simple Formal Language for Probabilistic Decision Problems
  Elena Di Lavore, Bart Jacobs, and Mario Román.
  (arXiv), Preprint, 2024.

• Effectful Mealy Machines: Bisimulation and Trace
  Filippo Bonchi, Elena Di Lavore, and Mario Román.
  (arXiv), Preprint, 2024.

• Context-Free Languages of String Diagrams
  Matt Earnshaw and Mario Román.
  (pdf), Preprint, 2024.

• String Diagrams for Premonoidal Categories.
  Mario Román and Pawel Sobocinski.
  (arXiv), Preprint, 2023.

• The Produoidal Algebra of Process Decomposition.
  Matt Earnshaw, James Hefford, and Mario Román.
  (pdf, notes) Computer Science Logic (CSL 2024).

• Collages of String Diagrams.
  Dylan Braithwaite and Mario Román.
  (pdf, arXiv) Applied Category Theory (ACT 2023).

• Evidential Decision Theory via Partial Markov Categories.
  Elena Di Lavore and Mario Román.
  (pdf, slides, notes) IEEE Symposium on Logic in Computer Science (LiCS, 2023).

• Optics for Premonoidal Categories.
  James Hefford and Mario Román.
  (arXiv) Applied Category Theory (ACT 2023).

• Monoidal Streams for Dataflow Programming.
  Elena Di Lavore, Giovanni de Felice, and Mario Román.
  (pdf, slides) IEEE Symposium on Logic in Computer Science (LiCS, 2022), Distinguished, Kleene Award.

• Span(Graph): a Canonical Feedback Algebra of Open Transition Systems.
  Elena Di Lavore, Alessandro Gianola, Nicoletta Sabadini, Mario Román, and Pawel Sobocinski.
  (pdf) Software and Systems Modeling, Volume 22, pages 495–520 (2023).

• A Canonical Algebra of Open Transition Systems.
  Elena Di Lavore, Alessandro Gianola, Nicoletta Sabadini, Mario Román, and Pawel Sobocinski.
  (pdf) Formal Aspects of Component Software (FACS, 2021).

• Promonads and String Diagrams for Effectful Categories.
  Mario Román.
  (pdf, notes) Applied Category Theory (ACT, 2022).

• Open Diagrams via Coend Calculus.
  Mario Román.
  (pdf, notes) Applied Category Theory (ACT, 2021).

• Cornering Optics.
  Guillaume Boisseau, Chad Nester, and Mario Román.
  (pdf, notes) Applied Category Theory (ACT, 2022).

• Profunctor Optics: a Categorical Update.
  Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore, and Mario Román.
  (pdf, notes) Compositionality, Volume 6, Issue 1 (2024).

• Profunctor Optics and Traversals.
  Mario Román. (pdf) MFoCS thesis, University of Oxford (2019).

• Mikrokosmos: an Educational Lambda Interpreter
  Supervised by Pedro García-Sánchez.
  (pdf) Journal of Open Source Education (JOSE, 2018).

• Monoidal Context Theory.
  Supervised by Pawel Sobocinski.
  (pdf, notes) Tallinn University of Technology, 2023.

• Partial Markov Categories (preprint), with Elena Di Lavore and Pawel Sobocinski.
• Solving Puzzles in Decision Theory (preprint), with Elena Di Lavore.
• String Diagrams for Physical Duoidal Categories (preprint), with Nayan Rajesh.
• Evidential Decision Theory via Partial Markov Categories (NWPT 2024), with Elena Di Lavore.
• Universal Properties of Asynchronous Message Passing (abstract), with Matt Earnshaw.
• Effectful Trace Semantics via Effectful Streams (preprint), with Filippo Bonchi and Elena Di Lavore.
• Coinductive Streams in Monoidal Categories (arXiv), with Elena Di Lavore and Giovanni de Felice.
• Polar Interleavings for Deadlock-Free Message-Passing (preprint), with Matt Earnshaw and Chad Nester.
• Symmetric monoidal automata (preprint), with Elena Di Lavore.
• Presentations of Premonoidal Categories by Devices (preprint), with Matt Earnshaw and Chad Nester.
• Contouring Prostar Autonomous Categories (preprint), with Matt Earnshaw and James Hefford.
• Be Careful with Duoidal Coherence (preprint).
• Comb Diagrams for Discrete-Time Feedback (preprint).
• Timing monoidal lax categories (preprint).
• Distributive laws of promonads (preprint).
• Composing optics (preprint).

• Partial Markov Categories, at the Topos Colloquium, 30 October 2024.
• String Diagrams for Premonoidal Categories, at the CS seminar, Pisa.
• Notes on profunctors, at the PUDDLE seminar, Oxford.
• Effectful Streams, at CMCS'24, Luxembourg.
• Polar Shuffles, at the CHESS-PTSPC'24 workshop, Tallinn.
• The Produoidal Algebra of Process Decomposition, at CSL'24, Naples.
• Notes on Fox’s theorem, at a Tallinn retreat, Matsalu park.
• Polar Interleavings, at NWPT'23, Västerås.
• Monoidal Context Theory, PhD Defence, Tallinn.
• Collages of String Diagrams, at ACT'23, Maryland.
• Timing Processes, at the Bob Walters Tribute 2023, Tallinn.
• Optics: the Algebra of Monoidal Context, at MFPS'23, Bloomington, Indiana.
• The Produoidal Algebra of Process Decomposition, at the Ottawa Logic Seminar.
• From theories to categories at the Lawvere Memorial Meeting, Tallinn.
• String diagrams of string diagrams at TallCat group meetings, Tallinn.
• Evidential Decision Theory via Partial Markov Categories at NWPT'22, Bergen.
• Premonoidal Streams, at the Intercats Seminar of the Topos Institute.
• Monoidal Streams for Dataflow Programming, at LiCS'22.
• Monoidal Streams for Dataflow Programming, at NWPT'21, Reykjavik.
• Notes on A Graphical View at TallCat Seminar, Tallinn.
• Monoidal Streams for Dataflow Programming, at the Bath Mathematical Foundations Seminar.
• Promonads and String Diagrams for Effectful Categories at ACT'22, Strathclyde.
• Notes on Compositional Markov Processes at the ACT'22 Adjoint School, Strathclyde.
• Monoidal Profunctors at Compositional Methods Retreat, Raudsilla.
• A Canonical Algebra of Transition Systems at ACT'21, Cambridge.
• A Canonical Algebra of Transition Systems at FACS'21, Grenoble.
• Picturing Multivariable Adjunctions, the 2-Chu construction at TallCat Seminar, Tallinn.
• Lesson on Monoidal Categories at the Category Theory course, Tallinn.
• Open Diagrams via Coend Calculus at ACT'20, MIT.
• Profunctor Optics: a Categorical Update at ACT'20, MIT.
• Profunctor Optics: a Categorical Update at NWPT'19, Tallinn.
• Profunctor Optics: a Categorical Update at SYCO 5, Birmingham.
• Profunctor Optics: a Categorical Update at MFoCS Dissertation, Oxford.

Activities.

• Compositionality, Executive Board, 2023-2025.
• Applied Category Theory Conference 2024 (ACT24), Program Committee.
• Applied Category Theory Conference 2023 (ACT23), Program Committee.
• Applied Category Theory Conference 2022 (ACT22), Program Committee.
• Mathematical Foundations of Programming Semantics (MFPS 40th), Local Organization.
• Applied Category Theory Conference 2024 (ACT24), Local Organization.

Awards, grants, distinctions.

• Kleene Award at LiCS'22, joint with Elena Di Lavore and Giovanni de Felice, 2022.
• Distinguished paper at LiCS'22, joint with Elena Di Lavore and Giovanni de Felice, 2022.
• EuroProofNet Short Term Scientific Mission visitor to Elena Di Lavore, 2024.
• EuroProofNet Short Term Scientific Mission host for Elena Di Lavore, 2024.
• Undergraduate Research Fellowship, Department of Algebra, Granada, 2018.
• Award to the best undergraduate thesis in Mathematics, Granada, 2018.

Teaching.

• TA for the Applied Category Theory Adjoint School, Glasgow, under Nicoletta Sabadini, 2022.
• TA for Category Theory, Tallinn University of Technology, under Pawel Sobocinski, 2020.
• TA for Functional Programming, Tallinn University of Technology, under Edward Morehouse, 2020.

Reviewing.

• Logical Methods in Computer Science (LMCS), reviewer.
• Mathematical Structures in Computer Science (MSCS), reviewer.
• Compositionality, reviewer.
• ACM/IEEE Symposium on Logic in Computer Science, reviewer (LiCS'20, LiCS'22, LiCS'23).
• Symposium on Principles of Programming Languages, reviewer (POPL'25).
• Applied Category Theory Conference, reviewer (ACT20, ACT21, ACT22, ACT23, ACT24).
• Symposium on Compositional Structures, reviewer (SYCO6, SYCO7, SYCO8, SYCO9).
• International Conf. on Curr. Trends in Th. and Pract. of Comp. Sci., reviewer (SOFSEM2023).
• International Conf. on Principles of Knowledge Representation and Reasoning, reviewer (KR2023).
• Coalgebraic Methods in Computer Science, reviewer (CMCS24).

Positions.

• Postdoc, Research Assistant. University of Oxford, under Sam Staton, 2023-2025.
• PhD in Software Science. Tallinn University of Technology, under Pawel Sobocinski, 2019-2023.
• MSc in Mathematics and Foundations of Computer Science, University of Oxford, 2019.
• Bachelor Degree in Computer Engineering, University of Granada, 2012-2018.
• Bachelor Degree in Mathematics, University of Granada, 2012-2018.

Events & News.

• National Institute of Informatics, Tokyo — visit, 18–22 November, 2024.
• Tallinn University of Technology — visit, 30 October – 14 November, 2024.
• Tallinn University of Technology — visit, 15-30 September, 2024.
• ARIA invited event — Safeguarded AI: creator kick-off. Manchester, 1–4 October, 2024.
• ARIA invited event — Safeguarded AI: Constructing safety by design. Birmingham, 4–5 March 2024.
• University of Pisa — visit, 2024.
• Finding the Right Abstractions Workshop 2023, Oxford.
• Finding the Right Abstractions Workshop 2023, San Francisco.
• University of Insubria — visit, 2022.
• Logic in Computer Science 2023, Boston.
• Logic in Computer Science 2022, Haifa.
• Applied Category Theory 2024, Oxford.
• Applied Category Theory 2023 — Maryland, 31 July – 4 August 2023.
• Applied Category Theory 2022, Glasgow.

I collect and hyperlink the notes I write while studying or developing any topic. They are not meant to be definitive and many of them do not contain original material. Think of these as atomic ideas that I am happy to share and discuss. You may want read about monoidal categories, profunctors, or duoidal categories, or to use the search box to jump to any topic. Any feedback is very welcome.