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.

• 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 (pdf).
  Elena Di Lavore, Alessandro Gianola, Nicoletta Sabadini, Mario Román, and Pawel Sobocinski.
  Software and Systems Modeling, Volume 22, pages 495–520 (2023).

• A Canonical Algebra of Open Transition Systems (pdf).
  Elena Di Lavore, Alessandro Gianola, Nicoletta Sabadini, Mario Román, and Pawel Sobocinski.
  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 (pdf)
  Guillaume Boisseau, Chad Nester, and Mario Román.
  Applied Category Theory (ACT, 2022).

• Profunctor Optics: a Categorical Update (pdf)
  Joint with Clarke, Elkins, Gibbons, Loregian, Milewski and Pillmore.
  Compositionality, Volume 6, Issue 1 (2024).

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

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

• 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.
• String Diagrams for Premonoidal Categories (arXiv), with Pawel Sobocinski.
• 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).

• 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.
• Finding the Right Abstractions Workshop 2023, Oxford.
• 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.

• Tallinn University of Technology — Academic visit, 30 October – 14 November, 2024.
• Tallinn University of Technology — Academic 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.
• Applied Category Theory 2023, Maryland, 31 July – 4 August 2023.