Fernando Lucatelli Nunes

Ph.D. in Mathematics Ph.D. in Computer Science (to be awarded in 2026)

Research Leadership and Collaborative Contributions

My research activity combines an independently directed programme with substantial contributions to externally funded collaborations. The sections below distinguish research leadership from participation in projects led by others, while stating my role and contribution in each case.

Research leadership

Projects Led as Principal Investigator

This section comprises my independently directed research programme and the fellowship-supported projects for which I served as principal investigator.

  • Freely generated categorical structures for programming language semantics

    Current research programme. Research leadership: Fernando Lucatelli Nunes.

    • Foundations: programming languages, considered up to their equational theories, as freely generated or presented categorical structures grounded in two-dimensional universal algebra.
    • Applications: categorical semantics and correct-by-construction transformations for advanced type systems, recursion, computational effects, differentiable programming, probabilistic programming, verification, program analysis, and compiler transformations, including defunctionalisation and closure conversion.

    category theoryprogramming languagesformal methodsverified transformations

  • Grothendieck descent theory, fibrations, and factorizations

    Fields Research Fellowship, Fields Institute for Research in Mathematical Sciences, Canada, 2023. Role: Fellowship holder and Principal Investigator.

    • Collaboration: Walter Tholen.
    • Focus: the passage from Grothendieck cofibrations to factorization systems, formulated through two-dimensional monad theory.

    pure mathematicsdescent theoryfibrationsfactorizations

  • Grothendieck descent, Galois theory, and presentations of categorical structures

    Oberwolfach Leibniz Fellowship, Mathematisches Forschungsinstitut Oberwolfach, Germany, 2022. Role: Fellowship holder and Principal Investigator.

    • Collaborators: Maria Manuel Clementino, Rui Prezado, Lurdes Sousa, and Matthijs Vákár.
    • Focus: effective descent, categorical Galois theory, and presentations by coinserters and computads.

    pure mathematicsGalois theorypresentationscategorical structures

Collaborative contributions

Contributions to Projects Led by Other Researchers

The externally funded projects below were led by, or awarded to, the researcher named in each entry.

  • Formalised reasoning about expectations

    ERC Starting Grant FoRECAST, grant 101164093: Formalised Reasoning about Expectations: Composable, Automated, Speedy, Trustworthy. Project period: 2025 to 2030. Principal Investigator: Matthijs Vákár.

    • My role: research collaborator and doctoral co-supervisor.
    • My research contribution: categorical foundations for probabilistic and differentiable programming, including reverse-mode automatic differentiation for variants and effectful languages.
    • Supervision: co-supervision of Diogo Simm with Matthijs Vákár.

    computer scienceformal methodsprobabilistic programmingautomatic differentiation

  • Higher-order monad-based programming and reasoning

    DFG Project HOMBRe: Higher-Order Monad-based Programming and Reasoning. Principal Investigator: Sergey Goncharov.

    • My role: Research Fellow; the appointment concluded in March 2026.

    • Correct expressive differential programming

      NWO Veni Grant VI.Veni.202.124: Correct Expressive Differential Programming: Laying the Mathematical Foundations for Tomorrow's Machine Learning. Project period: 2021 to 2024. Principal Investigator: Matthijs Vákár.

      • My contribution: led the research on iterative CHAD and established correctness results for automatic differentiation with partial features and recursive types.

      automatic differentiationrecursionlogical relationssoftware correctness