FERNANDO LUCATELLI NUNES

Ph.D. in Mathematics     Ph.D. in Computer Science

My research profile is deliberately balanced between mathematics and computer science, with each informing and shaping the other. In computer science, I work in programming language semantics and formal methods, with a particular focus on the use of mathematical structure as a foundation for the design of reliable and principled computational systems. My research addresses the semantic analysis of expressive programming languages and the development of correctness-by-construction methods for program transformation.

Alongside this, I maintain an active research programme in mathematics, centred on the theory and applications of low- and higher-dimensional generalised categorical structures, often developed through the lens of two- and three-dimensional universal algebra. This mathematical work is closely intertwined with my research in programming languages: it provides the structural tools required for semantic modelling, while questions arising from programming language semantics, in turn, inform and motivate new research directions in mathematics.

Research

Talks

Academic positions/stays

Organization of seminars/events

Mathematical Genealogy

Further information

Selected Talks

Seminars

All talks were 1-hour research seminars.

• IMPA, Brazil, 2025 — Biadjoint Triangles and Coherence
• University of Cape Town, South Africa, 2025 — Two-dimensional monad theory, pseudodistributive laws, and doubly-infinitary distributive and extensive categories as pseudoalgebras
• Stellenbosch University, South Africa, 2025 — Two-dimensional monad theory, and free extensive completions
• University of Cape Town, South Africa, 2025 — Bifibrations, Spans, and the Bénabou-Roubaud Theorem
• University of Coimbra, Portugal, 2024 — Unraveling the iterative CHAD
• University of Coimbra, Portugal, 2022 — Descent for Split Fibrations
• Utrecht University, Netherlands, 2021 — Automatic differentiation of expressive total functional languages
• University of Coimbra, Portugal, 2019 — On monadicity and descent
• University of Coimbra, Portugal, 2019 — Functorial Semantics and Descent II
• University of Coimbra, Portugal, 2018 — Functorial Semantics and Descent,
• University of Coimbra, Portugal, 2018 — Biadjoint Triangles and Applications,
• University of Coimbra, Portugal, 2018 — Towards semi left exactness and Janelidze-Galois within the lax idempotent context
• University of Coimbra, Portugal, 2016 — The deficiency of categories,
• University of Coimbra, Portugal, 2016 — Biadjoint triangles, descent and coherence
• Universidade do Porto, Portugal, 2016 — Kan construction of adjunctions
• University of Coimbra, Portugal, 2016 — Homotopy Excision
• University of Coimbra, Portugal, 2013 — Every prespectrum represents a homology theory
• Universidade de Brasília, Brazil, 2010 — Topological Dynamics and Applications in Number Theory,
• Universidade de Brasília, Brazil, 2010 — Dynamical Proof of the Van der Waerden Theorem

Special Talks

• Plenary Talk, International Conference on Category Theory, University of Azores, 2018
  Aspects of Descent via Bilimits
• Invited Talk, New Challenges in Programming Language Semantics, Lorentz Center, Leiden, Netherlands, 2022
  Categorical Approach to Semantic Logical Relations (for partial features and recursive types)

Conference Presentations

• 109th Peripatetic Seminar on Sheaves and Logic, Leiden University, Netherlands, 2024
  The semantic lax descent factorization of a functor
• International Conference on Category Theory, University of Santiago de Compostela, Spain, 2024
  Doubly-infinitary distributive categories
• SUMTOPO 2024, University of Coimbra, Portugal, 2024
  Homomorphic reverse differentiation for partial features
• 38th Summer Conference on Topology and its Applications, University of Coimbra, Portugal, 2024
  Free distributive and extensive categories
• XIV Portuguese Category Seminar, University of Coimbra, Portugal, 2023
  Freely generated bicartesian categories and exponentials
• International Conference on Category Theory, UCLouvain, Belgium, 2023
  Spanning the tale of “Monades et descente”
• XIII Portuguese Category Seminar, University of Coimbra, Portugal, 2022
  CHAD: elementary categorical aspects of automatic differentiation
• 8th European Congress of Mathematics, University of Primorska, Slovenia, 2021
  Eilenberg-Moore, Kleisli and descent factorizations
• XII Portuguese Category Seminar, University of Coimbra, Portugal, 2019
  Lax comma 2-categories
• International Conference on Category Theory, University of Edinburgh, Scotland, 2019
  Descent and Monadicity
• Categorical Structures in Algebra, Topology and Logic, Stellenbosch University, South Africa, 2019
  Eilenberg-Moore, Kleisli and descent factorization
• 103rd Peripatetic Seminar on Sheaves and Logic, Masaryk University, Brno, Czech Republic, 2018
  Biadjoint Triangles and Applications
• 102nd Peripatetic Seminar on Sheaves and Logic, Universidade de Santiago de Compostela, Spain, 2018
  Non-canonical isomorphisms
• 5th Workshop on Categorical Methods in Non-Abelian Algebra, UCLouvain, Belgium, 2017
  Biadjoint Triangles
• XI Portuguese Category Seminar, University of Coimbra, Portugal, 2017
  Freely generated n-categories and coinserters
• 4th Workshop on Categorical Methods in Non-Abelian Algebra, University of Coimbra, Portugal, 2016
  Bilimits Commutativity and Descent
• International Conference on Category Theory, University of Aveiro, Portugal, 2015
  Kan extensions and descent theory

Workshop Presentations

• LAFI 2024 – Tenth Workshop on Languages for Inference at POPL, London, UK
  Homomorphic Reverse Differentiation of Iteration

📄 For more details and the complete list of academic activities, please refer to my full Curriculum Vitae.