Célia Borlido

Since July 2019, I am a Junior researcher at CMUC (Center for Mathematics, University of Coimbra).

From June 2016 to July 2019 I was a postdoc under supervision of Mai Gehrke on the ERC project duaLL.
I obtained my PhD in Mathematics in 2016 at Faculdade de Ciências da Universidade do Porto, where I was advised by Jorge Almeida.

Research Interests:

• Pointfree topology


• Lattice and duality theory


• The use of Stone-type dualities use in the study of formal languages and logic on words


• Algebras of partial functions


• (Pro)finite semigroups, automata and formal languages

1. On semidirect products of quantale enriched monoids. Semigroup Forum (2024) [Preprint]


2. Filtral pretoposes and compact Hausdorff locales. (with P. Karazeris, L. Reggio, and K. Tsamis). Theory and Applications of Categories, 41, 41, 1439-1475 (2024) [Preprint]


3. Pervin spaces and Frith frames: bitopological aspects and completion. (with A. L. Suarez). Applied Categorical Structures, 31, 43 (2023) [Preprint]


4. Substitution Principle and semidirect products. (with M. Gehrke). Mathematical Structures in Computer Science, 33, 6, 486-535 (2023) [Preprint]


5. A pointfree theory of Pervin spaces. (with A. L. Suarez). Quaestiones Mathematicae, 46, 11, 2287-2326 (2023) [Preprint]


6. Difference-restriction algebras of partial functions with operators: discrete duality and completion. (with B. McLean). Journal of Algebra 604, 760-789 (2022) [Preprint]


7. Difference-restriction algebras of partial functions with operators: axiomatisations and representations.(with B. McLean). Algebra Universalis 83, 24 (2022) [Preprint]


8. Difference hierarchies and duality with an application to formal languages. (with M. Gehrke, A. Krebs, H. Straubing). Topology and its Applications, 273 (2020) [Preprint]
   


9. Some reducibility properties for pseudovarieties of the form DRH. Communications in Algebra 46, 4, 1813-1830 (2018) [Preprint]
   


10. Stone Duality and the Substitution principle. (with S. Czarnetzki, M. Gehrke, A. Krebs). Computer Science Logic:13:1-13:20 (2017)


11. The kappa-word problem over DRH. Theoretical Computer Science 702: 1-22 (2017) [Preprint]
    


12. Complete kappa-reducibility of pseudovarieties of the form DRH. (with J. Almeida). International Journal of Algebra and Computation 27(2): 189-236 (2017) [Preprint]
    

• A note on powers of Boolean spaces with internal semigroups. (with M. Gehrke) [Preprint]

Last update: December 2024.

• Métodos de programação I, exercise classes, 1st year BSc, 2nd Semester, Departamento de Matemática, Universidade de Coimbra.

• Métodos de programação I, exercise classes, 1st year BSc, 2nd Semester, Departamento de Matemática, Universidade de Coimbra.

• Métodos de programação I, exercise classes, 1st year BSc, 2nd Semester, Departamento de Matemática, Universidade de Coimbra.

• Programmation impérative, exercise classes, 1st year BSc, 2nd Semester, Département Informatique, Université Côte d'Azur,.
• Algèbre homologique et catégorielle, exercise classes, 2nd year MSc, 1st trimester, Laboratoire J. A. Dieudonné, Université Côte d'Azur.

• Álgebra linear, exercise classes, 1st year BSc, 2nd Semester, Instituto Superior Técnico, Universidade de Lisboa.
• Cálculo diferencial e integral, exercise classes, 1st Semester, Instituto Superior Técnico, Universidade de Lisboa.

• Álgebra linear, exercise classes, 1st year BSc, 2nd Semester, Instituto Superior Técnico, Universidade de Lisboa.
• Análise complexa e equações diferenciais, exercise classes, 2nd year BSc, 1st Semester, Instituto Superior Técnico, Universidade de Lisboa.

• (invited speaker) Extending Stone duality along full embeddings, presented at the workshop A day on pointfree topology, Departamento de Matemática, Universidade de Coimbra, Portugal, October 12, 2023.
• (invited speaker) Transitive and totally bounded quasi-uniformities on frames, presented at the conference AMS Fall Central Sectional Meeting, University of Texas, El Paso, United States of America (online), September 17, 2022.
• Difference-restriction algebras of partial functions: axiomatizations and representations, presented at TACL - Topology, Algebra, and Categories in Logic, Departamento de Matemática, Universidade de Coimbra, Portugal, June 21, 2022.
• (invited speaker) Difference-restriction algebras of partial functions with operators: discrete duality, presented at the workshop Duality and more, Laboratoire J.A. Dieudonné, Université Côte d'Azur, France, May~18, 2022.
• (invited speaker) Extending Stone-Priestley duality along full embeddings, presented at BLAST - Boolean Algebras; Lattices, Algebraic and Quantum logic; Universal Algebra; Set Theory; Set-theoretic and Point-free Topology, New Mexico State University, Las Cruces, United States of America (online), June 12, 2021.
• Contravariant power constructions, presented at the XII Portuguese Category Seminar, Departamento de Matemática da Universidade de Coimbra, Portugal, September 17, 2019.
• Difference hierarchies over lattices, presented at the conference on Topology, Algebra, and Categories in Logic (TACL 2019), Laboratoire J. A. Dieudonné, Université Côte d'Azur, France, June 21, 2019.
• Difference hierarchies over lattices, presented at the workshop on Algebra, Logic and Topology, Faculdade de Ciências da Universidade de Coimbra, Portugal, September 28, 2018.
• (invited speaker) Stone duality and the substitution principle, presented at the workshop Quantifiers and Duality, Institut de Recherche en Informatique Fondamentale, Université Paris Diderot, France, September 11, 2018.
• Stone duality and the substitution principle, presented at International Conference on Semigroups (ICS 2018), Faculdade de Ciências da Universidade de Lisboa, Portugal, July 12, 2018.
• (invited speaker) Profinite semigroups in formal language theory, presented at National Meeting of the Portuguese Mathematical Society, Instituto Politécnico de Bragança, Portugal, July 9, 2018.
• Stone duality and the substitution principle, presented at Computer Science Logic (CSL 2017), Stockholm University, Sweden, August 21, 2017.
• The \(\kappa\)-word problem over pseudovarieties of the form \(\sf DRH\), presented at International Conference on Semigroups and Automata (CSA 2016), Faculdade de Ciências da Universidade de Lisboa, Portugal, June 22, 2016.

• Pervin spaces and Frith frames: bitopological aspects and completion, presented at the seminar Algebra, Logic and Topology, Departamento de Matemática, Universidade de Coimbra, Portugal, January 24, 2023.
• Duality: from theory to applications, presented at the seminar of the PhD Program in Mathematics, Departamento de Matemática, Universidade de Coimbra, Portugal, November 30, 2022.
• A discrete duality for algebras of partial functions for a foundational signature, presented at the Category Theory Seminar , Departamento de Matemática, Universidade de Coimbra, Portugal, March 28, 2022.
• Algebras of partial functions for a foundational signature, presented at the seminar Semigroups, Automata and Languages, Centro de Matemática, Universidade do Porto, Portugal (online), October 29, 2021.
• Stone duality and the substitution principle, presented at the seminar ``MOVE : Modélisation et Vérification'', Laboratoire d'Informatique et Systèmes, Université d'Aix-Marseille, France, March 5, 2020.
• Difference hierarchies and duality, presented at Algebra-Coalgebra seminar, Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands, October 31, 2018.
• An Eilenberg-like Theorem beyond regular languages, presented at Algebra, Logic and Topology seminar, Faculdade de Ciências da Universidade de Coimbra, July 6, 2018.
• An Eilenberg-like Theorem beyond regular languages, presented at CEMAT seminar, Faculdade de Ciências da Universidade de Lisboa, Portugal, May 25, 2018.
• Semidirect products, monoids and categories, presented at Dualité de Stone, langages formels et logique seminar, Laboratoire J. A. Dieudonné, Université Côte d'Azur, France, November 21, 2017.
• Stone duality and the substitution principle, presented at Semigroup, automata and languages seminar, Faculdade de Ciências da Universidade do Porto, Portugal, May 5, 2017.
• Duality theory in the study of formal languages, presented at Semigroup, automata and languages seminar, Faculdade de Ciências da Universidade do Porto, Portugal, February 20, 2017.
• The \(\kappa\)-word problem over \(\sf DRG\), presented at Research Seminar Program, Faculdade de Ciências da Universidade de Coimbra, Portugal, March 10, 2016.
• The word problem and some reducibility properties for pseudovarieties of the from \(\sf DRH\), presented at DuaLL seminar, Institut de Recherche en Informatique Fondamentale, Université Paris Diderot, France, January 27, 2016.

Last update: October 2023.