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.