Algebra and Logic

NOVA Math > Research Groups > Algebra and Logic

About

The group focuses on various interconnected areas within Algebra and Logic. These areas include the investigation of structural and combinatorial properties of transformation semigroups, Young tableaux, crystals, automata algebra, semigroups, combinatorics on words, Ramsey theory, graph decomposition, and Turán functions. We also study linear and multilinear algebra, algebraic, differential, and non-commutative geometry, mathematical logic, ordered algebraic structures, and finite fields. Additionally, the group is interested in utilizing computational tools to develop experimental mathematics, aiming to gain fresh insights into the diverse realms of our research.

Team

Publications

Identities and bases in the sylvester and Baxter monoids
2023, JOURNAL OF ALGEBRAIC COMBINATORICS, Cain,AJ;Malheiro,A;Ribeiro,D
Sistema de Navegação Aérea de Gago Coutinho e Sacadura Cabral / Gago Coutinho and Sacadura Cabral's Air Navigation System
2022, , Teresa Sousa
Identities and bases in the hypoplactic monoid
2022, COMMUNICATIONS IN ALGEBRA, Cain,AJ;Malheiro,A;Ribeiro,D
p Efficiency of the principal eigenvector of some triple perturb e d consistent matrices
2022, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Fernandes,R;Furtado,S
Ockham Algebras—An Urquhart Legacy
2022, Outstanding Contributions to Logic, Blyth,TS;Silva,HJ
Jacques Tits motivic measure
2022, MATHEMATISCHE ANNALEN, Tabuada,G
The polynomial hierarchy of functions and its levels
2022, THEORETICAL COMPUTER SCIENCE, Oitavem,I
Reconstructing Young tableaux
2022, JOURNAL OF COMBINATORIAL THEORY SERIES A, Cain,AJ;Lehtonen,E
Matrix theory for independence algebras
2022, LINEAR ALGEBRA AND ITS APPLICATIONS, Araujo,J;Bentz,W;Cameron,PJ;Kinyon,M;Konieczny,J
Ranks and presentations of some normally ordered inverse semigroups
2022, PERIODICA MATHEMATICA HUNGARICA, Caneco,R;Fernandes,VH;Quinteiro,TM

Projects

Cohomology and extensions of inverse and restriction semigroups
No funding, Mykola Khrypchenko
Finitary incidence algebras and their generalized derivations
CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico (Brazil), Mykola Khrypchenko
Generalized Derivations of Non-associative Algebras
FAPESP - Fundação de Amparo à Pesquisa do Estado de São Paulo (Brazil), Mykola Khrypchenko
Generalized Derivations of Incidence Algebras
CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico (Brazil), Mykola Khrypchenko
Incidence Algebras
Fundação Araucária (Brazil), Mykola Khrypchenko
SemiComb - Semigroups: Conjugacy, Computation, Crystals and Combinatorics
FCT - Fundação para a Ciência e a Tecnologia, I.P., João Araújo, Tara Brough, Alan J. Cain, Ana Casimiro,...
Partial Actions, Restriction Semigroups and Monoidal Categories
No funding, Mykola Khrypchenko
Paul Bernays’ Philosophy of Mathematics
Swiss National Science Foundation (Switzerland), Reinhard Kahle
Hilbert's 24th Problem
FCT - Fundação para a Ciência e a Tecnologia, I.P., Reinhard Kahle, Alan James Cain, António José Mesquita...
"Research in Pairs" small grant
London Mathematical Society (United Kingdom), Alan J. Cain

Software

  •  
    • the kernel of a Theorem Prover interface: ProverX (under construction)
    • a package to find Forbidden Structure Conjectures: Forbidden Theorems
    • a package to find a base of identities for the variety of semigroups it generates: Semigroup Varieties
    • a package to translate proofs from Prover9 to other Automated Theorem Provers: Translator
    • a package to humanize proofs from Prover9: XPlain
    • to test if an identity is satisfied, given a set of semistandard tableaux