Hello, I'm Bruno Teheux

Assistant Professor at the University of Luxembourg

Welcome to my academic portfolio. This page presents my research contributions, my teaching activities, and my public engagement initiatives in mathematics.

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Bruno Teheux

About me

I am an Assistant Professor at the Department of Mathematics of the University of Luxembourg, focusing on research in mathematical logic and universal algebra. My work connects various semantics for non-classical logics.

My research interests include:

  • Many-valued logics and their algebraic semantics
  • Modal logics and their topological semantics
  • Logic for computer science
  • Universal algebras, lattice and duality theory
  • Ordered algebraic structures

My teaching portfolio spans multiple levels of instruction—bachelor’s, master’s, and continuing education—with courses ranging from Discrete Mathematics for IT students to Advanced Graph Theory.

Beyond research and teaching, I’m dedicated to developing innovative outreach initiatives that bridge contemporary mathematical concepts with broader audiences, creating various entry points to modern mathematics.

In my spare time, I learn trumpet, hike in Luxembourg and go to the playground with my kids.

Short CV

2009
PhD in Mathematics
ULiège
2010 - 2012
General Secretary
Animath, Paris
2012 - 2017
Postdoc
URMATH - Uni.lu
2017 - 2023
Senior Research Scientist
DMATH - Uni.lu
2023 - ···
Assistant Professor
DMATH - Uni.lu

Administrative & Service Roles

  Elected Member of the Staff Delegation

  Go-to Person of the Doctoral School

  Member of the Advance Mentorship Programi of Uni.lu

  Feature Editor for EMS Magazine

  Secretary of the Luxembourg Mathematical Society

Research

Publications

Each of the following publication is linked to an electronic version from a public repository.

Peer-reviewed Articles

  • Alexander Kurz, Wolfgang Poiger and Bruno Teheux. Many-valued coalgebraic logic over semi-primal varieties. Logical Methods in Computer Science, 20(3):6:1 - 6:32, 2024.
  • ALexander Kurz, Wolfgang Poiger and Bruno Teheux. New perspectives on semi-primal varieties. Journal of pure and applied algebra, 228(4):107525, 2024.
  • Wolfgang Poiger and Bruno Teheux. The Minor Order of Homomorphisms via Natural Dualities. Order, 40:99-125, 2023.
  • Georges Hansoul and Bruno Teheux. Extending maps to profinite completions in finitely generated quasivarieties. Contributions to Algebra and Geometry, 61(4):627--647, 2020.
  • Jimmy Devillet, Jean-Luc Marichal and Bruno Teheux. Classifications of quasitrivial semigroups. Semigroup Forum, 100(3):743--764, 2020.
  • Jimmy Devillet and Bruno Teheux. Associative, Idempotent, Symmetric, and Order-preserving Operations on Chains. Order, 37(1):45--58, 2020.
  • Gergely Kiss, Jean-Luc Marichal and Bruno Teheux. Generalization of the concept of distance based on the simplex inequality. Contributions to Algebra and Geometry, 59(2):247-266, 2018.
  • Miguel Couceiro and Bruno Teheux. Pivotal decomposition schemes inducing clones of operations. Contributions to Algebra and Geometry, 59(1):25--40, 2018.
  • Didier Dubois, Henri Prade, Agnès Rico and Bruno Teheux. Generalized qualitative Sugeno integrals. Information Sciences, 415-416:429-445, 2017.
  • Tomáš Kroupa and Bruno Teheux. Modal extensions of Łukasiewicz logic for modelling coalitional power. Journal of Logic and Computation, 27(1):129-154, 2017.
  • Jean-Luc Marichal and Bruno Teheux. On the generalized associativity equation. Aequationes Mathematicae, 91:265-277, 2017.
  • Miguel Couceiro, Jean-Luc Marichal and Bruno Teheux. Relaxations of associativity and preassociativity for variadic functions. Fuzzy Sets and Systems, 299:89-97, 2016.
  • Miguel Couceiro, Jean-Luc Marichal, and Bruno Teheux. Conservative median algebras and semilattices. Order, 33(1):121-132, 2016.
  • Jean-Luc Marichal and Bruno Teheux. Strongly barycentrically associative and preassociative functions. Journal of Mathematical Analysis and Applications, 437:181-193, 2016.
  • Jean-Luc Marichal and Bruno Teheux. A characterization of barycentrically preassociative functions. Results in Mathematics, 69(01): 245-256, 2016.
  • Bruno Teheux. Modal definability for Łukasiewicz validity relations. Studia Logica, 104(2):343-363, 2016.
  • Jean-Luc Marichal and Bruno Teheux. Preassociative aggregation functions. Fuzzy Sets and Systems, 268:15-26, 2015.
  • Jean-Luc Marichal and Bruno Teheux. Barycentrically associative and preassociative functions. Acta Mathematica Hungarica, 145(2):468-488, 2015.
  • Erkko Lehtonen, Jean-Luc Marichal, and Bruno Teheux. Associative string functions. Asian-European Journal of Mathematics, 07(04):1450059, 2014.
  • Jean-Luc Marichal and Bruno Teheux. Pivotal decompositions of functions. Discrete Applied Mathematics, 174:102-112, 2014.
  • Jean-Luc Marichal and Bruno Teheux. Associative and preassociative functions. Semigroup Forum, 89(2):431-442, 2014.
  • Bruno Teheux. Propositional dynamic logic for searching games with errors. Journal of Applied Logic, 12(4):377-394, 2014.
  • Georges Hansoul and Bruno Teheux. Extending Łukasiewicz logics with a modality: Algebraic approach to relational semantics. Studia Logica, 101(3):505-545, 2013.
  • Philippe Niederkorn, Pierre Mathonet and Bruno Teheux. Natural dualities for varieties generated by a set of subalgebras of a semi-primal algebra. Algebra and Discrete Mathematics, (1):67-85, 2007.
  • Bruno Teheux. Lattice of subalgebras in the finitely generated varieties of MV-algebras. Discrete Mathematics, 307(17–18):2261-2275, 2007.
  • Bruno Teheux. A duality for the algebras of a Łukasiewicz n+1-valued modal system. Studia Logica, 87(1):13-36, 2007.

Other Publications

  • Bruno Teheux. Algebraic approach to modal extensions of Łukasiewicz logics. PhD thesis, University of Liège, Liège, 2009.
  • Georges Hansoul and Bruno Teheux. Completeness results for many-valued Łukasiewicz modal systems and relational semantics. Working paper, 2006.

Projects

I am currently or have been recently involved in the following research projects.

GRACE
FNR-PRIDE, 2024 - 2029
Role: Co-PI
Choice
FNR AFR-PHD, 2023 - 2027
Role: Co-Supervisor
GPS
FNR-PRIDE, 2020 - 2025
Role: Co-PI

Research Team

Current Members

  • Franceso Tognetti - PhD Candidate
  • Simon Lemal - PhD Candidate (co-supervised with Nick Bezhanishvili)

Former Members

  • Wolfgang Poiger - PhD Candidate 2020 - 2024
  • Francesca Guffanti - Postdoc 2023-2024

Teaching

My teaching portfolio spans across various programs, disciplines, and levels. I regularly supervise student projects and theses, and oversee the “Math Forge” department initiative, which offers activities to help Bachelor of Mathematics students successfully transition from high school to university.

Here is a list and description of the recent courses I’ve been responsible for.

Period: 2016 - Present

This introductory course to discrete mathematics aims at providing a basic toolkit to first-year IT students. It covers fundamentals such as propositional logic, naive set theory, elements of combinatorics, basic arithmetic, and modular arithmetic. It also introduces notions of order and graph theory. Connections with problems arising from IT are made apparent throughout the course.
References:
  • Harris Kwong. A spiral Workbook for Discrete Mathematics. LibrTexts, 2O21.
  • Eric Lehman, F. Thomson Leighton and Alberty R. Meyer. Mathematics for Computer Science. LibreTexts, 2021
  • Franck Leprévost. How big is big? How fast is fast?: a hands on tutorial on mathematics of computation. S.I.: Amazon
  • Oscar Levin. Discrete Mathematics. An open Introduction, 3rd edition.

Period: 2023 - Present

This course serves two fundamental objectives. First, it introduces essential mathematical structures that form the foundation of the bachelor’s degree in mathematics. Second, it introduce students to authentic mathematical thinking—the systematic intellectual approach characteristic of the discipline.

The course introduces propositional calculus, naive set theory (including an introduction to infinite cardinals), relations and functions, the language of predicate logic, proof techniques, order and equivalence relations, modular arithmetic, permutations, groups, and homomorphisms. Weekly exercise sessions are organized to support student learning and provide hands-on practice with the theoretical concepts.

References:
  • Oscar Lewin. Discrete Mathematics - An Open Introduction.
  • Richard Hammack. Book of Proof, 3rd edition, 2018.
  • Paul Halmos. Naive Set Theory, Springer-Verlag, 1974.

Period: 2013 - 2023

This course provides a general introduction to the fundamental concepts of point-set topology. It aims to establish the necessary foundation for students to pursue further studies in algebraic topology. The course covers topological spaces and continuous transformations, connectedness, compactness, separation axioms, and product topology (quotient topology will be introduced if time permits).

The material is reinforced through essential weekly exercise sessions that help students develop problem-solving skills and deepen their understanding of abstract concepts.

The challenge of this course lies in its significant step up in abstraction from the first-year bachelor courses, requiring students to develop new mathematical intuition and reasoning abilities.

References:
  • John L. Kelley. General Topology. Dover Publications, 2017
  • J.Munkres. Topology. Pearson, 2014.

Period: 2021 - Present (every other year)

This course provides a standard introduction to graph theory for Bachelor students in mathematics. It focuses on the most relevant topics, problem-solving methods, and proof techniques, while occasionally considering algorithmic aspects.

The course content includes an introduction to graphs and digraphs, trees and spanning trees, shortest path algorithms, Eulerian graphs, Hamiltonian graphs, and planar graphs.

Exercises are an integral part of the learning process and will help students develop their problem-solving skills and deepen their understanding of theoretical concepts.

References:
  • J. Matousek and J. Nesetril. Invitation to Discrete Mathematics. Second edition. Oxford University Press, 2008.
  • J. A. Bondy and U. S. R. Murty. Graph Theory with Applications. North-Holland, 1976.
  • D. Jungnickel. Graphs, Networks and Algorithms. Fourth edition.i Springer-Verlag, 2013

Period: 2025 - Present (every other year)

References:
  • J. Matousek and J. Nesetril. Invitation to Discrete Mathematics. Second edition. Oxford University Press, 2008.

Period: 2021 - 2022

Graphs constitute a fundamental data structure for representing and analyzing complex relational information. This course offers a comprehensive introduction to graph theory, striking a careful balance between abstract mathematical concepts and practical algorithmic applications.

The curriculum begins with essential definitions and terminology before exploring key topics including: graph traversal techniques and shortest path algorithms, minimum spanning tree constructions, network flow analysis and the min cut-max flow theorem, and clustering algorithms and their applications.

References:
  • D. Jungnickel. Graphs, Networks and Algorithms. Fourth edition.i Springer-Verlag, 2013

Period: 2020 - Present

This course serves as a second course in Graph Theory for mathematics students. It introduces a selection of more advanced topics and problems that have significantly contributed to the development and reputation of the field.

The course is structured in two main parts. The first part focuses on vertex colorings, including an introduction to chromatic polynomials and perfect graphs. The second part explores algebraic flows and the flow-duality theorem.

Additionally, we examine selected sporadic problems of current interest in graph theory, which may vary from year to year.

References:
  • J. A. Bondy and U. S. R. Murty. Graph Theory with Applications. North-Holland, 1976.
  • D. Jungnickel. Graphs, Networks and Algorithms. Fourth edition.i Springer-Verlag, 2013

Period: 2024 - Present

This course serves a dual purpose. First, it introduces the foundational principles of lattice theory with computer science applications in mind. Second, it explores practical applications of lattices in computer science, including Conflict-Free Replicated Data Types, parallel programming, and abstract interpretation.

I am responsible for the lattice theory component, covering essential concepts such as partial orders, lattices, lattice constructions, complete lattices, fixed-point theorems, closure operators, and Galois connections.

References:
  • B. A. Davey and H. A. Priestley. Introduction to lattices and Order. Cambridge University Presse, 2002

Outreach

Under Construction

This section is currently being developed. Please check back later for updates on mathematical outreach activities.