Mai Gehrke                       

Laboratoire J.A. Dieudonné  (LJAD) 

Algèbre, Topologie et Géométrie


Bureau 3.718

+33(0)4 92 07 62 16


(postal address)

Laboratoire J.A. Dieudonné
Université Côte d’Azur

Parc Valrose
06108 NICE Cedex 02


Curriculum Vitae

Publication list

Nijmegen inaugural lecture











A blue book cover with white text

Description automatically generated    NEW book coauthored with Sam van Gool, available from Cambridge University Press. Get it on paper or in electronic form.  A preprint is available here.



Last time I was at CIRM, Stéphanie Vareilles did an interview



Submissions to the Houston Journal of Mathematics in logic and general algebra are welcome. For submission requirements please refer to the journal webpage  Information for Authors.


Upcoming events


Cracow Logic Conference LXIX and Trends in Logic XXIV, Kraków, 18-21 June 2024.


TOPOLOGY, ALGEBRA, AND CATEGORIES IN LOGIC (TACL 2024),  Barcelona,  25-28 June Summer School, 1-5 July Conference.




XXVIII Incontro di Logica AILA, Udine, 3-6 settembre.



Some papers


       Substitution Principle and semidirect products, with Célia Borlido.  


       Stone duality of spectral sheaves and the patch monad, with Clemens Berger. To appear in  Journal of Pure and Applied Algebra.


       A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures, with Tomas Jakl, and Luca Reggio. To appear in Samson Abramsky on Logic and Structure in Computer Science and Beyond, Outstanding Contribution to Logic, A. Palmigiano and M. Sadrzadeh (eds.), Springer.


       A duality theoretic view on limits of finite structures: extended version, with Tomas Jakl and Luca Reggio. Logical Methods in Computer Science 18 (1), pp. 16:1-16:38 (2022).


       Quantifiers on languages and codensity monads (Extended version), with Daniela Petrisan and Luca Reggio. Mathematical Structures in Computer Science 30(10), pp. 1054-1088 (2020).


       A duality theoretic view on limits of finite structures, with Tomas Jakl and Luca Reggio. In Goubault-Larrecq and B. König (Eds.), Foundations of Software Science and Computation Structures (FoSSaCS'20), Lecture Notes in Computer Science, volume 12077, pp. 299-318 (2020).


       A note on powers of Boolean spaces with internal semigroups, with Célia Borlido


       Difference hierarchies and duality with an application to formal languages, with Célia Borlido, Andreas Krebs, and Howard StraubingTopology and its Applications 273 (2020), 106975.


       Canonical extensions - an algebraic approach to Stone duality. Algebra Universalis 79 (3) 2018: 63


       An interpolant in predicate Gödel logic, with Matthias Baaz and Sam van Gool (preprint 2018)


       Stone Duality and the Substitution principle, with Silke Czarnetzki, Mai Gehrke, Andreas Krebs. Computer Science Logic:13:1-13:20 (2017)


       Stone duality for languages and complexity, with Andreas Krebs. ACM SIGLOG News 4 (2), April 2017, 29-53


       Quantifiers on languages and codensity monads, with Daniela Petrisan and Luca Reggio.  LICS 2017: 1-12


       Sheaves and duality, with Sam van Gool. Journal of Pure and Applied Logic, 222 (8) (2018) 2164-2180


       Duality in Computer Science, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016, New York, NY, USA, July 5-8, 2016, 12-26


       Uniform Birkhoff, with Michael Pinsker.  Journal of Pure and Applied Algebra 222(5), 2018,  1242-1250


       The Schützenberger product for Syntactic Spaces, with Daniela Petrişan and Luca Reggio.  ICALP 2016: 112:1-112:14


       Ultrafilters on words for a fragment of logic, with Andreas Krebs and Jean-Éric Pin. Theoretical Computer Science, Volume 610, Part A (2016), 37–58


       From ultrafilters on words to the expressive power of a fragment of logic, with Andreas Krebs and Jean-Éric Pin. Proceedings of the 16th International Workshop on Descriptional Complexity of Formal Systems. Jürgensen et al (eds.), Lecture Notes in Computer Science 8614 (2014), 138−149


       Stone duality, topological algebra, and recognition, Journal of Pure and Applied Algebra, Volume 220, Issue 7, July 2016, Pages 2711–2747


       Topological Duality and Algebraic Completions, Chapter to appear in Hiroakira Ono on Residuated Lattices and Substructural Logics, Outstanding Contributions Series (Springer)


       Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality, with Sam van Gool and Vincenzo Marra, Journal of Algebra 417 (2014), 290-332


       Distributive envelopes and topological duality for lattices via canonical extensions, with Sam van Gool. Order 31, Issue 3, (2014), 435-461


       Canonical extensions, Esakia spaces, and universal models, Chapter in Leo Esakia on duality in modal and intuitionistic logics, Trends in Logic (Outstanding Contributions subseries) 4 (2014), 9-41


       Bounded distributive lattice with operators, with Bjarni Jònsson, Mathematica Japonica 40 (1994), 207–215.






·      DuaLL, ERC project (2015-2021)






Jérémie Marques (2020-2023)

Axel Osmond  (2021; jointly supervised with Paul-André Melliès)

Mehdi Zaïdi  (2022; jointly supervised with Sam van Gool)

Luca Reggio  (2018)

Anna Carla Russo (2016; cotutelle with Antonio Di Nola, co-supervised with Olivia Caramello)

Rutger Kuyper (2014; co-director with Peter Stevenhagen, main adviser Sebastiaan Terwijn)

Sam van Gool (2014)

Dion Coumans (2012)

Jacob Vosmaer (2010)

Candida Palma (2005 dissertation)

Hideo Nagahashi (2002)

Alex Pogel (1998)


Axel Osmond (2017)

Zaïdi Mehdi (thesis 2016)

Lorijn van Rooijen (paper with Anna Chernilovskaya)

Mirte Dekkers (thesis)

Julie Manisha de Montgomery Nørgaard


Past events


TANCL’07 – Algebraic and Topological Methods in Non-Classical Logics III and its associated workshops, Oxford, 4-12 August. Pictures from the workshops by Juergen Koslowski: group, other.

Arbeitstagung Allgemeine Algebra – Lecture on Canonical extensions, duality theory, and Formal Concept Analysis, November 2-4, 2007, TU Darmstadt, Germany.

Second Indian Winter School on Logic – Course on Algebraic Logic, January 14-26, 2008, IIT Kanpur, India.

LINZ 2008, Foundations of Lattice-Valued Mathematics with Applications to Algebra and Topology – Lecture, 12-16 February, 2008, Linz, Austria.

DIAMANT/EIDMA Symposium – Lecture, 29-30 May, 2008, Leiden, the Netherlands.

ManyVal'08, Applications of topological dualities to measure theory in algebraic many-valued logic – Lecture, May 19-21, 2008, Milano, Italy.

E.W.Beth Centenary Minisymposium on Mathematical Logic, 5th European Congress of Mathematics (5ECM), Lecture: Duality theory as a Rosetta Stone for relational semantics, July 15, Amsterdam, Netherland.

Visiting Professorship,  PPS, Université de Paris Diderot – Paris 7, July 2008.

BLAST 2008, Lecture: Duality for MV-algebras, 6-10 August, 2008, Boulder, Colorado.

Sheaves in Geometry and Quantum Theory, a three-day workshop on the interplay between logic, topology/geometry and quantum theory, 3-5 September 2008.

AiML 2008, Advances in Modal Logic, Lecture: Using duality theory to export methods from modal logic, 9-12 September, Nancy, France.

Duality between two worlds, invited talk, Parallelle Werelden, Muziekgebouw aan 't IJ in Amsterdam, NL, 8 December 2008.

Workshop on Algebraic Logic ICLA 2009, Program Committee, January 7-11 2009.

Algebra and Geometry Seminar, An overview of canonical extensions of lattices,  Laboratoire de Mathematiques Nicolas Oresme, Caen, France, January 27 2009.

Duality, Oratie, Radboud Universiteit, Nijmgen, NL, March 12 2009.

Leiden Mathematics Colloquium, Duality as a Rosetta Stone, Leiden University, Leiden, NL, April 2, 2009.

Van Melsen Prijs, Opening of ceremony, FNWI, Radboud Universiteit, Nijmegen, NL, April 3, 2009.

Semantics Colloquium, Relational semantics for substructural logic, Nijmegen Center for Semantics, Radboud Universiteit, Nijmegen, NL, May 12, 2009.

Mathematical Logic in the Netherlands 2009 (MLNL09), Organiser,  Radboud Universiteit, Nijmegen, NL, May 25-26 2009.

AAA78, Arbeitstagung Allgemeine Algebra 78, Advances in topological duality theory, Bern, Switzerland, June 11-14, 2009.

Topology, Algebra, and Categories in Logics 2009 (TACL), Program Committee, Amsterdam, NL, July 7-11 2009.

Seventh Panhellenic Logic Symposium (PLS7), Invited talk, Patras, Greece, July 15-19 2009.

Conference on Algebra and Coalgebra in Computer Science 2009 (CALCO), Invited talk, Udine, Italy September 6-10 2009.

8th International Tbilisi Symposium on Language, Logic, and Computation, Tutorial on Logic, Tbilisi, Georgia, September 21-25, 2009.

Dagstuhl Seminar, Coalgebraic Logics, Schloss Dagstuhl, Germany, December 6-9, 2009.

MLNL 2010, 27-28 May 2010, Utrecht

DIAMANT/EIDMA Symposium Spring 2010, 27-28 May 2010, Nunspeet

Séminaire Complexité, Logique et Informatique, Groupe de Logique, 1 june, Paris

Séminaire de l’institut Gaspard-Monge, 22 juin, Marne-la-Vallée

ICALP 2010, July 5-10, 2010, Bordeaux

Tbilisi Topology Workshop 2010, June 8-10, 2010, Tbilisi

Logic Colloquium 2010, July 25-31, Paris

Categorical information flow in quantum physics and linguistics, 29-31 October 2010, CompLab, Oxford

Logique, catégories, sémantique, 12-13 November 2010, Bordeaux

DIAMANT/EIDMA Symposium, 25-26 November 2010, Lunteren

Workshop on Modal Logic and Stone Duality, 13 December 2010, ILLC, Amsterdam

PhDs in Logic III, 17-18 February 2011, Brussels

Workshop on Universal models, 24 February 2011, Amsterdam

Mathematics Colloquium, Korteweg-de Vries Institute, UvA, 20 April 2011, Amsterdam

Mathematical Logic in the Netherlands 2011 (MLNL11), Rijksuniversiteit Groningen, Groningen, NL, May 19-20 2011.

European Women in Mathematics Summer School, 6-10 June 2011, Leiden

Second International Conference in Order, Algebra and Logics, 6 - 10 June 2011, Krakow

Topology, Algebra, and Categories in Logic (TACL 2011), 25-30 July, Marseille

36th International Symposium on Mathematical Foundations of Computer Science (MFCS 2011), 22-26 August 2011, Warsaw

Ordered Groups and Lattices in Algebraic Logic, 20-23 September 2011, Tbilisi

Concept Lattices and their Applications, 17-21 October 2011, Nancy

ALCOP 2012, 16-18 April 2012, Prague

DIAMANT Symposium, 31 May-1 June 2012, Nunspeet

FREC meeting, 4-7 June 2012, Bordeaux

Duality theory in algebra, logic, and computer science, June 13-14  and  August 15-17, 2012, Oxford

Coalgebraic Logics, 7-12 October 2012, Dagstuhl

CUSO Winter School in Mathematics and Computer Science: Proof and Computation, 27-31 January 2013, Les Diablerets

Journées Topologie et Informatique/Topology and Informatics days, 21-22 March 2013, Paris

PhDs in Logic V, 8-10 April 2013, München

ALCOP 2013, April 18-20 2013, Utrecht

A scientific meeting in honor of Antonino Salibra, July 1-2 2013, Paris

Duality in Computer Science, 29 July- 2 August 2013, Dagstuhl

Boolean algebras, Lattices, Algebraic Logic, Set Theory, and Topology (BLAST 2013), August 5-9 2013, Chapman University, Orange

Master 2 – LMFI – cours: Théorie de la dualité en logique et informatique\Duality theory in logic and informatics, Winter 2014

Workshops on Duality and Probabilistic Systems (Belairs Research Center, McGill University), Holetown, Barbados, March 2014

Frontiers of Recognizability, Centre International de Rencontres Mathématiques (CIRM), 28-30 April 2014

Séminaire "Des Mathématiques", 2 avril, ENS Ulm, Paris

AAA88 Workshop on General Algebra, Warsaw, 19-22 June 2014

TOLO4 International Workshop on Topological Methods in Logic IV, Tbilisi, 23-27 June 2014

AiML 2014  Advances in Modal Logic, Groningen, August 5-8 2014

SLS2014 Scandinavian Logic Symposium, Tampere, 25-27 August 2014

Domains XI, 8-10 September 2014, Paris

BEYOND 2014, Florence, 3-5 December 2014

Master 2 – LMFI – cours: Théorie de la dualité en logique et informatique\Duality theory in logic and informatics, Winter 2015

FSMP funded Research visit of Achim Jung, LIAFA, Paris, 2 months in March-Mai 2015

Descriptive Set Theory Seminar, Théorie de Eilenberg-Reiterman et dualité de Stone, Paris 6, 24 March 2015

Visit, Logic group, University of Milan, 31 May- 6 June 2015

Member of CoNRS section 41 lead by the National Institute of Mathematical sciences and their interactions (INSMI), 2012-2015

TACL 2015, Ischia, 21-26 June 2015

Duality in Computer Science, Dagstuhl seminar, 25-30 October 2015

Logic, Algebra and Truth Degrees 2016, Phalaborwa, South Africa, 28-30 June 2016

LICS 2016, New York City, NEW York, 5-9 July 2016

Logic Colloquium, Berkeley, November 4, 2016

Logical Structures in Computation, Simon’s Institute, UC Berkeley, 17 August – 16 December, 2016

37th Linz Seminar on Fuzzy Set Theory: Enriched category theory and related topics, Linz Austria, February 7-10, 2017

Mathematics Colloquium, University College Cork, February 16, 2017

Topology, Algebra, and Categories in Logic 2017, Prague, June 26-30, 2017

Logic Colloquium ’17, Stockholm, August 14-20, 2017

CSL 2017, Stockholm, August 20-24, 2017

Logical Structures in Computation Reunion Workshop, Simons Institute, Berkeley, 11-14 December 2017

Journée Niçoises : Logique catégorique, topos et dualités, Laboratoire J.A. Dieudonné, Nice, 8-12 January 2018

Non-commutative structures 2018,  Portorož, 23-27 May 2018

SGSLPS  Spring school, Bern, May 28 2018

International Workshop on Topological Methods in Logic (Tolo VI), Tbilisi, 2-6 July 2018

International conference on semigroups, Lisbon, July 11-14, 2018

Computability in Europe 2018, Kiel, 30 July – 3 August 2018

AiML 2018, Bern, 27-31 August 2018

Achim Jung Fest, 8 September 2018

Workshop on Algebra, Logic and Topology, Coimbra, 27-29 September, 2018

Topological and categorical methods in algebra, with Carlos Simpson, 2nd trimester Master 2 course - 6 ECTS (2018-19)

Mathematics Colloquium, University of Oregon,  15 April 2019

Algebra seminar, University of Oregon, 17 April 2019

Lonseth Alumni Lecture, Oregon State University, 19 April 2019

De la triangulation p-adique à la théorie des modèles des algèbres de Heyting, et vice-versa, rapporteur, Fall 2019, HDR, Luck Darniere, Université d’Angers.

Circularity in Syntax and Semantics (CISS 2019), invited speaker, 20-22 November 2019

Logic and Structure in Computer Science and Beyond (LSCSB), participant, December 9-13 2019, Lorentz Center@Oort – Leiden

Symbolic reasoning and formal logics, with Carlos Simpson, 2nd trimester Master 2 course Math-Info UCA - 6 ECTS (2019-20)

99th Arbeitstagung Allgemeine Algebra, invited speaker, 21-23 February 2020, Siena

Resources and co-resources  workshop, 25-27 March, Cambridge

15th Workshop on Coalgebraic Methods in Computer Science (CMCS 2020), 25-26 April, Dublin

47th International Colloquium on Automata, Languages, and Programming (ICALP), PC member, 8-12 July 2020, Beijing

18th Relational and Algebraic Methods in Computer Science (RAMICS), PC member, 8-11 April 2020, Palaiseau

19th Relational and Algebraic Methods in Computer Science (RAMICS), co-organiser, 1-4 November 2021,CIRM Luminy

ERC funded project DuaLL running September 2015 to end of August 2021. For more information see DuaLL

Duality and More, May 16-20, 2022 LJAD, Nice

DaLFI : Duality and Logic in the passage from the Finite to the Infinite, 17 November 2022, Paris, France

JOURNEES HOMOTOPIQUES, Rencontre dédiée à Clemens Berger, pour ses 60 ans, 7 au 9 Décembre 2022, à Nice (LJAD)

Discrete mathematics and logic: between mathematics and the computer science (from the finite to the infinite), 16-20 January, CIRM 2023

Workshop on Springer Volume “Samson Abramsky on Logic and Structure in Computer Science and Beyond”, September 18th-20th, 2023

HOMOTOPICAL DAYS/ JOURNEES HOMOTOPIQUES, Rencontre dédiée à Clemens Berger, pour ses 60 ans Laboratoire J.-A. Dieudonné, Université Côte d'Azur, du  7 au 9 Décembre 2022




·      Pictures of my kids (2009)


·      Cameron Calk’s webpage


·      Maciej Krupa’s webpage


·      My favourite mathematician (by the Wiskundemeisjes)


·      Mathematica by David Bessis ( I see it is also availble in English)