Mai Gehrke
Laboratoire
J.A. Dieudonné (LJAD)
Algèbre,
Topologie et Géométrie

Sam van Gool and I have finished a book for Cambridge University Press: Topological
Duality for Distributive Lattices: Theory and Applications. A
preprint is available here.
Last time I was at CIRM, Stéphanie Vareilles did an interview with me.
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 
Algebra and Truth Degrees, 2023 (LATD
2023), Tbilisi, Georgia, September, 2023.
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. 16:116:38 (2022).
•
Quantifiers
on languages and codensity monads (Extended version),
with Daniela Petrisan and Luca Reggio. Mathematical
Structures in Computer Science 30(10), pp. 10541088 (2020).
•
A duality theoretic view on limits
of finite structures, with Tomas Jakl and Luca
Reggio. In GoubaultLarrecq and B. König (Eds.), Foundations
of Software Science and Computation Structures (FoSSaCS'20), Lecture Notes
in Computer Science, volume 12077, pp. 299318 (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 Straubing. Topology 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:13:113:20 (2017)
•
Stone duality for languages and
complexity, with Andreas Krebs. ACM SIGLOG
News 4 (2),
April 2017, 2953
•
Quantifiers
on languages and codensity monads, with Daniela Petrisan and Luca Reggio. LICS 2017: 112
•
Sheaves
and duality, with Sam van Gool. Journal
of Pure and Applied Logic, 222 (8) (2018) 21642180
•
Duality in
Computer Science, Proceedings of the
31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016, New
York, NY, USA, July 58, 2016, 1226
•
Uniform
Birkhoff, with Michael Pinsker. Journal of Pure and Applied Algebra 222(5), 2018,
12421250
•
The Schützenberger product for Syntactic Spaces, with
Daniela Petrişan and Luca Reggio. ICALP 2016: 112:1112:14
•
Ultrafilters on words for a fragment
of logic, with Andreas
Krebs and JeanÉric 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 JeanÉric 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 MValgebras and latticeordered
abelian groups via duality, with Sam van Gool and Vincenzo Marra, Journal of
Algebra 417 (2014), 290332
• Distributive
envelopes and topological duality for lattices via canonical extensions,
with Sam van Gool. Order 31, Issue 3, (2014), 435461
•
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), 941
• Bounded distributive lattice
with operators, with Bjarni Jònsson, Mathematica
Japonica 40 (1994), 207–215.
Links 
·
DuaLL,
ERC project (20152021)
Students 
(PhD)
Jérémie Marques (since 2020)
Axel Osmond (2021; jointly supervised with PaulAndré Melliès)
Mehdi Zaïdi (2022; jointly supervised with Sam van Gool)
Luca Reggio (2018)
Anna
Carla Russo (2016; cotutelle with Antonio Di Nola,
cosupervised with Olivia Caramello)
Rutger
Kuyper (2014; codirector 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)
(Master)
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 NonClassical Logics III and its
associated workshops, Oxford, 412 August. Pictures from the workshops by
Juergen Koslowski: group, other.
Arbeitstagung Allgemeine Algebra – Lecture on Canonical
extensions, duality theory, and Formal Concept Analysis, November 24, 2007, TU
Darmstadt, Germany.
Second
Indian Winter School on Logic – Course on Algebraic Logic, January 1426,
2008, IIT Kanpur, India.
LINZ
2008, Foundations of LatticeValued Mathematics with Applications to
Algebra and Topology – Lecture, 1216 February, 2008, Linz, Austria.
DIAMANT/EIDMA
Symposium – Lecture, 2930 May, 2008, Leiden, the Netherlands.
ManyVal'08, Applications of
topological dualities to measure theory in algebraic manyvalued logic –
Lecture, May 1921, 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 MValgebras, 610 August,
2008, Boulder, Colorado.
Sheaves in Geometry and
Quantum Theory, a threeday workshop on the interplay between logic,
topology/geometry and quantum theory, 35 September 2008.
AiML 2008,
Advances in Modal Logic, Lecture: Using duality
theory to export methods from modal logic, 912 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 711 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 2526 2009.
AAA78, Arbeitstagung Allgemeine Algebra 78, Advances in
topological duality theory, Bern, Switzerland, June 1114, 2009.
Topology, Algebra, and
Categories in Logics 2009 (TACL), Program Committee, Amsterdam, NL, July
711 2009.
Seventh Panhellenic Logic
Symposium (PLS7), Invited talk, Patras, Greece, July 1519 2009.
Conference on Algebra and
Coalgebra in Computer Science 2009 (CALCO), Invited talk, Udine, Italy
September 610 2009.
8^{th} International
Tbilisi Symposium on Language, Logic, and Computation, Tutorial on Logic,
Tbilisi, Georgia, September 2125, 2009.
Dagstuhl Seminar, Coalgebraic Logics, Schloss Dagstuhl, Germany, December 69, 2009.
MLNL 2010,
2728 May 2010, Utrecht
DIAMANT/EIDMA
Symposium Spring 2010, 2728 May 2010, Nunspeet
Séminaire
Complexité, Logique et Informatique, Groupe de Logique, 1 june,
Paris
Séminaire de
l’institut GaspardMonge, 22 juin, MarnelaVallée
ICALP 2010, July 510, 2010,
Bordeaux
Tbilisi Topology Workshop 2010,
June 810, 2010, Tbilisi
Logic Colloquium 2010, July 2531,
Paris
Categorical
information flow in quantum physics and linguistics, 2931 October 2010, CompLab, Oxford
Logique, catégories, sémantique, 1213 November 2010, Bordeaux
DIAMANT/EIDMA Symposium, 2526 November 2010, Lunteren
Workshop on Modal Logic and
Stone Duality, 13 December 2010, ILLC, Amsterdam
PhDs in Logic III,
1718 February 2011, Brussels
Workshop on Universal
models, 24 February 2011, Amsterdam
Mathematics
Colloquium, Kortewegde Vries Institute, UvA, 20 April 2011, Amsterdam
Mathematical Logic in the
Netherlands 2011 (MLNL11), Rijksuniversiteit
Groningen, Groningen, NL, May 1920 2011.
European
Women in Mathematics Summer School, 610 June 2011, Leiden
Second International Conference in
Order, Algebra and Logics, 6  10 June 2011, Krakow
Topology,
Algebra, and Categories in Logic (TACL 2011), 2530 July, Marseille
36th International Symposium on
Mathematical Foundations of Computer Science (MFCS 2011), 2226 August
2011, Warsaw
Ordered Groups and Lattices in
Algebraic Logic, 2023 September 2011, Tbilisi
Concept Lattices and their
Applications, 1721 October 2011, Nancy
ALCOP 2012, 1618
April 2012, Prague
DIAMANT
Symposium, 31 May1 June 2012, Nunspeet
FREC meeting, 47 June 2012, Bordeaux
Duality theory
in algebra, logic, and computer science, June 1314 and August
1517, 2012, Oxford
Coalgebraic Logics, 712
October 2012, Dagstuhl
CUSO Winter School in
Mathematics and Computer Science: Proof and Computation, 2731 January
2013, Les Diablerets
Journées Topologie
et Informatique/Topology
and Informatics days, 2122 March 2013, Paris
PhDs in Logic V,
810 April 2013, München
ALCOP 2013, April 1820 2013,
Utrecht
A scientific
meeting in honor of Antonino Salibra, July 12
2013, Paris
Duality
in Computer Science, 29 July 2 August 2013, Dagstuhl
Boolean
algebras, Lattices, Algebraic Logic, Set Theory, and Topology (BLAST 2013),
August 59 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), 2830 April 2014
Séminaire "Des Mathématiques", 2 avril, ENS Ulm,
Paris
AAA88 Workshop on General
Algebra, Warsaw, 1922 June 2014
TOLO4 International Workshop on
Topological Methods in Logic IV, Tbilisi, 2327 June 2014
AiML
2014 Advances in Modal Logic,
Groningen, August 58 2014
SLS2014 Scandinavian Logic
Symposium, Tampere, 2527 August 2014
Domains
XI, 810 September 2014, Paris
BEYOND 2014, Florence, 35 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 MarchMai 2015
Descriptive Set Theory Seminar, Théorie de
EilenbergReiterman 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), 20122015
TACL 2015, Ischia, 2126
June 2015
Duality
in Computer Science, Dagstuhl seminar, 2530
October 2015
Logic, Algebra and Truth Degrees
2016, Phalaborwa, South Africa, 2830 June 2016
LICS 2016,
New York City, NEW York, 59 July 2016
Logic
Colloquium, Berkeley, November 4, 2016
Logical
Structures in Computation, Simon’s Institute, UC Berkeley, 17 August – 16 December, 2016
37^{th} Linz Seminar
on Fuzzy Set Theory: Enriched category theory and related topics, Linz
Austria, February 710, 2017
Mathematics Colloquium, University College
Cork, February 16, 2017
Topology,
Algebra, and Categories in Logic 2017, Prague, June 2630, 2017
Logic Colloquium ’17,
Stockholm, August 1420, 2017
CSL
2017, Stockholm, August 2024, 2017
Logical
Structures in Computation Reunion Workshop, Simons Institute, Berkeley,
1114 December 2017
Journée
Niçoises : Logique catégorique, topos et dualités, Laboratoire J.A.
Dieudonné, Nice, 812 January 2018
Noncommutative structures 2018, Portorož, 2327 May
2018
SGSLPS Spring school, Bern, May 28 2018
International
Workshop on Topological Methods in Logic (Tolo VI), Tbilisi
, 26 July 2018
International conference on semigroups, Lisbon, July 1114,
2018
Computability in Europe 2018, Kiel, 30 July – 3 August 2018
AiML
2018, Bern, 2731 August 2018
Achim Jung Fest, 8 September 2018
Workshop on Algebra, Logic and Topology, Coimbra, 2729
September, 2018
Topological and categorical methods in algebra, with Carlos
Simpson, 2^{nd} trimester Master 2 course  6 ECTS (201819)
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 padique à la théorie des modèles des
algèbres de Heyting, et viceversa, rapporteur, Fall 2019, HDR, Luck Darniere, Université d’Angers.
Circularity in Syntax and Semantics (CISS 2019), invited speaker, 2022 November 2019
Logic
and Structure in Computer Science and Beyond (LSCSB), participant, December 913 2019, Lorentz
Center@Oort – Leiden
Symbolic reasoning and formal logics, with Carlos
Simpson, 2^{nd} trimester Master 2 course MathInfo UCA  6 ECTS
(201920)
99th Arbeitstagung
Allgemeine Algebra, invited speaker, 2123 February 2020, Siena
Resources and coresources workshop, 2527 March, Cambridge
15th Workshop on Coalgebraic Methods
in Computer Science (CMCS 2020), 2526 April, Dublin
47th International Colloquium on
Automata, Languages, and Programming (ICALP), PC member, 812 July 2020, Beijing
18th Relational and Algebraic
Methods in Computer Science (RAMICS), PC member, 811 April 2020, Palaiseau
19th
Relational and Algebraic Methods in Computer Science (RAMICS), coorganiser, 14 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 1620, 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), 1620 January, CIRM 2023

·
Pictures
of my kids (2009)
·
My
favourite mathematician (by the Wiskundemeisjes)