Mai Gehrke

Department of Mathematical Sciences

 

Phone: (575] 646-4218 

New Mexico State University

 

Fax: (575) 646-1064 

Las Cruces, NM 88003

 

mailto: mgehrke@nmsu.edu

Office Location: Science Hall Room 232 

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EDUCATION

Ph.D. in Mathematics, University of Houston, 1987.
M.S. in Mathematics, University of Houston, 1985.

Studenter Eksamen, Holte Gymnasium, 1982.

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PROFESSIONAL EXPERIENCE

4/05—5/05        Visiting Professor, Technical University of Denmark, Lyngby, Denmark.

9/04--4/05         Visiting Lektor, University of Copenhagen, Copenhagen, Denmark.

6/04—8/05        EPSRC Research Visitor, University of Oxford, Oxford, United Kingdom.

8/00--Present    Professor, New Mexico State University, Las Cruces,  New Mexico.
1/99--5/02          Part-time consulting, Physical Science Laboratory, Las Cruces,  New Mexico.
1/97--5/97         Visiting Professor, Vanderbilt University, Nashville, Tennessee.
8/96--12/96       Visiting Lektor, University of Copenhagen, Copenhagen, Denmark.
8/93 -- 5/00       Associate Professor, New Mexico State University, Las Cruces,  New Mexico.
8/90--5/93         Assistant Professor, New Mexico State University, Las Cruces,  New Mexico.
8/88--5/90         2-year position as Assistant Professor, Vanderbilt University, Nashville, Tennessee.
2/88--6/88         Assistante Associée, Université de Nice, Nice, France.
9/87--1/88         Assistante Associée, Université de Haute Alsace, Mulhouse, France.
1/83--7/87         Teaching Assistant, University of Houston, Houston, Texas.

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RESEARCH INTERESTS

Logic and its Applications, in particular, in databases, knowledge-based systems and computational logic
Universal Algebra, in particular, the theory of lattice-ordered algebraic structures
General Topology, in particular, applications in algebra and logic

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PUBLICATIONS

Mathematical Research Publications

 

  1. Canonical extensions of certain algebras with binary operations: an algebraic perspective on duality. with H. A. Priestley, submitted to Journal of Pure and Applied Algebra, July 2005.
  2. Profinite and canonical completions of Heyting algebras, with Guram Bezhanishvili, Ray Mines, and Patrick Morandi, submitted to Order, June 2005.
  3. Generalised Kripke semantics, manuscript invited for submission to the special issue '40 years of possible world semantics', Studia  Logica, submitted August 2005.
  4. Canonical extensions and relational completeness of  some substructural logics, with Michael Dunn and Alessandra Palmigiano, accepted for publication by Journal of Symbolic Logic, March 2004.
  5. MacNeille completions and canonical extensions, with John Harding and Yde Venema, in press Transactions of the American Mathematical  Society, to appear in 2006.
  6. A Sahlqvist Theorem for distributive modal logics, with Hideo Nagahashi and Yde Venema, Annals of Pure and Applied Logic 131, Issues 1-3, 65-102, January 2005.
  7. Completeness of S4 with respect to the real line: revisited, with Guram Bezhanishvili, Annals of Pure and Applied Logic 131, Issues 1-3, 287-301, January 2005.
  8. Varieties of algebras in fuzzy set theory, with  G. Bezhanisvili, J. Harding, C. Walker,and E. Walker, chapter in Triangular norms and related operations: Theory and Applications, Physica Verlag (2004).
  9. Varieties generated by t-norms, with C. Walker and E. Walker, Soft Computing 8, no. 4 (2004), 264-267.
  10. Bounded Distributive Lattice Expansions, with B. Jónsson,  Mathematica Scandinavica, 94 (2004), 13-45.
  11. Euclidean hierarchy in modal logic, with Guram Bezhanishvili and Johan van Benthem, Studia Logica 75, 327--344, 2003.
  12. Fuzzy Logics Arising from Strict De Morgan Systems, with C. Walker and E. Walker, Topological and Algebraic Structures in Fuzzy Sets, A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, S. Rodabaugh and E. P. Klement, Eds., Kluwer, Dordrecht, (2003) Chapter 9, 257-276.
  13. Normal forms and truth tables for fuzzy logics, with C. Walker and E. Walker, Fuzzy Sets and Systems: Special Focus Issue, volume 138, number 1 (2003), pp 25-51.
  14. Non-canonicity of MV-algebras, with H. Priestley, Houston Journal of Mathematics 28, No. 3, 449-455, 2002.
  15. Bounded Lattice Expansions, with John Harding, Journal of Algebra, 239(2001), 345-371.
  16. Monotone Distributive Lattice Expansions, with B. Jonsson,  Math. Japonica  52, No.2 (2000), 197-213.
  17. Algebraic aspects of Fuzzy sets and Fuzzy logic, with C. Walker and E. Walker, Proceedings of the First International Workshop on Current Trends and Developments in Fuzzy Logic, B. K. Papadopoulos and A. Syropoulos, Eds., Thessaloniki, Greece 1999,  101-170.
  18. Averaging Operators on the Unit Interval, with C. Walker and E. Walker, International Journal of Intelligent Systems 14, no. 9 (1999),  883-898.
  19. A Note on Negations and Nilpotent t-Norms, with C. Walker and E. Walker, International Journal of Approximate Reasoning, 21 (1999),  137-155.
  20. Propositional Fuzzy Logics: Decidable for Some (Algebraic) Operators, Undecidable for More Complicated Ones, with B. Bouchon-Meunier, and V. Kreinovich, Journal of Intelligent Systems 14, no. 9 (1999), 935-947.
  21. A Mathematical Setting for Fuzzy Propositional Logic, with C. Walker, and E. Walker, The International Journal of Uncertainty, Fuzziness, and Knowledge-based reasoning 5, no. 3 (1997), 223-238.
  22. deMorgan Systems on the Unit Interval, with C. Walker and E. Walker, Journal for Intelligent Systems 11 (1996), 733-750.
  23. Some Comments on Interval Valued Fuzzy Sets, with C. Walker and E. Walker, Journal for Intelligent Systems 11(1996), 751-759.
  24. Stone Algebra Extensions with Bounded Dense Sets, with C. Walker and E. Walker, Algebra Universalis 37 (1997), 1-23.
  25. Iterated Conditionals and Symmetric Stone Algebras, with Walker, E., Discrete Mathematics, 48(1996), 49-63.
  26. Bounded Distributive Lattices with Operators, with B. Jónsson, Math. Jap. 40, no. 2(1994), 207-215.
  27. GA Actions on , with Deveney, J.K., and Finston, D.R., Comm. in Algebra, 22(12), 4977-4988(1994).
  28. Uniquely Representable posets, Ann. N.Y. Acad. Sci. Vol. 728, 32-40(1994).
  29. Robinson Lattices and their Spectra, Algebra Universalis, 32(1994), 204-223.
  30. The Structure of Rough Sets, with Walker, E., Bull. Pol. Accad. Sci. Math.40(1992), 235-245.
  31. The Order Structure of Stone Spaces and the TD-Separation Axiom, Zeitschr.f.math.Logik und Grundl. d.Math., 37(1991), 5-15.
  32. Some Non-Standard Methods Applied to Distributive Lattice, with Kaiser, K., and Insall, M., Zeitschr. f.math.Logik und Grundl.d.Math., 36(1990), 123-131.
  33. La Dualité de Stone d'un Point de Vue Non Standard, Série du Séminaire Non Standard de Paris VII, 87/4 (1987), 1-8.
  34. On the Maximality of Some Conormal Extensions of a Lattice, with Kaiser, K., Zeitschr.f.math.Logik und Grund. d.Math., 33 (1987), 13-18.

 

Educational Research Publications

  1. Logik som anvendt matematik, Matilde (Magazine of the Danish Mathematical Association), nr. 13, June 2002.
  2. Legitimissering af Infinitessimalerne på den Reele Linie, expository article on Non-Standard Analysis in Famø s, Student magazine of the Mathematics Institute at the University of Copenhagen, December 1996.
  3. Towards Active Processes for Teaching and Learning, with David Pengelley, polemic on calculus reform requested by the editors of the national committee on Calculus Reform And the First Two Years(CRAFTY), to be published in the CRAFTY volume planned for publication by January 1996.
  4. Mathematics Courses using Themes, with J. Alvarez, D. Kurtz, P. Morandi, and R. Staffeldt, submitted to the Mathematical Association of America in May of 1995.
  5. Calculus Instruction at New Mexico State through Weekly Themes and Cooperative Learning, with Alvarez, J., Finston, D.R., and Morandi, P., PRIMUS, 1 vol. III (1993), 83-98.

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SOME RECENT TALKS AND WORKSHOPS

Algebraic methods in computer science logic, Colloquium, Department of Mathematical Sciences, New Mexico State University, September 2005.

 

New developments in the theory of canonical extensions: a categorical perspective, Department of Pure Mathematics and Mathematical Statistics Category Theory Seminar, Cambridge University. August 2005.

 

Resource sensitive frames, The Oxford Advanced Seminar on Informatic Structures, Computing Laboratory, Oxford University, July 2005.

 

Generalized Kripke frames, Algebraic and Topological Methods in Non-Classical Logics II, Barcelona, June 2005.

 

Relational semantics for substructural logics II, Seminar of the Logic Group, Department of Philosophy and Theory of Science, RUC, Roskilde, May 2005.

 

Relational semantics for logics of resource sensitive computation, Department of Computer Science and Engineering Seminar, Informatics and Mathematical Modelling, DTU, Lyngby, May 2005.

 

Relational semantics for substructural logics I, Seminar of the Logic

Group, Department of Philosophy and Theory of Science, RUC, Roskilde, April 2005.

 

Resource sensitive frames, Amsterdam Workshop on Modal Logic, Model Theory and (Co)Algebras, February, 2005.

 

Canonical extensions of partially ordered algebras, Colloquium of the Institute for Mathematics, Denmark's Technical University, November 2004.

 

Canonical extensions of partially ordered algebras, 999th AMS Meeting, Southeastern Section, Vanderbilt University, October 16-17, 2004.

 

Canonical extensions and discrete duals of partially ordered algebras, London Logic Forum Seminar Series, October 2004.

 

Relational duals of monotone maps on lattices, Algebra Seminar, St. Anne's College, University of Oxford, Oxford, July 2004.

 

Canonical extensions: Recent Results, plenary workshop lecture in Duality as a unifying framework, 19th Summer Topology Conference, Cape Town, South Africa, July 2004.

 

Canonical extensions of partially ordered algebras, E. Romanovska's seminar, Polytechnic University, Warsaw, Poland, May 2004.

 

Duality for double quasi-operator algebras, Special Session on Universal Algebra and Lattices, Combined Central and Western Sectional Meeting of the AMS, Boulder, Colorado, October, 2003.

 

Canonical Extensions and their relationship to topological duality, and relational semantics, plenary talk at the 2003 International Conference on Algebraic and Topological Methods in Non-Classical Logics, Tbilisi, Republic of Georgia, July 2003.

 

Canonical Extensions and their Relationship to Topological Duality, and Relational Semantics,  Analysis of Informatics Phenomena Seminar, Oxford University, June 6, 2003.

 

Canonicity, Duality, and Correspondence, plenary talk at Lattices, Universal Algebra and Applications, Lisbon, Portugal, May 2003.

 

Topological Aspects of the Theory of Canonical Extensions, Analytical Topology in Mathematics and Computer Science Seminar,

Oxford University, England, May 26, 2003.

 

Canonical Extensions and their Relationship to Topological Duality, and Relational Semantics, Interdisciplinary Logic Seminar at Indiana University, Bloomington, USA, March 2003.

 

Canonical Extensions and their Relationship to Topological Duality, and Kripke Semantics,  Algebra seminar at Vanderbilt University, Nashville,

USA, March 2003.

 

Canonical Extensions, Topological duality, and Kripke semantics, Interdsciplinary logic seminar at MacMaster University, Hamilton, Canada, April 2002.

 

Canonicity and duality, Seminar, Max Planks Institute for Informatics, Saarbrucken, Germany, June 2001.

 

Algebraic Tools for Modal Logic, One week workshop with Yde Venema, 13th European Summer School in Logic Language and Information (ESSLLI XIII), 13-24 August 2001, Helsinki, Finland.

Applications of modal logic in algebra, Book Launch for 'Modal Logic' by Patrick Blackburn, Maarten de Rijke and Yde Venema, University of Amsterdam, 4 July 2001.

The interplay of modal logic and duality theory for lattice ordered algebras, Colloquium, University of Lisbon, July 2001.

Canonical Extensions of Bounded Distributive Lattice Expansions, Tarski Centenary Conference, May 28-June 1, 2001, Warsaw, Poland.

Canonical Extensions of Bounded Distributive Lattice Expansions, Colloquium, Washington State University, April 2001.

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OTHER TALKS AND WORKSHOPS

Anselms Gudsbevis, Dansk Forskning i Matematikkens Historie og Filosofi IV, Conference organised by Netværk i Matematikkens Historie og Filosofi, November, 2004.

 

An Algebraic Perspective on Fuzzy Logic, Guest lectures, Department of Software and Media Technology, Aalborg University, September 2004.

 

Logik, Tro, Viden, Interdisciplinary seminar series (3 x 2 hrs.) for the special focus area: Religion in the 21. century, University of Copenhagen, September 2004.

 

Shaping a career in Mathematics, Panelist at AWM workshop panel discussion, Baltimore, Maryland, January 2003.

 

Helping Students Become Active Learners of Mathematics,  NSF Chautauqua three day workshop, with D. Pengelley, Austin, Texas, April 1996.

Helping Students Become Active Learners of Mathematics, NSF Chautauqua three day workshop, with D. Pengelley, Austin, Texas, March 1995.

Video of my Math 191 class and an interview, Video Conference on Calculus Renewal, October 1993.

Student Projects at New Mexico State University and their Recent Migration into Classroom Activities, two hour Mathematicians and Education Reform (MER)\ workshop for Calculus Reform: Issues, Policies and Programs, Bowdoin College, Brunswick, Maine, July 1992.

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GRADUATE STUDENTS

Candida Palma,  Ph. D. student co-advised with Raquel Santos, University of Lisbon, 2002-2005. Dissertation defense, June 2005.

Thesis on Semi De Morgan Algebras.

 

Hideo Nagahashi, Ph. D. student, New Mexico State University, Fall 1995- Fall 2001. Dissertation defense, November 2001.

Alex Pogel, Ph.D. student, Spring 1995- Summer 1998. Dissertation Title: Stone Triples and Self-Duality.  Ph.D. completed Summer 1998.

mgehrke@nmsu.edu


October 2005.