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New Mexico State University
College of Arts and Sciences
Department of Mathematical Sciences

Guram Bezhanishvili

Address
Department of Mathematical Sciences
New Mexico State University
Box 30001 Dept 3MB
Las Cruces, NM 88003-0001
USA
Tel: 1-575-646-2837
Fax: 1-575-646-1064
e-mail: gbezhani@nmsu.edu

Birth Date: December 6, 1970.
Birth Place: Tbilisi, Georgia.
Citizenship: Georgian
Residence Status: Permanent resident

Education

  • March 1998: Ph.D. from Tokyo Institute of Technology. Thesis: An algebraic approach to intuitionistic modal logics over MIPC. Advisors: Professor Leo Esakia and Professor Hiroakira Ono.
  • June 1992: M.S. from Tbilisi State University. Thesis: On the variety of monadic Heyting algebras (in Georgian). Advisor: Professor Leo Esakia.

Employment

  • 2001–present: Assistant Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.
  • 2000–2001: Visiting Assistant Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.
  • 2000: Postdoctoral Fellow, Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands.
  • 1998-2000: Assistant Professor, Tbilisi State University, Department of Mechanics and Mathematics, Tbilisi, Georgia.
  • 1998-2000: Research Associate, Institute of Cybernetics, Georgian Academy of Sciences, Tbilisi, Georgia.

    Teaching Experience

    I have been in charge of several courses at New Mexico State University and at Tbilisi State University. In particular, I have been giving graduate courses in:

    • Universal Algebra (Math 585), Fall 2003, New Mexico State University.
    • Axiomatic Set Theory (Math 557), Spring 2001, New Mexico State University.
    • Mathematical Logic (Math 454/504), Fall 2005, Fall 2004, New MexicoState University.
    • Foundations of Geometry (Math 452/502), Spring 2002, New Mexico StateUniversity.
    • Modern Algebra II (Math 482/526), Spring 2003, New Mexico State University.
    • Modern Algebra I (Math 481/525), Fall 2002, New Mexico State University.
    • Logic and Set Theory, Fall 1999, Tbilisi State University.
    • Lattice Theory and Categorical Logic, Spring 1999, Tbilisi State University.

      I have also been giving undergraduate courses in:

    • Vector Spaces and Matrix Algebra (Math 480), Spring 2005, Spring 2004, New Mexico State University.
    • Introduction to Linear Algebra (Math 280), Fall 2005, New Mexico State University.
    • Introduction to Modern Algebra (Math 331), Fall 2000, New Mexico State University.
    • Discrete Mathematics (Math 330), Fall 2001, New Mexico State University.
    • Introduction to Finite Mathematics (Math 279), Spring 2005, Spring 2001, Fall 2000, New Mexico State University.
    • Calculus and Analytic Geometry III (Math 291), Fall 2003, New Mexico State University.
    • Calculus and Analytic Geometry II (Math 192), Spring 2003, Fall 2002, New Mexico State University.
    • Mathematics Appreciation (Math 210), Spring 2004, Spring 2002, Fall 2001, New Mexico State University.

    Grants/Awards Received

    • 2003-2005: NSF Grant: “Teaching Discrete Mathematics via Original Historical Sources”.
    • 2003-2004: GRDF/CRDF Georgian-U.S. Bilateral Grant: “Applications of Topology and Universal Algebra to Modal Logic”
    • 2001: Grant of MRC (Mathematical Research Center, Barcelona, Spain) for joint collaboration with Professor Ramon Jansana of University of Barcelona.
    • 1997-1999: Fellowship of the President of Georgia.
    • 1997-1999: Grant number 1.25 of the Georgian Academy of Sciences.
    • 1996-1998: Fellowship of the Japanese Government.
    • 1995-1996: George Soros Fellowship..

    Service and Professional Duties

    Editorial:

  • Associate Editor of Studia Logica.

    Reviews:
  • Reviewer for Mathematical Reviews
  • Reviewer for Bulletin of Symbolic Logic

    Journal Refereeing:
  • Referee for Journal of Symbolic Logic
  • Referee for Annals of Pure and Applied Logic.
  • Referee for Studia Logica.
  • Referee for Order.
  • Referee for IGPL (Logic Journal of the Interest Group in Pure and Applied Logics).
  • Referee for Logical Methods in Computer Science.
  • Referee for Fundamenta Informaticae.
  • Referee for IJMMS (International Journal of Mathematics and Mathematical Sciences).

    Handbook Refereeing

    • Second reader of the chapter "Locales and Toposes as Spaces" by Steven Vickers of The Open Univerisity, United Kingdom, for the handbook of The Logic of Space, M. Aiello, J. van Benthem, I. Pratt-Hartman, editors. Kluwer, 2005. In Preparation.

    Conference Refereeing:

  • Referee for the series of Advances in Modal Logic.
  • Referee for ESSLLI’05 (European Summer School in Logic, Language and Information).
  • Referee for the 6th International Tbilisi Symposium on Language, Logic and Computation, 2005.
  • Referee for the 5th International Tbilisi Symposium on Language, Logic and Computation, 2003.
  • Referee for the 4th International Tbilisi Symposium on Language, Logic and Computation, 2001.
  • Referee for the Computer Science Logic 2000 Conference.

    Conference Organization:

  • Program committee member for the Advances in Modal Logic 2006 (AiML '06)
  • Co-organizer and program committee co-chair of the International Conference on Algebraic and Topological Methods in Non-Classical Logics, Tbilisi, Georgia, July 7–11, 2003 (The other chair: Professor Patrick J. Morandi).
  • Co-organizer of the workshop on Reasoning About Space as part of the Logic & Computation Section of the 2nd North American Summer School in Logic, Language and Information (NASSLLI '03), Bloomington, Indiana, June 17-21, 2003. (The other organizers: Dr. Marco Aiello and Mr. Darko Sarenac.)
  • Program committee member and referee for Fifth International Tbilisi Symposium on Language, Logic, and Computation, 2003.
  • Program committee member and referee for Fourth International Tbilisi Symposium on Language, Logic, and Computation, 2001.

    Student Advising:

  • Advisor of an NMSU Ph.D.student Joel Lucero-Bryan, 2005-present.
  • Advisor of an NMSU Master’s student Joel Lucero-Bryan. Thesis: “An Extension of the Blok-Esakia Theorem”, NMSU, 2005.
  • Co-advisor of an ILLC Master’s student David Gabelaia. Thesis: “Diamonds of Space”, University of Amsterdam, 2001.(The other advisor: Professor Yde Venema).
  • Co-advisor of an ILLC Master’s student Nick Arevadze. Thesis: “Finite Projective Formulas”, University of Amsterdam, 2001. (The other advisor: Professor Dick de Jongh)
  • Co-advisor of a JAIST Master’s student Yasusi Hasimoto. Thesis: “A Semantical Study of Intuitionistic Modal Logics”, Japan Advanced Institute of Science and Technology, 1998. (The other advisor: Professor Hiroakira Ono.)
  • External Member of the Ph.D. Oral Exam for Darco Sarenac, Stanford University, Spring 2005.
  • Chairof Master's Oral Exam for Joel Lucero Bryan, NMSU, Spring 2005.
  • Member of Ph.D. Qualifying Exam for Jea-Pil Cho, NMSU, Spring 2003.
  • Member of Ph.D. Oral Exa for Hideo Nagahashi, NMSU, Spring 2002.

    Other Duties:

  • Co-organizer of weekly Lattice Theory Seminar, NMSU, 2003–present. (The oter organizers: Professors Mai Gehrke and John Harding)
  • Organizer of weekly Algebra Seminar, NMSU, Spring 2003.
  • Course coordinator for Calculus and Analytic Geometry II (Math 192), NMSU, Spring 2003.
  • Member of Graduate Faculty, NMSU, 2002–present.
  • Member of Computer Committee, NMSU, 2005-present.
  • Member of Liaison Committee, NMSU, 2005-present.
  • Member of Graduate Studies Committee, NMSU, 2004–2005.
  • Member of Undergraduate Studies Committee, NMSU, 2001–2004.

    Invited Talks

  • November 2005: Stone-like dualties and their applications to non-classical logics, Indiana Univerisity, Bloomington, Indiana.
  • June 2005: Subframe logics, nuclei, and pointless topologies, An International Conference on Algebraic and Topological Methods in Non-Classical Logics II,Barcelona, Spain.
  • December 2004: MacNeille completions in modal logic, University of Amsterdam, The Netherlands.
  • December 2004: MacNeille completions of modal algebras, Bonn University, Germany.
  • November 2004: Modal logics of space, Workshop on Handbook of Spatial Logics, Freiburg University, Freiburg, Germany.
  • June 2003: Scattered and hereditarily irresolvable spaces, The 2nd North American Summer School in Logic, Language, and Information, Indiana University, Bloomington, Indiana.
  • June 2002: Canonical, topo-canonical, and MacNeille completions of Heyting algebras, Salerno University, Italy.
  • June 2002: Topo-canonicity and topo-definability, Milan University, Italy.
  • June 2002: MacNeille completions of Heyting algebras, Milan University, Italy.
  • June 2001: Topological perspective on modal logic, Barcelona University, Spain.
  • May 2001: Modal logic from topological point of view, Stanford University, Palo Alto, California.
  • February 2000: Projectivity and extendability, Utrecht University, The Netherlands.
  • January 2000: Finite variable fragments of the intuitionistic predicate logic and their relation to the provability logic, University of Amsterdam, The Netherlands.
  • October 1997: An algebraic approach to intuitionistic modal logics over MIPC, Japan Advanced Institute of Science and Technology, Japan.
  • May 1997: Locally finite varieties, Japan Advanced Institute of Science and Technology, Japan.
  • November 1996: Intuitionistic modal logics, Japan Advanced Institute of Science and Technology, Japan.

Contributed Talks

  • August 2004: MacNeille completions of Heyting algebras, Algebras, Lattices,Varieties - A Conference in Honor of Walter Taylor, University of Colorado,Boulder, Colorado.
  • June 2002: Functional monadic Heyting algebras, Annual Meeting of Association for Symbolic Logic, Las Vegas, Nevada.
  • July 2000: Locally finite varieties, The 6th Barcelona Logic Meeting, Barcelona, Spain.
  • September 1999: Q-Heyting algebras as reducts of monadic , The Tbilisi International Symposium on Language, Logic and Computation, Chakvi, Georgia
  • October 1998: Locally tabular extensions of MIPC, Advances in Modal Logic’ 98, Uppsala, Sweden.
  • November 1997: Monadic version of Glivenko’s theorem, Annual Meeting of Mathematical Logic, Shizuoka, Japan.
  • June 1997: Logics over MIPC, Sequent Calculi and Kripke Semantics for Non-Classical Logics, Kyoto, Japan.
  • March 1997: Modal intuitionistic logics and superintuitionistic predicate logics: correspondence theory, New Aspects of Non-Classical Logics and Their Kripke Semantics, Kyoto, Japan.
  • December 1996: A partial solution of some problems of H. Ono, FOLLI Workshop on Logics for Linguistics, Philosophy and Cognitive Science, Chiba, Japan.
  • November 1996: Splitting monadic Heyting algebras, Annual Meeting of Mathematical Logic, Kanazawa, Japan.
  • October 1995: Some results in monadic Heyting algebras, The Tbilisi International Symposium on Logic, Language and Computation, Gudauri, Georgia.
  • August 1995: Monoquantified extentions of linear intermediate propositional logics, Xth International Congress of Logic, Methodology and Philosophy of Science, Florence, Italy.

Math Education Talk

  • April 2005 Introducing primary historical sources in discrete mathematics and computer science curriculum (Joint presentation with Karen Villaverde and Joel Lucero-Bryan), Annual Meeting of the Southwestern Section of Mathematics Association of America, El Paso, Texas.

Publications

Journal Publications

1. J. van Benthem, G. Bezhanishvili, B. ten Cate, D. Sarenac. Multimodal logics of products of topologies, Studia Logica, 2005, to appear.
2. G. Bezhanishvili, R. Grigolia. Locally finite varieties of Heyting algebras, Algebra Universalis, 2005, to appear.
3. G. Bezhanishvili, L. Esakia, D. Gabelaia. Some results on modal axiomatization and definability for topological spaces, Studia Logica, 81 (2005), pp. 325-356.
4. G. Bezhanishvili, M. Gehrke. Completeness of S4 with respect to the real line: revisited, Annals of Pure and Applied Logic, 131 (2005), pp. 287-301.
5. J. Harding, G. Bezhanishvili. MacNeille completions of Heyting algebras, Houston Journal of Mathematics, 30 (2004), pp. 937-952.
6. M. Aiello, J. van Benthem, G. Bezhanishvili. Reasoning about space: the modal way, Journal of Logic and Computation, 13 (2003), pp. 889-920.
7. J. van Benthem, G. Bezhanishvili, M. Gehrke. Euclidean hierarchy in modal logic, Studia Logica, 75 (2003), pp. 327-345.
8. G. Bezhanishvili, R. Mines, P. Morandi. Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces, Topology and Its Applications, 132 (2003), pp. 291-306.
9. G. Bezhanishvili, J. Harding. Functional monadic Heyting algebras, Algebra Universalis, 48 (2002), pp. 1-10.
10. G. Bezhanishvili, R. Mines, P. Morandi. The Priestley separation axiom for scattered spaces, Order, 19 (2002), pp.
1-10.
11. G. Bezhanishvili. Locally finite varieties, Algebra Universalis, 46 (2001), pp. 531-548.
12. G. Bezhanishvili. Glivenko type theorems for intuitionistic modal logics, Studia Logica, 67 (2001), pp. 89-109.
13. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part III, Studia Logica, 64 (2000), pp. 215-256.
14. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part II: Duality theory, Studia Logica, 62 (1999), pp. 21-48.
15. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part I, Studia Logica, 61 (1998), pp. 367-402.

Handbook Chapter:

16. J. van Benthem, G. Bezhanishvili. Modal logics of space, Handbook of The Logic of Space, M. Aiello, J. van Benthem, I. Pratt-Hartman, editors. Kluwer, 2005. In Preparation.

Invited Chapters:

17. G. Bezhanishvili, M. Gehrke, J. Harding, C. Walker, E. Walker. Varieties of algebras in fuzzy set theory, Logical, Algebraic, and Probabilistic Aspects of Triangular Norms, E. Klement and R. Mesiar, editors. Elsevier, 2005, pp. 321-344.
18. G. Bezhanishvili, R. Grigolia. Locally tabular extensions of MIPC, Advances in Modal Logic, Volume 2, M. Zakharyaschev, K. Segerberg, M. de Rijke, and H. Wansing, editors. Lecture Notes. Stanford, CA. CSLI Publications, 2001, pp. 101-120.
19. G. Bezhanishvili. Some results in monadic Heyting algebras, The Tbilisi Symposium on Logic, Language and Computation. Selected papers. October 1995, Gudauri, Georgia. J. Ginzburg, Z. Khasidashvili, C. Vogel, J.-J. Levy, and E. Valduvi (editors), 1997, CSLI, Stanford, pp. 251-261.

Conference Proceedings:

20. G. Bezhanishvili, M. Zakharyaschev. Logics over MIPC, Proceedings of Sequent Calculus and Kripke Semantics for Non-Classical Logics, RIMS Kokyuroku 1021, Kyoto University, 1997, pp. 86-95.
21. G. Bezhanishvili. Modal intuitionistic logics and superintuitionistic predicate logics: correspondence theory, Proceedings of New Aspects of Non-Classical Logics and Their Kripke Semantics, RIMS Kokyuroku 1010, Kyoto University, 1997, pp. 1-6.

Conference Abstracts:

22. G. Bezhanishvili. Q-Heyting algebras as reducts of monadic Heyting algebras, Abstracts of the 3rd International Tbilisi Symposium on Language, Logic and Computation, Chakvi, Georgia, 1999, pp. 6-7.
23. G. Bezhanishvili. Monadic version of Glivenko’s theorem, Extended Abstracts of the 31st MLG Meeting at Miho, Shimizu, Japan 1997, pp. 42-44.
24. G. Bezhanishvili. A partial solution of some problems of H. Ono, FOLLI Workshop on Logics for Linguistics, Philosophy and Cognitive Science, Chiba, Japan, 1996, Volume of Abstracts, p. 10.
25. G. Bezhanishvili. The lattice of quantified extentions of the three-valued intermediate propositional logic, The 10th International Congress of Logic, Methodology and Philosophy of Science, Italy, Florence, Published by Comune di Cesena, 1995, Volume of Abstracts, p. 196.
26. G. Bezhanishvili. Monoquantified extentions of linear intermediate propositional logics, Logic, Methodology and Philosophy of Science, Moscow-Obninsk, RGNF Press, 1995, Vol. 2, pp. 3-6 (In Russian).

Other Publications:

27. G. Bezhanishvili, L. Esakia, D. Gabelaia. Modal logics of submaximal and nodec spaces, Collection of Essays Dedicated to Dick de Jongh on Occasion of His 65th Birthday, J. van Benthem, F. Veltman, A. Troelstra, A. Visser, editors. 2004, pp.
1-13.
28. G. Bezhanishvili, Review of the book by M. Kracht Tools and techniques in modal logic, Bulletin of Symbolic Logic 7 (2001), pp. 278-279.
29. G. Bezhanishvili, R. Grigolia. Subalgebras and homomorphic images of the Rieger-Nishimura lattice, Proceedings of the Institute of Cybernetics of the Georgian Academy of Sciences, Vol. 1, N1, 2000, pp. 9-16.
30. G. Bezhanishvili. An Algebraic Approach to Intuitionistic Modal Logics Over MIPC, Ph.D. Thesis (167 pages), Tokyo Institute of Technology, 1998.
31. G. Bezhanishvili. On the Variety of Monadic Heyting Algebras (In Georgian), Master’s Thesis (24 pages), Tbilisi State University, 1992.

Technical Reports
32. G. Bezhanishvili, M. Gehrke. A new proof of completeness of S4 with respect to the real line, ILLC Prepublication Series, Technical Report PP-2002-06, University of Amsterdam, 2002.
33. G. Bezhanishvili, R. Grigolia. Pro-finite and ind-finite Heyting algebras, Prepublication Series in Logic and Foundations of Mathematics, Report ] L-FM-00-03, Department of Logic, Institute of Cybernetics, Georgian Academy of Sciences, 2000.
34. G. Bezhanishvili. Splitting monadic Heyting algebras, Report ] IS-RR-97-0044F, JAIST, 1997.

Submitted Papers
35. G. Bezhanishvili and S. Ghilardi. An algebraic approach to subframe logics. Part I, 2005.
36. G. Bezhanishvili, M. Gehrke, R. Mines, P. Morandi. Profinite and canonical completions of Heyting algebras, 2005.
37. J. Harding and G. Bezhanishvili. MacNeille completions of modal algebras, 2005.