CV

Education

  • 1998: PhD from Tokyo Institute of Technology. Thesis: An algebraic approach to intuitionistic modal logics over MIPCAdvisors: Leo Esakia and Hiroakira Ono.
  • 1992: MS from Tbilisi State University. Thesis: On the variety of monadic Heyting algebras (in Georgian). Advisor: Leo Esakia.

Employment

  • 2011-present: Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.
  • 2006-2011: Associate Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.
  • 2001-2006: Assistant Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.
  • 2000-2001: Visiting 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.

Grants, Fellowships, and Scholarships

  • 2018: NMSU College of Arts and Sciences Travel Award.
  • 2017-2020: GNSF Grant “Propositional calculi for topology and geometry” (with David Gabelaia, Nick Bezhanishvili, Mamuka Jibladze, and Levan Uridia).
  • 2016-2019: European Union Grant “SYSMICS: Syntax meet semantics: methods, interactions, and connections in substructural logics.” Involved more than 50 researchers in 23 universities worldwide in 13 different countries.
  • 2012-2015: GNSF Grant “Topological Semantics of Modal Logic” (with David Gabelaia, Nick Bezhanishvili, and Mamuka Jibladze).
  • 2012: NMSU College of Arts and Sciences Travel Grant.
  • 2009-2011: GNSF Grant “Duality Theory and its Applications to the Semantics of Non-Classical Logics” (with Leo Esakia, David Gabelaia, Nick Bezhanishvili, Mamuka Jibladze, and Dimitri Pataraia).
  • 2008-2011: NSF Grant “Learning Discrete Mathematics and Computer Science via Primary Historical Sources” (with Jerry Lodder, David Pengelley, Desh Ranjan, Hing Leung, Inna Pivkina, and Janet Barnett).
  • 2006-2008: GNSF Grant “Semantics of Intuitionistic Modal Logic: Algebraic and Topological Models” (with Leo Esakia, David Gabelaia, Nick Bezhanishvili, Mamuka Jibladze, and Dimitri Pataraia).
  • 2006-2007: NMSU ISSS Cluster Award “Learning Discrete Mathematics via Historical Sources” (with Jerry Lodder, David Pengelley, Desh Ranjan, Hing Leung, and Inna Pivkina).
  • 2003-2005: NSF Grant “Teaching Discrete Mathematics via Original Historical Sources” (with Jerry Lodder, David Pengelley, Desh Ranjan, and Hing Leung).
  • 2003-2004: GRDF/CRDF Georgian-U.S. Bilateral Grant “Applications of Topology and Universal Algebra to Modal Logic” (with Mai Gehrke, John Harding, Pat Morandi, Leo Esakia, Mamuka JIbladze, and Dimitri Pataraia).     
  • 2001: Grant of MRC (Mathematical Research Center, Barcelona, Spain) for joint collaboration with Ramon Jansana of University of Barcelona.
  • 1997-1999: Fellowship of the President of Georgia.
  • 1996-1998: Fellowship of the Japanese Government.
  • 1995-1996: George Soros Scholarship.
  • 1992-1995: Scholarship of Tbilisi State University for Ph.D. students.
  • 1991-1992: Scholarship of Tbilisi State University for Master’s students.
  • 1989-1991: Scholarship of Tbilisi State University for promising undergraduate students.

Editorial Boards

Refereeing

  • Reviewed for Mathematical Reviews, Zentralblatt, Bulletin of Symbolic Logic.
  • Refereed for over 30 international journals in my area of expertise.
  • Referee for the conference series AiML (Advances in Modal Logic).
  • Referee for the conference series TACL (Topology, Algebra, and Categories in Logic).
  • Referee for the conference series TbiLLC (International Tbilisi Symposium on Language, Logic, and Computation).
  • Refereed for many other conferences, workshops, and summer schools.

Steering Committees

  • AiML (Advances in Modal Logic)
  • BLAST (Boolean Algebras, Lattices, Algebraic Logic, Quantum Logic, Universal Algebra, Set Theory, Set-Theoretic Topology, and Point-Free Topology).
  • TACL (Topology, Algebra, and Categories in Logics)
  • TbiLLC (International Tbilisi Symposium on Language, Logic, and Computation)
  • ToLo (Topological Methods in Logic)

Organized the following conferences  

  • ToLo 2018, Tbilisi, Georgia, July 2-6, 2018.
  • ToLo 2016, Tbilisi, Georgia, June 13-17, 2016.
  • BLAST 2014, Las Cruces, New Mexico, January 5-9, 2015.
  • ToLo 2014, Tbilisi, Georgia, June 23-27, 2014.
  • ToLo 2012, Tbilisi, Georgia, July 24-27, 2012.
  • Workshop on Authorship of Student Projects Based on Primary Historical Sources for Courses in Mathematics or Computer Science, New Mexico State University, Las Cruces, New Mexico, April 16-17, 2012.
  • ToLo 2010, Georgian American University, Tbilisi, Georgia, June 810, 2010.
  • BLAST 2009, Las Cruces, New Mexico, August 1014, 2009.
  • ToLo 2008, Georgian American University, Tbilisi, Georgia, June 3-5, 2008.
  • 1st Joint NMSU/UTEP Workshop on Mathematics and Computer Science, New Mexico State University, Las Cruces, New Mexico, April 14, 2007.
  • TACL 2003, Tbilisi, Georgia, July 7-11, 2003.      
  • The workshop Reasoning About Space in Logic & Computation Section of NASSLLI’03 (the 2nd North American Summer School in Logic, Language, and Information), Bloomington, Indiana, June 17-21, 2003.

Chaired the PCs of the following conferences

  • AiML 2018, Bern, Switzerland, August 27-31, 2018.
  • TbiLLC 2011, Kutaisi, Georgia, September 2630, 2011.
  • TbiLLC 2009, Bakuriani, Georgia, September 2125, 2009.
  • TACL 2007, Oxford, England, August 5-9, 2007.

PC member of the following conferences

  • Annual International Tbilisi Summer Schools in Logic and Language, Tbilisi, Georgia.
  • AiML 2020, Helsinki, Finland, August 17-21, 2020.
  • TbiLLC 2019, Tbilisi, Georgia, September 16-20, 2019.
  • WoLLIC 2016, Puebla, Mexico, August 16-19, 2016.
  • TACL 2013, Vanderbilt University, Nashville, Tennessee, July 28-August 1, 2013.
  • AiML 2012, Copenhagen, Denmark, August 2225, 2012.
  • Ordered Groups and Lattices in Algebraic Logic, Tbilisi, Georgia, September 2023, 2011.
  • TACL 2011, Marseilles, France, July 2530, 2011.
  • AiML 2010, Moscow, Russia, August 2427, 2010.
  • TACL 2009, Amsterdam, The Netherlands, July 711, 2009.
  • AiML 2008, Nancy, France, September 9-12, 2008.
  • The Student Session of ESSLLI 2008 (European Summer School in Logic, Language, and Computation 2008), Hamburg, Germany, August 4-15, 2008.
  • 2nd Joint NMSU/UTEP Workshop on Mathematics and Computer Science, University of Texas at El Paso, El Paso, Texas, November 17, 2007.
  • TbiLLC 2007, Tbilisi, Georgia, October 1?5, 2007.
  • AiML 2006, Queensland, Australia, September 25-28, 2006.
  • TbiLLC 2003, Tbilisi, Georgia, October 6-10, 2003.
  • TbiLLC 2001, Borjomi, Georgia, September 23-28, 2001.

Invited Talks

  • June 2018: Topological completeness above S4.3, The Workshop on Algebra and Duality in Non-Classical Logic, Amsterdam, The Netherlands.
  • May 2018: Modal logics arising from metric spaces, SEP 2018, Storrs, Connecticut.
  • August 2017: Jonsson’s contributions to the study of lattices of logics, BLAST 2017, Nashville, Tennessee.
  • October 2016: On the proof that compact Hausdorff Boolean algebras are powersets, AMS Sectional Meeting, 2016, Denver, Colorado.
  • August 2016: The modal logic of topology: New directions, AiML 2016, Budapest, Hungary.
  • May 2015: How far can the McKinsey-Tarski theorem be extended?, 4th Annual CSLI Workshop on Logic, Rationality, and Intelligent Interaction, Stanford University, California.
  • June 2012: An algebraic approach to Gelfand duality, Workshop on Duality Theory in Algebra, Logic and Computer Science, Oxford, England.
  • July 2011: Scientific legacy of Leo Esakia, TACL 2011, Marseille, France.
  • July 2009: Duality theory in logic, 24th Summer Conference on Topology and its Applications, Brno, Czech Republic.
  • June 2008: A new representation of distributive and implicative semilattices, ToLo 2008, Tbilisi, Georgia.
  • October 2007: Modal logic and topology, TbiLLC 2007, Tbilisi, Georgia.
  • March 2006: Completions and compactifications, The Amsterdam-London Workshop on Modal Logic, Amsterdam, The Netherlands.
  • June 2005: Subframe logics, nuclei, and pointless topologies, TACL 2005, Barcelona, Spain.
  • November 2004: Modal logics of space, Workshop on the 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.

Colloquium Talks

  • June 2018: How to extend de Vries duality to completely regular spaces, University of Amsterdam, The Netherlands.
  • March 2016: The algebra of topology: Tarski’s program 70 years later, University of California, Berkeley, California.
  • April 2015: What does ‘less than or equal’ really mean?, New Mexico State University, Las Cruces, New Mexico.
  • April 2012: Around Gelfand duality, University of Texas at El Paso, El Paso, Texas.
  • March 2009: Stone duality, Smirnov’s theorem, and compact Hausdorff spaces, Baruch College, City University of New York, New York.
  • November 2008: An algebraic approach to canonical formulas: Intuitionistic case, Indiana University, Bloomington, Indiana.
  • May 2008: Priestley order-compactifications and a generalization of Dwinger’s theorem, University of Amsterdam, Amsterdam, The Netherlands.
  • April 2008: Bitopological duality for distributive lattices and Heyting algebras, University of Amsterdam, Amsterdam, The Netherlands.
  • April 2008: Spatial logics over S4, University of Groningen, Groningen, The Netherlands.
  • December 2007: New results in topological completeness of modal and superintuitionistic logics, University of Leicester, Leicester, UK.
  • December 2007: Topological completeness in modal logic, City University of New York, New York.
  • November 2007: Topological completeness of modal and superintuitionistic logics, Cornell University, Ithaca, New York.
  • March 2006: Stone-like dualities in algebra, University of Houston, Houston, Texas.
  • November 2005: Stone-like dualities and their applications to non-classical logics, Indiana University, Bloomington, Indiana.
  • December 2004: MacNeille completions in modal logic, University of Amsterdam, The Netherlands. 
  • December 2004: MacNeille completions of modal algebras, Bonn University, Germany.
  • 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.
  • March 2001: Algebraic and topological approaches to super-intuitionistic logics, New Mexico State University, Las Cruces, New Mexico.
  • 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.

Conference Talks

  • June 2007: Priestley order-compactifications, Order, Algebra, Logics, Vanderbilt University, Nashville, Tennessee.
  • June 2007: The universal modality, the center of a Heyting algebra, and the Blok-Esakia theorem, Logical Foundations of Computer Science 2007, City University of New York, New York.
  • 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 Heyting algebras, TbiLLC 1999, Chakvi, Georgia.
  • October 1998: Locally tabular extensions of MIPC, AiML 1998, 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, TbiLLC 1995, 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 Joel Lucero-Bryan and Karen Villaverde), Annual Meeting of the Southwestern Section of Mathematics Association of America, El Paso, Texas.