Curriculum Vitae

 

Education

1.      1998: PhD from Tokyo Institute of Technology. Thesis: An algebraic approach to intuitionistic modal logics over MIPC. Advisors: Leo Esakia and Hiroakira Ono.

2.      1992: MS from Tbilisi State University. Thesis: On the variety of monadic Heyting algebras (in Georgian). Advisor: Leo Esakia.

 

Employment

1.       2011—present: Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.

2.       2006—2011: Associate Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.

3.       2001—2006: Assistant Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.

4.       2000—2001: Visiting Professor, New Mexico State University, Department of Mathematical Sciences, Las Cruces, New Mexico, USA.

5.       2000: Postdoctoral Fellow, Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands.

6.       1998—2000: Assistant Professor, Tbilisi State University, Department of Mechanics and Mathematics, Tbilisi, Georgia.

 

Teaching

Graduate Courses

1.       Point-Free Topology, Fall 2011, New Mexico State University.

2.       General Topology, Spring 2007, New Mexico State University.

3.       Lattice Theory, Spring 2011, Spring 2007, Spring 2006, New Mexico State University.

4.       Universal Algebra, Fall 2003, New Mexico State University.

5.       Modern Algebra II, Spring 2003, New Mexico State University.

6.       Modern Algebra I, Fall 2002, New Mexico State University.

7.       Foundations of Geometry, Spring 2002, New Mexico State University.

8.       Axiomatic Set Theory, Spring 2001, New Mexico State University.

9.       Mathematical Logic, Fall 2008, Fall 2006, Fall 2004, New Mexico State University.

10.   Gödel’s Incompleteness Theorems, Fall 2009, New Mexico State University.

11.   Logic and Set Theory: Fall 1999, Tbilisi State University.

12.   Lattice Theory and Categorical Logic: Spring 1999, Tbilisi State University.

Undergraduate Courses

1.       Vector Spaces and Matrix Algebra (Math 480), Spring 2009 (Distance Education Course), Spring 2005, Spring 2004, New Mexico State University.

2.       Introduction to Linear Algebra (Math 280), Fall 2005, New Mexico State University.

3.       Introduction to Modern Algebra (Math 331), Fall 2000, New Mexico State University.

4.       Introduction to Finite Mathematics (Math 279), Fall 2011, Spring 2011, Fall 2006, Spring 2005, Spring 2001, Fall 2000, New Mexico State University.

5.       Discrete Mathematics for Computer Science (Math/CS 278), Fall 2009, New Mexico State University.

6.       Discrete Mathematics (Math 330), Fall 2001, New Mexico State University.

7.       Ordinary Differential Equations (Math 392), Spring 2006, New Mexico State University.

8.       Calculus and Analytic Geometry III (Math 291), Fall 2003, New Mexico State University.

9.       Calculus and Analytic Geometry II (Math 192), Fall 2010, Spring 2003, Fall 2002, New Mexico State University.

10.   Calculus and Analytic Geometry I (Math 191), Fall 2005, New Mexico State University.

11.   Mathematics Appreciation (Math 210), Spring 2004, Spring 2002, Fall 2001, New Mexico State University.

Summer Schools

1.       Lattices and Topologies, European Summer School in Logic, Language, and Information 2008 (ESSLLI 2008), 1115 August 2008, Hamburg, Germany (jointly with Mamuka Jibladze).

2.       Lattices and Topologies, Third ViennaTbilisi Summer School in Logic and Language, 2728 September 2007, Tbilisi State University (jointly with Mamuka Jibladze).

 

Grants

1.       2012: NMSU College of Arts and Sciences Travel Grant.

2.       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).

3.       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).

4.       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).

5.       2006—2007: NMSU ISSS Cluster Award “Learning Discrete Mathematics via Historical Sources” (with Jerry Lodder, David Pengelley, Desh Ranjan, Hing Leung, and Inna Pivkina).

6.       2003—2005: NSF Grant “Teaching Discrete Mathematics via Original Historical Sources” (with Jerry Lodder, David Pengelley, Desh Ranjan, and Hing Leung)

7.       2003—2004: GRDF/CRDF Georgian-U.S. Bilateral Grant “Applications of Topology and Universal Algebra to Modal Logic” (with Mai Gehrke, John Harding, Patrick J. Morandi, Leo Esakia, Mamuka Jibladze, and Dimitri Pataraia).

8.       2001: Grant of MRC (Mathematical Research Center, Barcelona, Spain) for joint collaboration with Ramon Jansana of University of Barcelona.

 

Editorial

1.       Associate editor of Studia Logica.

2.       Member of the editorial board of Tbilisi Mathematical Journal.

3.       Member of the editorial board of Journal of Language, Logic, and Computation.

 

Reviewer

1.       Mathematical Reviews.

2.      Zentralblatt.

3.       Bulletin of Symbolic Logic.

 

Referee

Refereed for over 20 international journals in my area of expertise.

Also refereed for about a dozen international conferences in mathematics and theoretical computer science.

 

Conference Organization

1.       Steering committee member of

a.       TACL (a conferences series on Topology, Algebra, and Categories in Logics).

b.       TbiLLC (International Tbilisi Symposium on Language, Logic, and Computation).

c.       BLAST (a conference series focusing on Boolean Algebras, Lattices, Algebraic Logic, Quantum Logic, Universal Algebra, Set Theory, Set-Theoretic Topology, and Point-Free Topology).

2.       Chair of

a.       TbiLLC 2011, Kutaisi, Georgia, September 2630, 2011.

b.       TbiLLC 2009, Bakuriani, Georgia, September 2125, 2009.

c.       TACL 2007, Oxford, England, August 5—9, 2007.

3.       Organizer of

a.       ToLo 2010, Georgian American University, Tbilisi, Georgia, June 810, 2010.

b.       BLAST 2009, Las Cruces, New Mexico, August 1014, 2009.

c.       ToLo 2008, Georgian American University, Tbilisi, Georgia, June 3—5, 2008.

d.       1st Joint NMSU/UTEP Workshop on Mathematics and Computer Science, New Mexico State University, Las Cruces, New Mexico, April 14, 2007.

e.       TACL 2003, Tbilisi, Georgia, July 7—11, 2003.

f.        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.

4.       Program committee member of

a.       AiML 2012, Copenhagen, Denmark, August 2225, 2012.

b.       Ordered Groups and Lattices in Algebraic Logic, Tbilisi, Georgia, September 2023, 2011.

c.       7th International Tbilisi Summer School in Logic and Language, Tbilisi, Georgia, September 1923, 2011.

d.       TACL 2011, Marseilles, France, July 2530, 2011.

e.       6th International Tbilisi Summer School in Logic and Language, Svaneti, Georgia, August 30 September 4, 2010.

f.        AiML 2010, Moscow, Russia, August 2427, 2010.

g.       5th International Tbilisi Summer School in Logic and Language, Tbilisi, Georgia, September 28 October 2, 2009.

h.       TACL 2009, Amsterdam, The Netherlands, July 711, 2009.

i.         4th International Tbilisi Summer School in Logic and Language, Tbilisi, Georgia, September 2226, 2008.

j.         AiML 2008, Nancy, France, September 9—12, 2008.

k.       The Student Session of ESSLLI 2008 (European Summer School in Logic, Language, and Computation 2008), Hamburg, Germany, August 4—15, 2008.

l.         2nd Joint NMSU/UTEP Workshop on Mathematics and Computer Science, University of Texas at El Paso, El Paso, Texas, November 17, 2007.

m.    TbiLLC 2007, Tbilisi, Georgia, October 1—5, 2007.

n.       3rd International Tbilisi Summer School in Logic and Language, Tbilisi, Georgia, September 24—28, 2007.

o.       AiML 2006, Queensland, Australia, September 25—28, 2006.

p.       TbiLLC 2003, Tbilisi, Georgia, October 610, 2003.

q.       TbiLLC 2001, Borjomi, Georgia, September 2328, 2001.

 

Invited Talks

1.       July 2011: Scientific legacy of Leo Esakia, TACL 2011, Marseille, France.

2.       July 2009: Duality theory in logic, 24th Summer Conference on Topology and its Applications, Brno, Czech Republic.

3.       June 2008: A new representation of distributive and implicative semilattices, ToLo 2008, Tbilisi, Georgia.

4.       October 2007: Modal logic and topology, TbiLLC 2007, Tbilisi, Georgia.

5.       March 2006: Completions and compactifications, The Amsterdam—London Workshop on Modal Logic, Amsterdam, The Netherlands.

6.       June 2005: Subframe logics, nuclei, and pointless topologies, TACL 2005, Barcelona, Spain.

7.       November 2004: Modal logics of space, Workshop on the Handbook of Spatial Logics, Freiburg University, Freiburg, Germany.

8.       June 2003: Scattered and hereditarily irresolvable spaces, The 2nd North American Summer School in Logic, Language, and Information, Indiana University, Bloomington, Indiana.

 

Colloquium Talks

1.       March 2009: Stone duality, Smirnov's theorem, and compact Hausdorff spaces, Baruch College, City University of New York, New York.

2.       November 2008: An algebraic approach to canonical formulas: Intuitionistic case, Indiana University, Bloomington, Indiana.

3.       May 2008: Priestley order-compactifications and a generalization of Dwinger's theorem, University of Amsterdam, Amsterdam, The Netherlands.

4.       April 2008: Bitopological duality for distributive lattices and Heyting algebras, University of Amsterdam, Amsterdam, The Netherlands.

5.       April 2008: Spatial logics over S4, University of Groningen, Groningen, The Netherlands.

6.       December 2007: New results in topological completeness of modal and superintuitionistic logics, University of Leicester, Leicester, United Kingdom.

7.       December 2007: Topological completeness in modal logic, City University of New York, New York.

8.       November 2007: Topological completeness of modal and superintuitionistic logics, Cornell University, Ithaca, New York.

9.       March 2006: Stone-like dualities in algebra, University of Houston, Houston, Texas.

10.   November 2005: Stone-like dualities and their applications to non-classical logics, Indiana University, Bloomington, Indiana.

11.   December 2004: MacNeille completions in modal logic, University of Amsterdam, The Netherlands.

12.   December 2004: MacNeille completions of modal algebras, Bonn University, Germany.

13.   June 2002: Canonical, topo-canonical, and MacNeille completions of Heyting algebras, Salerno University, Italy.

14.   June 2002: Topo-canonicity and topo-definability, Milan University, Italy.

15.   June 2002: MacNeille completions of Heyting algebras, Milan University, Italy.

16.   June 2001: Topological perspective on modal logic, Barcelona University, Spain.

17.   May 2001: Modal logic from topological point of view, Stanford University, Palo Alto, California.

18.   March 2001: Algebraic and topological approaches to super-intuitionistic logics, New Mexico State University, Las Cruces, New Mexico.

19.   February 2000: Projectivity and extendability, Utrecht University, The Netherlands.

20.   January 2000: Finite variable fragments of the intuitionistic predicate logic and their relation to the provability logic, University of Amsterdam, The Netherlands.

21.   October 1997: An algebraic approach to intuitionistic modal logics over MIPC, Japan Advanced Institute of Science and Technology, Japan.

22.   May 1997: Locally finite varieties, Japan Advanced Institute of Science and Technology, Japan.

23.   November 1996: Intuitionistic modal logics, Japan Advanced Institute of Science and Technology, Japan.

 

Conference Talks

1.       June 2007: Priestley order-compactifications, Order, Algebra, Logics, Vanderbilt University, Nashville, Tennessee.

2.       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.

3.       August 2004: MacNeille completions of Heyting algebras, Algebras, Lattices, Varieties—A Conference in Honor of Walter Taylor, University of Colorado, Boulder, Colorado.

4.       June 2002: Functional monadic Heyting algebras, Annual Meeting of Association for Symbolic Logic, Las Vegas, Nevada.

5.       July 2000: Locally finite varieties, The 6th Barcelona Logic Meeting, Barcelona, Spain.

6.       September 1999: Q-Heyting algebras as reducts of monadic Heyting algebras, TbiLLC 1999, Chakvi, Georgia.

7.       October 1998: Locally tabular extensions of MIPC, AiML 1998, Uppsala, Sweden.

8.       November 1997: Monadic version of Glivenko's theorem, Annual Meeting of Mathematical Logic, Shizuoka, Japan.

9.       June 1997: Logics over MIPC, Sequent Calculi and Kripke Semantics for Non-Classical Logics, Kyoto, Japan.

10.   March 1997: Modal intuitionistic logics and superintuitionistic predicate logics: correspondence theory, New Aspects of Non-Classical Logics and Their Kripke Semantics, Kyoto, Japan.

11.   December 1996: A partial solution of some problems of H. Ono, FOLLI Workshop on Logics for Linguistics, Philosophy, and Cognitive Science, Chiba, Japan.

12.   November 1996: Splitting monadic Heyting algebras, Annual Meeting of Mathematical Logic, Kanazawa, Japan.

13.   October 1995: Some results in monadic Heyting algebras, TbiLLC 1995, Gudauri, Georgia.

14.   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.