John Harding

 

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Education:              

 

Ph.D., McMaster University, 1991, Advisor G. Bruns

M. Sc., McMaster University, 1988, Advisor G. Bruns

            B.Sc., McMaster University, 1987

 

Career history:      

 

            Professor, New Mexico State University, 2005 –

            Associate Professor, New Mexico State University, 1999 – 2005

Assistant Professor, New Mexico State University, 1996 – 1999

Assistant Professor, Brandon University, 1993 –1996

NSERC Postdoctoral Fellow, Vanderbilt University, 1991-1993

                                               

Awards:      

           

            Arts and Sciences Outstanding Faculty Award for NMSU, 2007

D. C. Rousch Award for Excellence in Teaching, received January 2004.

            International Quantum Structures Association Research Award 2000.

                                   

Courses Taught:

 

Undergraduate: Calculus I, II, III, Vector Analysis, Differential Equations, Analysis, Algebra, Discrete Mathematics, Linear Algebra, Programming in Pascal, Data Structures, Statistics, Applied Statistics, Survey Sampling, Combinatorics, Great Theorems in Mathematics, Math Appreciation

 

Graduate: Logic, Lattice Theory, Set Theory, Universal Algebra, Model Theory, Algebra I, II, Linear Algebra, Foundations of Geometry, Measure Theory.

                                   

Service and Professional Duties:

 

         President, International Quantum Structures Association, 2014-2016          

Councilor, International Quantum Structures Association, 1998-2002, 2006-2010

Editorial Board of Order, 2001 –

Advisory Board Mathematica Slovaca, 2007 –

 

Chair, Graduate Studies for Mathematical Sciences, NMSU 2005 – 2009

Chair, Graduate recruiting for Mathematical Sciences, NMSU 2011-2013

 

Some Recent Talks

 

The Type-2 Truth Value Algebra, Talk at a workshop in Amsterdam, September 2015.

 

         Products or Sums, Talk at Quantum Workshop in Amsterdam, May 2015

 

Quantum Structures, Colloquium Iowa State, September 2014.

 

Topological Boolean Algebras, seminar talk, Iowa State, September 2014.

 

Projective Bichains, BLAST, Chapman, July 2013.

 

         Type-2 fuzzy sets, Talk at AMS meeting Akron, October 2012.

 

            Modal compact Hausdorff spaces, talk at the Duality Workshop, Oxford, June 2012.

 

Proximities, Colloquium at UTEP, El Paso, November 2011.

 

Proximity frames, Talk at BLAST, Lawrence KS, June 2010.

 

            Projective bichains, undelivered talk, planned for BLAST 2010.

 

Subalgebras of orthomodular lattices, Colloquium at Chapman University, Los Angeles, November, 2010.

        

            Orthomodular structures and categories or Everything old is new again, IQSA meeting, Boston, June 2010.

 

Logics of Stone spaces, BLAST 2010, Boulder, June 2010.

 

Daggers, kernels, Baer *-semigroups and orthomodularity, ASL annual meeting, Washington, March 2010.

 

Orthomodularity in a categorical setting, QPL, Oxford June 2009.

 

Completions of Ordered Algebraic Structures: A Survey, at UncLog JAIST, Ishikawa Japan, March 2008.

 

Some Quantum Logic and a few Categories, at the Categorical Quantum Logic Workshop, Oxford, August 2007.

 

 

Publications  (click on the link for a .pdf file)

 

 

1.               J. Harding and A. Romanowska, Varieties of Birkhoff systems part I, submitted to Order.

 

2.               J. Harding and A. Romanowska, Varieties of Birkhoff systems part II, submitted to Order.

 

3.               J. Harding and T. Yang, The logic of bundles, to appear in Internat. J. of Theoret. Physics.

 

4.               J. Harding, C. Walker, and E. Walker, The Type-2 Truth Value Algebra, monograph to be published by CRC Press.

 

5.               G. Bezhanishvili and J. Harding, On the proof that compact Hausdorff Boolean algebras are power sets, to appear in Order.

 

6.               G. Bezhanishvili and J. Harding, Compact Hausdorff Heyting algebras, to appear in Algebra Universalis.

 

7.               J. Harding and Taewon Yang, Sections in orthomodular structures of decompositions, to appear in The Houston J. Math..

 

 

8.               J. Harding and Tim Hannan, Automorphisms of Decompositions, to appear in Math. Slovaka, arXiv:1308.5020 Sage code for programs

 

9.               J. Harding, C. Walker, and E. Walker, Partial orders on fuzzy truth value algebras, Internat. J. of Uncertainty, Fuzziness, and Knowledge-based Systems, 23 (2015), no. 2, 193-219.

 

10.            G. Bezhanishvili and J. Harding, Stable Compactifications of frames, to appear in Cahiers de Topologie et Geometrie Differentielle Categoriques.

 

11.            G. Bezhanishvili, N. Bezhanishvili, and J. Harding, Modal operators on compact regular frames and de Vries algebras, Applied Categorical Structures, 23 (2015), no. 3, 365-379.

 

12.            G. Bezhanishvili, N. Bezhanishvili, and J. Harding, Modal compact Hausdorff spaces, Journal of Logic and Computation, 25 (2015) no. 1, 1-35.

 

13.            A. Doering and J. Harding, Abelian subalgebras and the Jordan structure of a von Neumann algebra, to appear in The Houston J. of Math.

 

14.            G. Bezhanishvili and J. Harding, Proximity frames and regularization, Applied Categorical Structures, 22 (2014), no. 1, 43-78.

 

15.            J. Harding, C. Walker and E. Walker, Categories with fuzzy sets and relations, Fuzzy Sets and Systems, 256 (2014), no. 1, 43-78. 

 

16.            J. Harding, Daggers, kernels, Baer *-semigroups, and orthomodularity, J. Phil. Logic 42 (2013) no. 3, 535-549.

 

17.            J. Harding, Decidability of the equational theory of the continuous geometry CG(F), J. Phil. Logic 42 (2013), no. 3, 461-465.

 

18.            J. Harding, C. Walker, and E. Walker, Type II fuzzy sets and bichains, an invited chapter for Recent Advances in Type-2 Fuzzy Sets and Systems --- Theory and Applications”, a book in the series Studies in Fuzziness and Soft Computing vol. 301, pg. 97-112, 2013.

 

19.            J. Harding, A Boolean topological orthomodular poset, Algebra Universalis 68 (2012), no. 3-4, 193-196.

 

20.            J. Harding, C. Walker, and E. Walker, Projective bichains, Algebra Universalis 67 (2012), no. 4, 347-374.

 

21.            G. Bezhanishvili and J. Harding, Modal logics of Stone spaces, Order 29 (2012), no. 2, 271-292. 

 

22.            J. Harding and Qin Yang, Regular completions of lattices. Houston J. of Mathematics 38 (2012), no. 3., 685-691.

 

23.            J. Harding and M. Navara, Subalgebras of orthomodular lattices, Order 28 (2011), 549-563.  

 

24.            J. Harding, C. Walker, and E. Walker, The variety generated by the truth value algebra of type-II fuzzy sets, Fuzzy Sets and Systems 161 (2010), no. 5, 735 – 749.

 

25.            J. Harding, C. Walker, and E. Walker, Convex normal functions revisited, Fuzzy Sets and Systems 161 (2010), 1343 – 1349.

 

26.            Q. Deng, J. Harding, and T. Hu, Hausdorff dimension of self-similar sets with overlaps, Science in China, Series A: Mathematics 52 (2009), no. 1, 119 – 128.

 

27.            J. Harding, A link between quantum logic and categorical quantum mechanics, International J. of Theoretical Physics (2009), no. 3, 769 – 802.

 

28.            G. Bezhanishvili and J. Harding, The modal logic of β(N), Archiv. Math. Logic. 48 (2009), 231 – 242.

 

29.            J. Harding, κ – complete uniquely complemented lattices, Order 25 (2008), no. 2, 121 – 129.

 

30.            J. Harding, Completions of Ordered Algebraic Structures: A Survey, invited chapter for the Proceedings of the International Workshop on Interval/Probabilistic Uncertainty and Non-classical Logics, Ono et. al. Ed.s, Advances in Soft Computing vol. 46, 2008, Springer, 231 – 244.

 

31.            J. Harding, C. Walker, and E. Walker, Lattices of convex normal functions, Fuzzy Sets and Systems 159 (2008), no. 9, 1061 – 1071.

 

32.            J. Harding, A regular completion for the variety generated by the three-element Heyting algebra, The Houston J. of Math. 34 (2008), no. 3, 649 – 660.

 

33.            J. Harding, The Source of the Orthomodular Law, a book chapter in The Handbook of Quantum Logic and Quantum Structures, Elsevier, 2007.

 

34.            Bezhanishvili and J. Harding, MacNeille completions of modal algebras, The Houston. J of Math. 33 (2007), no. 2, 355 – 384.

 

35.            J. Harding, Orthomodularity of decompositions in a categorical setting. International J. of Theoretical Physics 45 (2006), no. 6, 1117 – 1128.

 

36.            M. Gehrke, J. Harding, Y. Venema, MacNeille completions and canonical extensions. Trans. Amer. Math. Soc. 358 (2006), no. 2, 573 – 590.

 

37.            J. Harding, On profinite completions and canonical extensions, Algebra Universalis 55 (2006), no. 2-3, 293 – 296.

 

38.            J. Harding, D. Smith and E. Jager, Group-valued measures on the lattice of closed subspaces of a Hilbert space. International J. of Theoretical Physics. 44 (2005), no. 5, 539 – 548.

 

39.            G. Bezhanishvili, M. Gehrke, J. Harding, C. Walker and E. Walker, Varieties of Algebras that arise in Fuzzy Set Theory. Logical, algebraic, analytic, and probabilistic aspects of triangular norms, 321 – 344, Elsevier, Amsterdam, 2005.

 

40.            J. Harding, Remarks on concrete orthomodular lattices. International J. of Theoretical Physics 43 (2004), no. 10, 2149 – 2168.

 

41.            G. Bezhanishvili and J. Harding, MacNeille completions of Heyting algebras. The Houston J. of Math. 30 (2004), no. 4, 937 – 952.  

 

42.            J. Harding and M. Roddy, Obituary: Günter Bruns. Order 20 (2004), pp. 329-332.

 

43.            J. Harding, The free orthomodular lattice on countably many generators is a subalgebra of the free orthomodular lattice on three generators. Algebra Universalis, 48 (2) (2002), pp. 171-182.

 

44.            G. Bezhanishvili and J. Harding, Functional monadic Heyting algebras. Algebra Universalis, 48 (1) (2002), pp. 1-10.

 

45.            J. Harding and P. Ptak, On the set representation of an orthomodular poset. Coll. Math. 89 (2) (2001), pp. 233-240.

 

46.            J. Harding, States on orthomodular posets of decompositions. International J. of Theoretical Physics 40 (2001), pp. 1061-1069.

 

47.            M. Gehrke and J. Harding, Bounded lattice expansions. J. of Algebra 238 (2001), pp. 345-371.

 

48.            G. Bruns and J. Harding, Algebraic aspects of orthomodular lattices, Current Research in Operational Quantum Logic: Algebras, Categories, Languages, B. Cooke, D. Moore and A. Wilce ed., Kluwer 2000.

 

49.            J. Harding and M. Navara, Embeddings into orthomodular lattices with given centers, state spaces and automorphism groups. Order 17 (2000), pp. 239-254.

 

50.            G. Bruns and J. Harding, Epimorphisms in certain varieties of algebras. Order 17 (2000), pp. 195-206.

 

51.            J. Harding and A. Pogel, Every lattice with 1 and 0 is embeddable in the lattice of topologies of some set by an embedding which preserves the 1 and 0. Topology and Its Applications 105 (2000), pp. 99-101.

 

52.            J. Harding, The axioms of an experimental system. International J. of Theoretical Physics 38 (6) (1999), pp. 1643-1675.

 

53.            J. Harding, Regularity in quantum logic. International J. of Theoretical Physics 37 (4) (1998), pp. 1173-1212.    

 

54.            J. Harding, Canonical completions of lattices and ortholattices. Tatra Mountains Math. Publ. 15 (1998), pp. 85-96.  

 

55.            G. Bruns and J. Harding, Amalgamation of ortholattices. Order 14 (1998), pp. 193-209.

 

56.            J. Harding, M. Marinacci, N. Nguyen, and T. Wang, Local Radon-Nikodym derivatives of set functions. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5 (3) (1997), pp. 379-394.

 

57.            J. Harding and M. F. Janowitz, A bundle representation for continuous geometries. Advances in Applied Math. 19 (1997), pp. 282-293.

 

58.            J. Harding, Decompositions in quantum logic. The Trans. Amer. Math. Soc. 348 (5) (1996), pp. 1839-1862.

 

59.            G. D. Crown, J. Harding, and M. F. Janowitz, Boolean products of lattices. Order 13 (2) (1996), pp. 175-205.

 

60.            J. Harding, Free central extensions. The Houston J.  of Math.  22 (4) (1996), pp. 665-686.

 

61.            J. Harding, The MacNeille completion of a uniquely complemented lattice. The Canad. Math. Bull. 37 (2) (1994), pp. 222-227.

 

62.            J. Harding, Completions of orthomodular lattices II. Order 10 (1993), pp. 283-294.

 

63.            J. Harding, Any lattice can be regularly embedded into the MacNeille completion of a distributive lattice. The Houston Journal of Math. 19 (1993), pp. 39-44.

 

64.            J. Harding, Irreducible orthomodular lattices which are simple. Algebra Universalis 29 (1992), pp. 556-563.

 

65.            J. Harding, Orthomodular lattices whose MacNeille completions are not orthomodular. Order 8 (1991), pp. 93-103.

 

66.            J. Harding, Sheaves of orthomodular lattices and MacNeille completions. Ph.D. thesis. McMaster University, 1991.

 

67.            G. Bruns, R. J. Greechie, J. Harding, and M. Roddy, Completions of orthomodular lattices.  Order 7 (1990), pp. 67-76.

 

68.            J. Harding, Boolean factors of orthomodular lattices. Algebra Universalis 25 (1988), pp. 281-282.

 

69.            J. Harding, Varieties of ortholattices containing the orthomodular lattices. M.Sc. thesis. McMaster University, 1988.