John Harding

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

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

Service and Professional Duties:

Councilor, International Quantum Structures Association, 1998-2002, 2006-2008

Editorial Board of Order, 2001 –

Advisory Board Mathematica Slovaca, 2007 –

Chair, Graduate Studies for Mathematical Sciences, NMSU 2005 –

Recent Talks

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

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

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

[1] J. Harding, κ – complete uniquely complemented lattices, to appear in Order.

[2] J. Harding, C. Walker, and E. Walker, Convex normal functions revisited, submitted to Fuzzy Sets and Systems.

[3] J. Harding, Orthomodularity in dagger biproduct categories, submitted to International J. of Theoretical Physics.

[4] G. Bezhanishvili and J. Harding, The modal logic of β(N), submitted to Archiv. Math. Logic.

[5] J. Harding, Completions of ordered algebraic structures: a survey, invited chapter for the Proceedings of the International Workshop on Interval and Probabilistic Uncertainty and Non-classical Logics, Ono et. Al. Ed.s, to be published by Springer.

[6] J. Harding, C. Walker, and E. Walker, A lattice of convex normal functions, submitted paper to appear in Fuzzy Sets and Systems.

[7] J. Harding, A regular completion for the variety generated by the three-element Heyting algebra. To appear in The Houston J. of Math.

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

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

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

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

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

[6] 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.

[7] 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.

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

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

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

[11] 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.

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

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

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

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

[16] 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.

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

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

[19] 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.

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

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

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

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

[24] 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.

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

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

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

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

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

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

[31] 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.

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

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

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

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

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

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