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, Math
Appreciation
Graduate: Logic, Lattice Theory, Set Theory, Universal
Algebra, Model Theory, Algebra I, II, Linear Algebra, Foundations of Geometry.
Service
and Professional Duties:
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
Some
Recent Talks
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.
G.
Bezhanishvili, N. Bezhanishvili, and J. Harding, Modal de Vries algebras,
submitted to Journal of Logic and
Computation September 2011.
2.
J. Harding, A
Boolean topological orthomodular poset, submitted to Algebra Universalis September 2011.
3.
J. Harding,
C. Walker, and E. Walker, Type II fuzzy sets and bichains, submitted to 2010 Proceedings of the NAFIPS International
Conference, July 12 - 14, Toronto, submitted July 2011.
4.
G.
Bezhanishvili and J. Harding, Proximity frames and regularization, submitted to
Math. Proc. of the Cambridge Phil. Soc. March
2011.
5.
J. Harding, C.
Walker, and E. Walker, Projective bichains, to appear in Algebra Universalis.
6.
A. Doering and J.
Harding, Abelian subalgebras and the Jordan structure of a von Neumann algebra,
submitted to J. Functional Analysis, arXiv:1009.4945
7.
J. Harding and M.
Navara, Subalgebras of orthomodular lattices, to appear in Order. arXiv:1009.4433
8.
G.
Bezhanishvili and J. Harding, Modal logics of Stone spaces, Submitted August
2010, accepted and to appear in Order.
9.
J. Harding and Q.
Yang, Regular completions of lattices, to appear in The Houston J. Math..
10.
J. Harding,
Decidability of the equational theory of the continuous geometry CG(F),
submitted to J. Phil. Logic, Feb. 2010.
11.
J. Harding, Daggers,
kernels, Baer *-semigroups, and orthomodularity, submitted to J. Phil. Logic, Feb. 2010.
12.
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.
13.
J. Harding, C.
Walker, and E. Walker, Convex normal functions revisited, Fuzzy Sets and Systems 161 (2010), 1343 – 1349.
14.
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.
15.
J. Harding, A link
between quantum logic and categorical quantum mechanics, International J. of
Theoretical Physics (2009), no. 3, 769 – 802.
16.
G. Bezhanishvili and
J. Harding, The modal logic of β(N), Archiv. Math. Logic. 48 (2009), 231 – 242.
17.
J. Harding, κ –
complete uniquely complemented lattices, Order 25 (2008), no. 2, 121 – 129.
18.
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.
19.
J. Harding, C.
Walker, and E. Walker, Lattices of convex normal functions, Fuzzy Sets and
Systems 159 (2008), no. 9, 1061 – 1071.
20.
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.
21.
J. Harding, The
Source of the Orthomodular Law, a book chapter in The Handbook of Quantum Logic
and Quantum Structures, Elsevier, 2007.
22.
Bezhanishvili and J.
Harding, MacNeille completions of modal algebras, The Houston. J of Math. 33
(2007), no. 2, 355 – 384.
23.
J. Harding,
Orthomodularity of decompositions in a categorical setting. International J. of
Theoretical Physics 45 (2006), no. 6, 1117 – 1128.
24.
M. Gehrke, J.
Harding, Y. Venema, MacNeille completions and canonical extensions. Trans.
Amer. Math. Soc. 358 (2006), no. 2, 573 – 590.
25.
J. Harding, On
profinite completions and canonical extensions, Algebra Universalis 55 (2006),
no. 2-3, 293 – 296.
26.
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.
27.
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.
28.
J. Harding, Remarks
on concrete orthomodular lattices. International J. of Theoretical Physics 43
(2004), no. 10, 2149 – 2168.
29.
G. Bezhanishvili and
J. Harding, MacNeille completions of Heyting algebras. The Houston J. of Math.
30 (2004), no. 4, 937 – 952.
30.
J. Harding and M.
Roddy, Obituary: Günter Bruns. Order 20 (2004), pp. 329-332.
31.
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.
32.
G.
Bezhanishvili and J. Harding, Functional monadic Heyting algebras. Algebra Universalis, 48 (1) (2002), pp.
1-10.
33.
J. Harding
and P. Ptak, On the set representation of an orthomodular poset. Coll. Math. 89 (2) (2001), pp. 233-240.
34.
J. Harding,
States on orthomodular posets of decompositions. International J. of Theoretical Physics 40 (2001), pp. 1061-1069.
35.
M. Gehrke and
J. Harding, Bounded lattice expansions. J.
of Algebra 238 (2001), pp. 345-371.
36.
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.
37.
J. Harding
and M. Navara, Embeddings into orthomodular lattices with given centers, state
spaces and automorphism groups. Order
17 (2000), pp. 239-254.
38.
G. Bruns and
J. Harding, Epimorphisms in certain varieties of algebras. Order 17 (2000), pp. 195-206.
39.
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.
40.
J. Harding,
The axioms of an experimental system. International
J. of Theoretical Physics 38 (6) (1999), pp. 1643-1675.
41.
J. Harding,
Regularity in quantum logic. International
J. of Theoretical Physics 37 (4) (1998), pp. 1173-1212.
42.
J. Harding,
Canonical completions of lattices and ortholattices. Tatra Mountains Math. Publ. 15
(1998), pp. 85-96.
43.
G. Bruns and
J. Harding, Amalgamation of ortholattices. Order
14 (1998), pp. 193-209.
44.
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.
45.
J. Harding
and M. F. Janowitz, A bundle representation for continuous geometries. Advances in Applied Math. 19 (1997), pp.
282-293.
46.
J. Harding,
Decompositions in quantum logic. The
Trans. Amer. Math. Soc. 348 (5) (1996), pp. 1839-1862.
47.
G. D. Crown,
J. Harding, and M. F. Janowitz, Boolean products of lattices. Order 13 (2) (1996), pp. 175-205.
48.
J. Harding,
Free central extensions. The Houston
J. of Math. 22 (4) (1996), pp. 665-686.
49.
J. Harding,
The MacNeille completion of a uniquely complemented lattice. The Canad. Math. Bull. 37 (2) (1994),
pp. 222-227.
50.
J. Harding,
Completions of orthomodular lattices II. Order
10 (1993), pp. 283-294.
51.
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.
52.
J. Harding,
Irreducible orthomodular lattices which are simple. Algebra Universalis 29 (1992), pp. 556-563.
53.
J. Harding,
Orthomodular lattices whose MacNeille completions are not orthomodular. Order 8 (1991), pp. 93-103.
54.
J. Harding,
Sheaves of orthomodular lattices and MacNeille completions. Ph.D. thesis. McMaster
University, 1991.
55.
G. Bruns, R.
J. Greechie, J. Harding, and M. Roddy, Completions of orthomodular
lattices. Order 7 (1990), pp. 67-76.
56.
J. Harding,
Boolean factors of orthomodular lattices. Algebra
Universalis 25 (1988), pp. 281-282.
57.
J. Harding,
Varieties of ortholattices containing the orthomodular lattices. M.Sc. thesis.
McMaster University, 1988.