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,
Measure Theory, Real Analysis.
Service
and Professional Duties:
President, International Quantum Structures Association,
2014-2016
Vice President, International Quantum
Structures Association, 2016-2018
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
ESSLLI
Lectures on Lattice Theory: Lec
1, Lec 2, Lec
3, Lec 4, Lec
5
The Convolution Algebra,
talk at TACL, Prague, June 2017
An Operational View of
Schrodinger’s Equation, talk at the IQSA meeting, Nijmegen, July 2017
The
Type-2 Truth Value Algebra, Talk at AMS meeting, Denver, September 2016
Automorphisms
of Decompositions, talk at the IQSA meeting, Leicester, July 2016
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, C. Heunen, and M. Navara,
Boolean subalgebras of orthoalgebras,
manuscript.
2.
G.
Bezhanishvili, J. Harding, J. Ilin,
and Frederik Lauridsen, MacNeille
transferability and stable classes of Heyting
algebras, submitted to Algebra Univ..
3.
J.
Harding, The convolution algebra, ArXiv:1702.02847.
4.
J.
Harding, Dynamics in the decompositions approach to quantum mechanics, accepted
to The Inter. J. Theor.
Phys..
5.
J.
Harding, Wigner’s theorem for an infinite set, submitted to Mathematica Slovaka.
6.
J.
Harding and A. Romanowska, Varieties of Birkhoff systems part I, Order 34 (2017) no. 1, 45-68.
7.
J.
Harding and A. Romanowska, Varieties of Birkhoff systems part II, Order 34 (2017) no. 1, 69-89.
8.
J. Harding, C. Walker, and E. Walker, The Type-2
Truth Value Algebra, CRC Press, 2016.
9.
A. Doering and J. Harding,
Abelian subalgebras and the Jordan structure of a von
Neumann algebra, The Houston J. of Math. 42
(2016) no. 2, 559-568.
10.
G.
Bezhanishvili and J. Harding, On the proof that
compact Hausdorff Boolean algebras are power sets, Order 33 (2016) no. 2, 263-268.
11.
G.
Bezhanishvili and J. Harding, Compact Hausdorff Heyting algebras, Algebra Universalis
76 (2016) 301-304.
12.
J.
Harding and Taewon Yang, Sections in orthomodular structures of decompositions, The Houston J. Math. 42 (2016) no. 4,
1079-1092.
13.
J.
Harding and Tim Hannan, Automorphisms
of Decompositions, Math. Slovaka 66 (2016) no. 2, 493-526. Sage code
for programs
14.
J.
Harding and T. Yang, The logic of bundles, Internat. J. of Theoret. Physics 54 (2015) no. 12,
4601-4614.
15.
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.
16.
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.
17.
G.
Bezhanishvili, N. Bezhanishvili,
and J. Harding, Modal compact Hausdorff spaces, Journal of Logic and Computation, 25
(2015) no. 1, 1-35.
18.
J.
Harding, C. Walker, and E. Walker, Equations in type-2 fuzzy sets, Inter. J. of Uncertainty, Fuzziness, and
Knowledge-Based Systems 23 (2015), 31-42.
19.
G.
Bezhanishvili and J. Harding, Stable Compactifications
of frames, Cahiers de Topologie
et Geometrie Differentielle
Categoriques 55 (2014) no. 1, 37-65.
20.
G.
Bezhanishvili and J. Harding, Proximity frames and
regularization, Applied Categorical
Structures, 22 (2014), no. 1, 43-78.
21.
J.
Harding, C. Walker and E. Walker, Categories with fuzzy sets and relations, Fuzzy Sets and Systems, 256 (2014), no.
1, 43-78.
22.
J.
Harding, Daggers, kernels, Baer *-semigroups, and orthomodularity,
J. Phil. Logic 42 (2013) no. 3,
535-549.
23.
J. Harding, Decidability of the equational theory of the
continuous geometry CG(F), J. Phil. Logic 42 (2013), no. 3, 461-465.
24.
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.
25.
J.
Harding, A Boolean topological orthomodular poset, Algebra Universalis 68 (2012), no. 3-4, 193-196.
26.
J. Harding, C. Walker, and E. Walker, Projective bichains, Algebra Universalis 67 (2012), no. 4, 347-374.
27.
G.
Bezhanishvili and J. Harding, Modal logics of Stone
spaces, Order 29 (2012), no. 2,
271-292.
28.
J.
Harding and Qin Yang, Regular completions of lattices. Houston J. of Mathematics 38 (2012), no. 3., 685-691.
29.
J. Harding and M. Navara, Subalgebras of orthomodular
lattices, Order 28 (2011), 549-563.
30.
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.
31.
J. Harding, C.
Walker, and E. Walker, Convex normal functions revisited, Fuzzy Sets and Systems 161 (2010), 1343 – 1349.
32.
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.
33.
J. Harding, A link
between quantum logic and categorical quantum mechanics, International J. of
Theoretical Physics (2009), no. 3, 769 – 802.
34.
G. Bezhanishvili and J. Harding, The modal logic of β(N), Archiv. Math. Logic. 48 (2009), 231 – 242.
35.
J. Harding, κ –
complete uniquely complemented lattices, Order 25 (2008), no. 2, 121 – 129.
36.
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.
37.
J. Harding, C.
Walker, and E. Walker, Lattices of convex normal functions, Fuzzy Sets and
Systems 159 (2008), no. 9, 1061 – 1071.
38.
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.
39.
J. Harding, The
Source of the Orthomodular Law, a book chapter in The
Handbook of Quantum Logic and Quantum Structures, Elsevier, 2007.
40.
Bezhanishvili and J. Harding, MacNeille completions of modal algebras, The Houston. J of
Math. 33 (2007), no. 2, 355 – 384.
41.
J. Harding, Orthomodularity of decompositions in a categorical setting.
International J. of Theoretical Physics 45 (2006), no. 6, 1117 – 1128.
42.
M. Gehrke, J. Harding, Y. Venema, MacNeille completions and canonical extensions. Trans.
Amer. Math. Soc. 358 (2006), no. 2, 573 – 590.
43.
J. Harding, On profinite completions and canonical extensions, Algebra Universalis 55 (2006), no. 2-3, 293 – 296.
44.
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.
45.
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.
46.
J. Harding, Remarks
on concrete orthomodular lattices. International J.
of Theoretical Physics 43 (2004), no. 10, 2149 – 2168.
47.
G. Bezhanishvili and J. Harding, MacNeille
completions of Heyting algebras. The Houston J. of
Math. 30 (2004), no. 4, 937 – 952.
48.
J. Harding and M.
Roddy, Obituary: Günter Bruns. Order 20 (2004), pp.
329-332.
49.
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.
50.
G. Bezhanishvili and J. Harding, Functional monadic Heyting algebras. Algebra
Universalis, 48 (1) (2002), pp. 1-10.
51.
J. Harding
and P. Ptak, On the set representation of an orthomodular poset. Coll. Math. 89 (2) (2001), pp. 233-240.
52.
J. Harding,
States on orthomodular posets
of decompositions. International J. of
Theoretical Physics 40 (2001), pp. 1061-1069.
53.
M. Gehrke and J. Harding, Bounded lattice expansions. J. of Algebra 238 (2001), pp. 345-371.
54.
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.
55.
J. Harding
and M. Navara, Embeddings
into orthomodular lattices with given centers, state
spaces and automorphism groups. Order 17 (2000), pp. 239-254.
56.
G. Bruns and J. Harding, Epimorphisms
in certain varieties of algebras. Order
17 (2000), pp. 195-206.
57.
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.
58.
J. Harding,
The axioms of an experimental system. International
J. of Theoretical Physics 38 (6) (1999), pp. 1643-1675.
59.
J. Harding,
Regularity in quantum logic. International
J. of Theoretical Physics 37 (4) (1998), pp. 1173-1212.
60.
J. Harding,
Canonical completions of lattices and ortholattices. Tatra Mountains Math. Publ. 15 (1998), pp. 85-96.
61.
G. Bruns and J. Harding, Amalgamation of ortholattices.
Order 14 (1998), pp. 193-209.
62.
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.
63.
J. Harding
and M. F. Janowitz, A bundle representation for
continuous geometries. Advances in
Applied Math. 19 (1997), pp. 282-293.
64.
J. Harding,
Decompositions in quantum logic. The Trans.
Amer. Math. Soc. 348 (5) (1996), pp. 1839-1862.
65.
G. D. Crown,
J. Harding, and M. F. Janowitz, Boolean products of
lattices. Order 13 (2) (1996), pp. 175-205.
66.
J. Harding,
Free central extensions. The Houston
J. of Math. 22 (4) (1996), pp. 665-686.
67.
J. Harding,
The MacNeille completion of a uniquely complemented
lattice. The Canad.
Math. Bull. 37 (2) (1994), pp. 222-227.
68.
J. Harding,
Completions of orthomodular lattices II. Order 10 (1993), pp. 283-294.
69.
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.
70.
J. Harding,
Irreducible orthomodular lattices which are simple. Algebra Universalis
29 (1992), pp. 556-563.
71.
J. Harding, Orthomodular lattices whose MacNeille
completions are not orthomodular. Order 8 (1991), pp. 93-103.
72.
J. Harding,
Sheaves of orthomodular lattices and MacNeille completions. Ph.D. thesis. McMaster University,
1991.
73.
G. Bruns, R. J. Greechie, J.
Harding, and M. Roddy, Completions of orthomodular
lattices. Order 7 (1990), pp. 67-76.
74.
J. Harding,
Boolean factors of orthomodular lattices. Algebra Universalis
25 (1988), pp. 281-282.
75.
J. Harding,
Varieties of ortholattices containing the orthomodular lattices. M.Sc. thesis. McMaster University,
1988.