Dr Marcel G

Dr Marcel G Jackson

Associate Professor, ARC Future Fellow

College of Science, Health and Engineering

School of Engineering and Mathematical Sciences

Department of Mathematics and Statistics

Physical Sciences 2, Room 308c, Melbourne (Bundoora)

Qualifications

BSc, PhD UTAS.

Role

Academic

Area of study

Mathematics and Statistics

Teaching units

In 2017: Discrete Mathematics (1st year), Discrete Structures and Algorithms (3rd year), Probability Models (second year), Computational Complexity (4th year).

 

Recent publications

This is a selection of some recent publications.  For a more complete list, many with downloads available, go to my personal webpage http://marceljackson.ltumathstats.com/

  • A. Egri-Nagy, M. Jackson, J. Rhodes and B. Steinberg, On the atoms of algebraic lattices arising in q-theory, to appear in Internat. J. Algebra Comput., 28 pp.
  • M. Jackson and E.W.H. Lee, Monoid varieties with extreme properties, to appear in Trans. Amer. Math. Soc., 27 pp.
  • M. Jackson, T. Kowalski and T. Niven, Complexity and polymorphisms for digraph constraint problems under some basic constructions, Internat. J. Algebra Comput., 31 pp.  DOI: 10.1142/S0218196716500600
  • R. Hirsch, M. Jackson and Sz. Mikulas, The algebra of functions with antidomain and range, J. Pure Appl. Algebra 220 (2016), no. 6, 2214–2239.
  • J. Bulin, D. Delic, M. Jackson and T. Niven, A finer reduction of constraint problems to digraphs, Logical Methods in Computer Science 11(4:18) (2015), 1–33.
  • C. Carvhalo, L. Egri, M. Jackson and T. Niven, On Maltsev digraphs, Electronic Journal of Combinatorics 22(1) (2015), #1.47.
  • M. Jackson and T. Stokes, Monoids with tests and the algebra of possibly non-halting programs, J. Log. Algeb. Program 84 (2015), 259–275.
  • M. Jackson, Natural dualities, nilpotence and projective planes, Algebra Universalis, 72 (2015), 65–85.
  • M. Jackson and T. Stokes, On representing semigroups with subsemilattices, J. Algebra 376 (2013), 228–260.
  • M. Jackson and B. Trotta, Constraint satisfaction, irredundant axiomatisability and continuous colouring, Studia Logica 101 (2013), 65–94.
  • R. Goldblatt and M. Jackson, Well structured program equivalence is highly undecidable, ACM Trans. Comput. Logic 13(3) (2012), Article number 26.
  • R. Hirsch and M. Jackson, Undecidable problems on representability as binary relations, J. Symbolic Logic 77 (2012), 1211–1244.
  • B. Davey, M. Jackson, J. Pitkethly and Cs. Szabo, Finite degree: algebras in general and semigroups in particular, Semigroup Forum 83 (2011), 89–110.
  • M. Jackson and T. Stokes, Modal restriction semigroups: towards an algebra of functions and deterministic computation, Internat. J. Algebra Comput. 21 (2011), 1053–1095.

Older publications

A selection from 2008 to 2010.  For a complete list go to http://marceljackson.ltumathstats.com/

  • M. Jackson and M. Volkov, The algebra of adjacency patterns: Rees matrix semigroups with reversion, Gurevich Festschrift (A. Blass, N. Dershowitz, and W. Reisig Eds.), LNCS 6300, pp. 414–443, 2010.
  • M Jackson and M. V. Volkov, Relatively inherently nonfinitely q-based finite semigroups, Trans. Amer. Math. Soc., 361 (2009), 2181–2206.
  • M. Jackson and M. Volkov, Undecidable problems for completely 0-simple semigroups, J. Pure Appl. Algebra 213 (2009), 1961–1978.
  • D. M. Clark, B. A. Davey, M. Jackson and J. G. Pitkethly, The axiomatizability of topological prevarieties, Adv. Math. 218 (2008), 1604–1653.
  • M. Jackson, Flat algebras and the translation of universal Horn logic into equational logic, J. Symb. Logic, 73 (2008), 90–128.

Research projects

 My research interests are semigroups, universal algebra and their application.  A sample of specific topics of interest include:

  • Finite basis problems for varieties, quasivarieties;
  • Computational complexity and decidability/undecidability, especially for problems relating to finite semigroups/algebras;
  • Semigroups of relations (relation algebras), functions (function semigroups), and their applications in computer science;
  • The theory of natural dualities;
  • Boolean topological algebras/structures;
  • Algebraic methods in the study of Constraint Satisfaction Problems. 

I am an associate editor for the following journals: