Academic Staff

Before coming to Essex as a lecturer in Mathematics, I had experience of work as a programmer in the financial sector and as a lecturer in computer science.

• Bloom filters and other models for compact storage of sets, especially as applied to forwarding information packets in computer networks
• Threshold graphs, scale-free graphs and other models of social networks represented by telephone or e-mail contacts

• Applications of discrete mathematics to computer science (for example, current research in optimisation of routing of information packets in computer networks)
• Universal algebra (especially semigroup theory, but also problems related to groups and graphs).
• Communication networks (for example, social networks as represented by telephone or e-mail contacts) and their properties (including problems related to scale-free networks)

I invite PhD applications in the above areas.

Also,

• As a part of other research, I often consider questions related to algorithms, including time complexity and computability
• As a part of other research, I consider some questions related to computer security

Vernitski, A. with M. V. Volkov, ‘The proof and the generalization of Higgins's theorem on divisors of semigroups of order-preserving mappings', Izv. Vyssh. Uchebn. Zaved., Mat. 392 (1995), 38-44 [English translation: Russ. Math. 39(1995), 34-39].

Vernitski, A., ‘Semigroups of order-decreasing graph endomorphisms’, Semigroup Forum 58(1999), 222-240.

Vernitski, A., ‘The finite basis problem for the semigroups of order-preserving mappings’, Proceedings A (Mathematics) of the Royal Society of Edinburgh, 129A(1999), 641-647.

Vernitski, A., ‘Posets and their semigroups of decreasing endomorphisms’, Acta Scientarum Mathematicarum, 65(1999), 77-84.

Vernitski, A. with V. B. Repnitskii, ‘Semigroups of order-preserving mappings’ , Communications in Algebra, 28(2000), 3635-3641.

Vernitski, A., ‘Studying semigroups of mappings using quasi-identities’, Semigroup Forum, 63 (2001), 387-395.

Vernitski, A. with D. McAlister and B. Stephens, ‘Embedding of the symmetric inverse semigroup into a two-generated inverse semigroup’, Proceedings of the Edinburgh Mathematical Society, 45(2002), 1-4.

Vernitski, A., ‘Finite quasivarieties and recursive conditions’, Studia Logica, vol. 78 (2004), 337-348.

Vernitski, A., ‘Can unbreakable mean incomputable?’, The Computer Journal, vol. 49 (2006), 108-112.

Vernitski, A., ‘A generalisation of symmetric inverse semigroups', Semigroup Forum, 75(2007), 417-426.

Vernitski, A., ‘On using the join operation to define classes of algebras', Communications in Algebra, 36(2008), 1088-1096.

Vernitski, A., Ordered and J-trivial semigroups as divisors of semigroups of languages, International Journal of Algebra and Computation, 18(2008) 1223-1229.

Vernitski, A., Inverse subsemigroups and classes of finite aperiodic semigroups, Semigroup Forum, 78 (2009), 486-497.

Vernitski, A., One-side Nielsen transformations in free groups, International Journal of Algebra and Computation, vol. 19 (2009) 855–871.

Vernitski, A., with Z. Juhasz, Filters in (quasiordered) semigroups and lattices of filters, Communications in Algebra, 39 (11), 4319-4335, 2011.

Vernitski, A., with Z. Juhasz, Using filters to describe congruences and band congruences of semigroups, Semigroup Forum, Vol. 83, 2011, pp. 320-334..

Vernitski, A. and Pyatkin, A., Astral graphs (threshold graphs), scale-free graphs and related algorithmic questions, Journal of Discrete Algorithms, 12, 24-28, 2012.

Vernitski, A. and Peng, S. and Nejabati, R. and Escalona, E. and Simeonidou, D. and Anastasopoulos, M. and Georgakilas, K. and Tzanakaki, A., Performance modelling and analysis of dynamic virtual optical network composition, Optical Network Design and Modeling (ONDM), 2012 16th International Conference on, 1-5, 2012.

Refereed Conference Papers

The semigroups of order-preserving mappings: quest for quasi-identities, Proceedings of the Conference on Semigroups and Applications in St. Andrews, 1998, 229-238.

The distance between classes of groupoids and an application to confidentiality (refereed extended abstract, with P. M. Higgins and C. J. Saker), International Algebraic Conference, Ekaterinburg, Russia, 2005.

• Linked with the School of Computer Science and Electronic Engineering.
• My logical games on the Department's web site.
• A research workshop "Algorithms, Computability, Combinatorics, Algebra" that was held on Thursday 16th August 2007.
• A research workshop "SAGE 08" which was co-organised by Dr Gerald Williams in the Department.
• The Crypto Group research group founded by me was active in 2003-2005.