Academic Staff

Dr Alexei Vernitski PhD

Position in departmentSenior Lecturer in Pure Mathematics/Computer Science
Staff positionExams Officer (second and final year)
Telephone01206 873024

My PhD is in universal algebra (more precisely, semigroup theory). Before starting my work at Essex, I worked as a programmer in the financial sector and as a lecturer in computer science.

Most of my research is in algebra. I supervised one PhD student (Dr Zsofia Juhasz) in semigroup theory. Within algebra, currently I concentrate on algebraic techniques in knot theory. I introduced and study new concepts of knot semigroups and braid semigroups.

Also I conduct research in applications of mathematics to computer science. Currently my research in computer science concentrates on a method of compressing data called Bloom filters. Our team published several papers on improving performance of Bloom filters. I supervise one PhD student in this area (Gokce Caylak). 

Current research

My current research (updated March 2016) concentrates on:

  • Generalisations of the Bloom filter data type. This is a computer science research developing new ways of compressing data.
  • Knot semigroups. This is a theoretical research developing new algebraic techniques for knot theory.
  • Mathematical mindsets. This is teaching mathematics using ideas of mindset theory.

Research interests

In general, my research interests include

  • Semigroup theory, graph theory and other parts of discrete mathematics
  • Applications of discrete mathematics to computer science
  • Teaching mathematics

Teaching responsibilities

I teach modules in mathematics (Linear Algebra, Analysis) and computer science (Computer Security)


Refereed Journal Papers

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.

Vernitski, A. and L. Carrea, M. J. Reed, Optimized hash for network path encoding with minimized false positives, Computer Networks, 2014.

An Approximate Dynamic Programming Approach for Improving Accuracy of Lossy Data Compression by Bloom Filters, X. Yang, A. Vernitski, L. Carrea - European Journal of Operational Research, 2015

Conjugacy and Other Properties of One-Relator Groups, by S. J. Pride, A. Vernitski, K. B. Wong and P. C. Wong, Communications in Algebra, 2016.

Vernitski, A., with Z. Juhasz, Semigroups with operation-compatible Green’s quasiorders, Semigroup Forum, accepted.

[V1] A Way of Eliminating Errors When Using Bloom Filters for Routing in Computer Networks, G. Çaylak Kayaturan and Alexei Vernitski, ICN 2016, The Fifteenth International Conference on Networks, 52-57.

Vernitski, A., Describing semigroups with defining relations of the form xy = yz and yx = zy and connections with knot theory, Semigroup Forum, accepted.

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.

Additional information

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