Clearing 2021

Dr Alexei Vernitski

Senior Lecturer
Department of Mathematical Sciences
Dr Alexei Vernitski
  • Email

  • Telephone

    +44 (0) 1206 873024

  • Location

    STEM 5.15, Colchester Campus



My current research is in 1) mathematics education, especially increasing motivation of learners of mathematics; 2) using reinforcement learning, deep neural networks and universal algebra to study knot theory, with possible applications in computer vision. Previously, most of my research was in universal algebra. My PhD is in semigroup theory. Currently I supervise PhD students in mathematics education. I supervised one PhD student (Dr Zsofia Juhasz) in universal algebra (semigroup theory). Also I conducted research in applications of mathematics to computer science, mostly on a method of compressing data called Bloom filters. I supervised two PhD students in this area (Dr Gokce Caylak Kayaturan and Dr Laura Carrea). Before starting work at Essex, I worked as a programmer in the financial sector and as a lecturer in computer science.

Research and professional activities

Research interests

Applying algebra (especially semigroups) to study knots, graphs etc.

My plans include 1) applying semigroups to study bounded rationality and, in particular, the negotiations scenario known as the repeated prisoner's dilemma; 2) using algebra to study certain classes of knots related to so-called rational tangles.

Key words: group theory
Open to supervise

Mathematical education; in particular, increasing motivation of learners of mathematics

Inspired by Carol Dweck's growth mindsets and Jo Boaler's mathematical mindsets, I research how this creative and nurturing approach can help learners of mathematics.

Key words: teaching
Open to supervise

Machine learning in mathematics; reinforcement learning applied to knot theory

One of my current interests is combining mathematics and new machine learning technology to enable the computer to manipulate mathematical objects.

Key words: machine learning
Open to supervise

Teaching and supervision

Current teaching responsibilities

  • Calculus (MA101)

  • Matrices and Complex Numbers (MA114)

  • Discrete Mathematics (MA181)

Previous supervision

Gokce Caylak
Gokce Caylak
Thesis title: Representing Shortest Paths in Graphs Using Bloom Filters Without False Positives and Applications to Routing in Computer Networks
Degree subject: Mathematics
Degree type: Doctor of Philosophy
Awarded date: 29/6/2018
James Christopher Waumsley
James Christopher Waumsley
Thesis title: An Analysis of Various Heuristic Approaches for Satisfying Routing Requests in Networks
Degree subject: Mathematics
Degree type: Master of Science (by Dissertation)
Awarded date: 22/9/2014
Laura Carrea
Laura Carrea
Thesis title: Optimised Probabilistic Data Structures for Forwarding in Information Centric Networking
Degree subject: Computing and Electronic Systems
Degree type: Doctor of Philosophy
Awarded date: 26/7/2013


Journal articles (28)

Carrea, L., Vernitski, A. and Reed, MJ., Yes-no Bloom filter: A way of representing sets with fewer false positives

Higgins, PM. and Vernitski, A., A new formulation of the semigroup of orientation-preserving and orientation-reversing mappings

Khan, A., Lisitsa, A. and Vernitski, A., Experimental Mathematics Approach to Gauss Diagrams Realizability

Daly, I., Bourgaize, J. and Vernitski, A., (2019). Mathematical mindsets increase student motivation: Evidence from the EEG. Trends in Neuroscience and Education. 15, 18-28

East, J. and Vernitski, A., (2018). Ranks of ideals in inverse semigroups of difunctional binary relations. Semigroup Forum. 96 (1), 21-30

Vernitski, A., Tunsi, L., Ponchel, C. and Lisitsa, A., (2018). Dihedral semigroups, their defining relations and an application to describing knot semigroups of rational links. Semigroup Forum. 97 (1), 75-86

Vernitski, A., (2017). Describing semigroups with defining relations of the form xy=yz xy and yx=zy and connections with knot theory. Semigroup Forum. 95 (1), 66-82

Juhász, Z. and Vernitski, A., (2016). Semigroups with operation-compatible Green’s quasiorders. Semigroup Forum. 93 (2), 387-402

Pride, SJ., Vernitski, A., Wong, KB. and Wong, PC., (2016). Conjugacy and Other Properties of One-Relator Groups. Communications in Algebra. 44 (4), 1588-1598

Yang, X., Vernitski, A. and Carrea, L., (2016). An approximate dynamic programming approach for improving accuracy of lossy data compression by Bloom filters. European Journal of Operational Research. 252 (3), 985-994

Carrea, L., Vernitski, A. and Reed, M., (2014). Optimized hash for network path encoding with minimized false positives. Computer Networks. 58 (1), 180-191

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

Juhász, Z. and Vernitski, A., (2011). Using filters to describe congruences and band congruences of semigroups. Semigroup Forum. 83 (2), 320-334

Juhasz, Z. and Vernitski, A., (2011). Filters in (Quasiordered) Semigroups and Lattices of Filters. Communications in Algebra. 39 (11), 4319-4335

VERNITSKI, A., (2009). ONE-SIDE NIELSEN TRANSFORMATIONS IN FREE GROUPS. International Journal of Algebra and Computation. 19 (07), 855-871

Vernitski, A., (2009). Inverse subsemigroups and classes of finite aperiodic semigroups. Semigroup Forum. 78 (3), 486-497

Vernitski, A., (2009). One-side Nielsen transformations in free groups. International Journal of Algebra and Computation. 19 (07), 855-871

VERNITSKI, A., (2008). ORDERED AND $\mathcal{J}$-TRIVIAL SEMIGROUPS AS DIVISORS OF SEMIGROUPS OF LANGUAGES. International Journal of Algebra and Computation. 18 (07), 1223-1229

Vernitski, A., (2008). On Using the Join Operation to Define Classes of Algebras. Communications in Algebra. 36 (3), 1088-1096

Vernitski, A., (2008). Ordered and J-trivial semigroups as divisors of semigroups of languages. International Journal of Algebra and Computation. 18 (07), 1223-1229

Vernitski, A., (2007). A Generalization of Symmetric Inverse Semigroups. Semigroup Forum. 75 (2), 417-426

Vernitski, A., (2006). Can Unbreakable Mean Incomputable?. The Computer Journal. 49 (1), 108-112

Vernitski, A., (2005). Russian revolutionaries and English sympathizers in 1890s London. Journal of European Studies. 35 (3), 299-314

Vernitski, A., (2004). Finite quasivarieties and self-referential conditions. Studia Logica. 78 (1-2), 337-348

McAlister, DB., Stephen, JB. and Vernitski, AS., (2002). Embedding In in a 2-generator inverse subsemigroup of In+2. Proceedings of the Edinburgh Mathematical Society. 45 (1), 1-4

McAlister, DB., Stephen, JB. and Vernitski, AS., (2002). EMBEDDING ℐn IN A 2-GENERATOR INVERSE SUBSEMIGROUP OF ℐn+2. Proceedings of the Edinburgh Mathematical Society. 45 (1), 1-4

Vernitski, A., (2002). Women work, men muse: Gender roles in Platonov's articles and short stories. Essays in Poetics. 27, 162-173

Vernitski, AS., (2001). Studying semigroups of mappings using quasi-identities. Semigroup Forum. 63 (3), 387-395

Books (1)

(2004). Russian and Soviet Film Adaptations of Literature, 1900-2001. Routledge. 020301104X. 9780203011041

Book chapters (1)

Lisitsa, A. and Vernitski, A., (2017). Automated Reasoning for Knot Semigroups and  $$\pi $$ π -orbifold Groups of Knots. In: Mathematical Aspects of Computer and Information Sciences. Springer International Publishing. 3- 18. 9783319724522

Conferences (10)

Khan, A., Lisitsa, A. and Vernitski, A., (2021). Gauss-Lintel, an Algorithm Suite for Exploring Chord Diagrams

Fish, A., Lisitsa, A. and Vernitski, A., (2018). Visual Algebraic Proofs for Unknot Detection

Fish, A., Lisitsa, A. and Vernitski, A., (2018). Towards human readability of automated unknottedness proofs

Karapetyan, D. and Vernitski, A., (2017). Efficient adaptive implementation of the serial schedule generation scheme using preprocessing and bloom filters

Kayaturan, GC. and Vernitski, A., (2017). Encoding Shortest Paths in Triangular Grids for Delivery Without Errors

Kayaturan, GC. and Vernitski, A., (2016). Routing in hexagonal computer networks: How to present paths by Bloom filters without false positives

Kayaturan, G. and Vernitski, A., (2016). A Way of Eliminating Errors When Using Bloom Filters for Routing in Computer Networks

Krol, K., Papanicolaou, C., Vernitski, A. and Sasse, MA., (2015). “Too Taxing on the Mind!” Authentication Grids are not for Everyone

Vernitski, A., (2013). Authentication grid

Shuping Peng, Nejabati, R., Escalona, E., Simeonidou, D., Anastasopoulos, M., Georgakilas, K., Tzanakaki, A. and Vernitski, A., (2012). Performance modelling and analysis of dynamic virtual optical network composition

Reports and Papers (1)

Kayaturan, GC. and Vernitski, A., (2018). Encoding shortest paths in graphs assuming the code is queried using bit-wise comparison

Other (2)

Vernitski, A., (2015).An invariant of scale-free graphs,University of Essex

Vernitski, A., (2015).A simple technique for choosing and managing secure passwords: passwords with a random on-paper part,University of Essex, Department of Mathematical Sciences

Grants and funding


Machine learning for recognising tangled 3D objects

Leverhulme Trust


Reducing socio-economic inequalities in HE participation: the role of information, peers and mindset

Office for Students


Support of collaborative research

London Mathematical Society

+44 (0) 1206 873024


STEM 5.15, Colchester Campus