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Mikhail V. Volkov

Mikhail V. Volkov
https://csseminar.freemath.ch/volkov/
Ural Federal University, Ekaterinburg, Russian Federation

Institute of Natural Sciences and Mathematics

Department of Algebra and Fundamental Informatics, Сhief Researcher

PhD (Phys., Math.), Professor

ScopusID: 7101793575

ResearcherID: F-1407-2014

ORCID ID: 0000-0002-9327-243X

Scientific interests: Associative rings; Automata and formal languages; Combinatorics on words; Computational complexity; Group representations; Non-associative rings; Semigroups; Universal algebra

Scientific achievements: The finite basis problem and the structure of variety lattices for semigroups and associative rings have been extensively investigated. In particular, Evans’s problem, giving a classification of semigroup varieties with modular subvariety lattice, has been solved. In the theory of synchronizing automata, which forms an important class of controllable discrete system, new estimates have been obtained and the investigated computational complexity of several problems has been studied. Several influential survey articles (some of them are written with co-authored) become standard references for  respective areas.

Main publications:

  1. Shevrin L.N., Volkov M.V. Identities of semigroups // Soviet Math. (Iz. VUZ), 1985. Vol. 29, no. 11. P. 1–64.  Translation in Russian: Izv. Vyssh. Uchebn. Zaved. Mat. 1985. No. 11. P. 3–47.
  2. Volkov M.V. The finite basis problem for finite semigroups // Sci. Math. Jpn. 2001,  Vol. 53, no. 1. P. 171–199.
  3. Almeida J., Margolis S., Steinberg B., Volkov M. Representation theory of finite semigroups, semigroup radicals and formal language theory // Trans. Amer. Math. Soc., 2009. Vol. 361, no. 3. P. 1429–1461. DOI: 10.1090/S0002-9947-08-04712-0 
  4. Volkov M.V. Synchronizing automata and the Černý conjecture // Language and Automata Theory and Applications. LATA 2008. Lecture Notes in Computer Science. Vol. 5196. Springer, Berlin, 2008. DOI: 10.1007/978-3-540-88282-4_4
  5. Volkov M.V. The finite basis property of varieties of semigroups // Math. Notes, 1989. Vol. 45, no. 3. P. 187–194. DOI: 10.1007/BF01158553 Translation in Russian: Mat. Zametki, 1989. Vol. 45, no. 3, P. 12–23. 
  6. Almeida J., Volkov M.V. The gap between partial and full // Internat. J. Algebra Comput., 1998. Vol. 8, no. 3. P. 399–430. DOI: 10.1142/S0218196798000193
  7. Almeida J., Volkov M.V. Subword complexity of profinite words and subgroups of free profinite semigroups // Internat. J. Algebra Comput., 2006. Vol. 16, no. 2. P. 221–258. DOI: 10.1142/S0218196706002883
  8. Shevrin L.N., Vernikov B.M., Volkov M.V. Lattices of semigroup varieties //  Russian Math. (Iz. VUZ), 2009. Vol. 53, no. 3. P. 1–28. DOI: 10.3103/S1066369X09030013 Translation in Russian: Izv. Vyssh. Uchebn. Zaved. Mat. 2009, no. 3, p. 3–36.
  9. Lee E.W.H., Volkov M.V. On the structure of the lattice of combinatorial Rees-Sushkevich varieties // Semigroups and formal languages, World Sci. Publ., Hackensack, NJ, 2007. P. 164–187.  DOI: 10.1142/9789812708700_0012
  10. Lee E.W.H., Volkov M.V. Limit varieties generated by completely 0-simple semigroups // Internat. J. Algebra Comput., 2011. Vol. 21, no. 1-2, P. 257–294. DOI: 10.1142/S0218196711006169