Work number - M 37 AWARDED
Aseriesofworksconsistsof2 academictextbooks, 12scientific articles and7conference abstracts published for the last 5years.
Aseriesofworksisdevotedtothestudyofalgebraicandgeometricobjectsrelatedtofiniteautomata,andtoapplications of obtained results in other areas of mathematics. Several algorithmic problems concerning groups generated by automata were solved, in particular, it was proved that the word problem in groups generated by polynomial automata is solvable in subexponential time. Algebraic properties of groups generated by polynomial automata were studied, in particular, a question from Kourovka notebook was answered. The measure theory on limit spaces of automaton groups was developed, and fundamental results about the associated limit dynamical system were proved. These results have been applied to problems in fractal geometry on the Lebesgue measure of self-affine tiles.Several results onaction graphs offinite automata were derived, inparticular, theconjectureofV.Nekrashevych on the growth of action graphs of polynomial automata was confirmed. It is shown that action graphs ofautomata may produce afamily ofex panding graphs, which have numerous applicationsin computer science.
The complete number of author’s publications: 25scientific articles(including 11 articles in foreign journals), 2academic textbooks, 13conference abstracts.