English language proficiency: C1

Supervisor’s research interests:

In algebra, supervisor’s research focuses on one of the major open problems on the edge between the semigroup theory and the universal algebra: Tarski’s problem for finite semigroups. This fundamental problem reveals surprising connections to the modern computer science, in particular, to the complexity theory.

In computer science, supervisor’s research is related to a longstanding conjecture in the theory of finite automata: the Černý conjecture. It deals with so-called synchronizing automata that are of both theoretical interest and practical value.

Supervisor’s specific requirements to prospective PhD students:

• For algebraic topics: basic knowledge of semi group theory, universal algebra, and computational complexity
• For topics in automata theory: knowledge of some basics of automata theory, formal languages, and computational complexity
• Programming skills will be an advantage.