Oleg Pikhurko (University of Warwick) will give an online mini-course on limits of discrete structures. The course is intended for Ukrainian students, both undergraduate and graduate, as well as everybody who is interested in related topics. The prerequisites are: basic notions and results about graphs, measure spaces and the Lebesgue integral. Lectures will be given in English.

In the limit approach to combinatorial problems, one defines the appropriate distance between any two finite discrete structures and takes the completion of the obtained metric space. The new added elements, which can be viewed as "limits" of discrete structures, can often be represented by analytical objects, allowing us to use tools from measure theory, probability, functional analysis, etc. Conversely, this connection also opens a way to apply combinatorial techniques to some analytic questions such as, for example, constructive circle squaring (i.e. partitioning a disc in the plane so that the obtained pieces can be rearranged to partition a square). This mini-course will provide an introduction to this area, concentrating on graphons and graphings, the two main limit objects for graphs.

Oleg Pikhurko has been a professor of Mathematics at the University of Warwick (UK) since 2011. He graduated from the Cambridge University in 2000, with his undergraduate received at Lviv State University in 1995. Professor Pikhurko is one of the leading experts worldwide in limits of discrete structures, analytic and probabilistic methods in combinatorics, as well as extremal and probabilistic combinatorics.