Welcome to the home page of the **Optimization and Control Theory Department** of the Faculty of Mathematics and Computer Science of the Adam Mickiewicz University in Poznań.

The staff of the Department conduct research in selected problems of two domains: convex and nonlinear analysis. In particular, algebraic, analytic, geometrical and topological properties of **pairs of closed convex sets** are investigated, among others:

- translation property,
- shadowing of sets,
- Sallee sets,
- minimal pairs,
- Minkowski-Radström-Hörmander space with applications, and
- quasidifferential calculus

are recurrent topics.

Another direction of research is **nonlinear analysis**. Among the topics discussed are:

- differential and integral equations (in particular, Hammerstein, Volterra and fractional order equations; existence and uniqueness of solutions in various classes of functions, like almost periodic functions of different types or functions of bounded variation, also of different types; topological properties of solution sets, in particular Aronszajn type theorems);
- single- and multivalued fixed point theorems;
- selected topics between analysis and general topology (among others, hyperconvex spaces, R-trees, measures of noncompactness);
- some problems from operator theory (in particular, the superposition operator).

This year two books authored or coauthored by dr Marcin Borkowski were publushed. In June, a textbook on LaTeX entitled LaTeX – a cookbook (in Polish, unrelated to other similarly entitled book), coauthored by mgr Bartłomiej Przybylski, was published by the Polish Mathematical Society. The book is available electronically under the Creative Commons BY-NC-SA license.

In September, the Juliusz P. Schauder Center for Nonlinear Studies in Toruń published a book entitled *Theory of Hyperconvex Metric Spaces – a Beginner's Guide*, also by Marcin Borkowski. The book is part of the Lecture Notes in Nonlinear Analysis series.

From 29 September to 2 October 2015 dr hab. Daria Bugajewska visited the Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic.

She delivered a lecture entitled *On nonlinear operators in the spaces of functions of bounded variations*.

From 14 to 18 September 2015 prof. UAM dr hab. Dariusz Bugajewski, dr Marcin Borkowski, dr Piotr Kasprzak and mgr Jędrzej Sadowski took part in the VII Symposium on Nonlinear Analysis conference in Toruń, Poland.

Prof. Dariusz Bugajewski delivered a talk entitled *On some classes of almost periodic functions*.

Dr Marcin Borkowski delivered a talk entitled *On certain properties of diversities*.

Dr Piotr Kasprzak delivered a talk entitled *Nonlinear superposition operators in -spaces*.

Mgr Jędrzej Sadowski delivered a talk entitled *Nonautonomous superposition operators in the spaces of functions of Lambda bounded variation*.