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).

From 2 to 5 August 2016 prof. UAM dr hab. Dariusz Bugajewski took part in the *31st Summer Conference on Topology and Applications* in Leicester, UK, where he delivered a talk entitled *Basic open problems in the theory of nonlinear superposition operators in BV spaces*.

From 23.05.2016 to 27.05.2016 dr Daria Bugajewska and dr Piotr Kasprzak visited Universita della Calabria, Cosenza, Italy, where they conducted research and delivered lectures for Ph.D. students concerning selected topics in nonlinear analysis.

Dr Daria Bugajewska gave a mini-course entitled *Nonlinear operators in the spaces of functions of bounded variation of various types and their applications*.

Dr Piotr Kasprzak gave a mini-course entitled *Eigenvalues of nonlinear operators with applications to integral and differential equations*.

The courses for Ph.D. students and young researchers were delivered in the frame of the Erasmus+ Programme.

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.