# Department of Non-Linear Analysis and Applied Topology

Welcome to the website of the Department of Non-Linear Analysis and Applied Topology at the Faculty of Mathematics and Computer Science of Adam Mickiewicz University in Poznan.

The Department of Non-Linear Analysis and Applied Topology was established on January 01, 2020.

The department staff works on the problems in the following fields: non-linear analysis, convex analysis and applied topology.

The issues of broadly defined non-linear analysis are examined. The topics related to non-linear differential and integral equations (e.g. Hammerstein integral equations, Volterra integral equations or fractional equations) in terms of the existence and the uniqueness of the solutions in different classes (e.g. in the classes of almost periodic functions of different types - Bohr’s, Bochner’s, Stiepanow’s, Lewitan’s types – or in the classes of bounded variation functions in the sense of Jordan and Young) and the topological properties of solution sets (particularly so-called Aronszajn type theorems) are discussed. Special attention is also devoted to some issues of operator theory (particularly superposition operators) and of formal analysis. Moreover there are questions related to the theory of fixed point of functions and multifunctions and selected issues of general topology (hyperconvex spaces, R-tress, measures of non-compactness etc.) under consideration.

The subject of the research also concerns the problems related to the algebraic, analytic, geometric and topological properties of pairs of convex and closed sets (e.g. the property of translation, set shadowing, Salle’s sets etc.), of minimal pairs (in terms of the existence and the uniqueness with accuracy of translation) and of Minkowski-Radström-Hörmander’ spaces over any linear-topological Hausdorff’s space as well as the quasidifferential calculus (e.g. sublinear functions and their differences). It also includes the applications of Minkowski-Radström-Hörmander’ spaces, e.g. to the theory of multifunctions or to the description of crystal growth.

Since 2012 the group of Professor Marzantowicz has carried out research with the use of applied topology. In particular: on different versions of Bouring-Yang theorem and related topics but also the theory of topological complexity as geometric model of robot motion. We introduced and examined the following generalisations of topological complexity: invariant complexity, effective complexity and efficient complexity. The group’s research effort is also focused on the issues related to applied topology, that is: optimisation, group calculus, computer algebra, high dimensional manifold topology, surgery theory and covariant surgery theory, knot symmetry and applying computer methods when solving problems of theoretical topology. Applications of Reeb’s graph to algebra and analysis are also a point of interest for this group.

**Non-linear analysis **

Date: Tuesdays, 16:00-17:30*Currently the seminar is held online.*

**Geometry and topology **

Date: Wednesdays, 13:30-15:00

Room: B1-37

**SONATASeminar on non-linear analysis and its applications **

Date: Fridays, 11:00-13:00 (once per month)

Room: B1-37