Here are the titles and abstracts of the seminars which were held in 2011:

Jędrzej Sadowski**Definitions of the N-almost periodic functions**

We will show differend ways to define N-almost periodic functions and prove their equivalence.

Marcin Wachowiak**Applications of Theorem Hopf-Lefschetz fixed point**

(Continuation of the 2011-11-22 Nonlinear Seminar and 2011-11-29 Nonlinear Seminar and 2011-12-06 Nonlinear Seminar).

Marcin Wachowiak**Applications of Theorem Hopf-Lefschetz fixed point**

(Continuation of the 2011-11-22 Nonlinear Seminar and 2011-11-29 Nonlinear Seminar).

Marcin Wachowiak**Applications of Theorem Hopf-Lefschetz fixed point**

(Continuation of the 2011-11-22 Nonlinear Seminar).

Marcin Wachowiak**Applications of Theorem Hopf-Lefschetz fixed point**

In the first part of the discussion we introduce the necessary concepts and facts about the homology and cohomology, then we will discuss the Hopf-Lefschetz theorem and its applications

Marcin Borkowski, Piotr Maćkowiak (Poznań University of Economics)**On superposition of formal power series**

(Continuation of the 2011-11-08 Nonlinear Seminar)

Marcin Borkowski, Piotr Maćkowiak (Poznań University of Economics)**On superposition of formal power series**

We will present a new proof of a criterion for existence of superposition of formal power series given by Gan and Knox. We will also give some properties concerning the behavior of such series on the boundary of their convergence circle.

Adam Burchardt**Schauder fixed point, revisited**

(Continuation of the 2011-10-18, 2011-10-11 and 2011-10-04 nonlinear seminars).

Adam Burchardt**Schauder fixed point, revisited**

(Continuation of the 2011-10-11 and 2011-10-04 nonlinear seminars).

Adam Burchardt**Schauder fixed point, revisited**

(Continuation of the 2011-10-04 Nonlinear Seminar).

Adam Burchardt**Schauder fixed point, revisited**

During the seminar we are going to discuss the following generalization of the classical Schauder fixed point theorem due to R. Cauty:

*Let be a convex subset of a topological vector space . If is a continuous function such that is contained in a compact subset of , then has a fixed point.*

The talk is based on the following paper: R. Cauty, *Solution du problème de point fixe de Schauder*, Fund. Math. **170** (2001), 231-246.

Marcin Borkowski**Some remarks on convergence of power series at the boundary of the convergence circle**

We will present a theorem concerning convergence of power series—together with all its derivatives—at the boundary of the convergence circle.

Joanna Wypych**On superposition of formal power series**

(Continuation of the 2011-05-10 and 2011-05-17 seminars)

Joanna Wypych**On superposition of formal power series**

(Continuation of the 2011-05-10 Nonlinear Seminar)

Joanna Wypych**On superposition of formal power series**

In the beginning we will present basic definitions concerning formal power series and their properties. Then we will discuss two theorems on superposition of such series. The talk is based on a paper *On composition of formal power series* by Xiao-Xiong Gan and Nathaniel Knox.

Piotr Kasprzak**On the equivalent characterizations of Levitan almost periodic functions**

(Continuation of the 2011-02-22 Nonlinear Seminar)

Marcin Borkowski**On formal power series**

(Continuation of the 2010-12-21 and 2011-03-15 Nonlinear Seminar seminars)

Adam Nawrocki**Examples of Henstock-Kurzweil integrable functions**

We will present methods of proving Henstock-Kurzweil integrability of real functions.

Piotr Kasprzak**On a new class of almost periodic functions**

During the talk not only will we define the so-called quasi almost automorphic functions but also we will prove some basic properties of these functions.

Joanna Wypych**Formal power series**

(Continuation of the 2011-01-18 and 2011-03-08 seminars)

Marcin Borkowski**On formal power series**

(Continuation of the 2010-12-21 Nonlinear seminar).

Joanna Wypych**Formal power series**

(Continuation of the 2011-01-18 Nonlinear Seminar)

**On the dual space to the space of Henstock-Kurzweil integrable functions**

During the talk we will present the result of Alexiewicz which gives a characterization of the dual space to the space of Henstock-Kurzweil integrable functions defined on a bounded interval.

Piotr Kasprzak**On the equivalent characterizations of Levitan almost periodic functions**

Joanna Wypych**Formal power series**

We will discuss basic properties of formal power series and the Krull topology. Among others, we will present theorems on the distributive laws and invertibility of a series. The talk will be based on the book by S. Łojasiewicz and J. Stasica *Formal analysis and analytic functions* (in Polish).

Marcin Wachowiak**A fixed point theorem for mappings satisfying the interior condition**

(Continuation of the 2010-11-23, 2010-11-30 and 2010-12-07 Nonlinear seminars).

Wojciech Jankowski**On a certain fixed point theorem for discontinuous mappings**