**Department of Mathematics**

**"****Concepts of Aggregation for Evolution Equations in
Banach Spaces****"**

**FATİHCAN ATAY**

**(BİLKENT UNIVERSITY)**

** Abstract:** This talk
deals with exact reduction methods for dynamical systems, namely, the possibility
of projecting the dynamics onto a smaller state space in which a self-contained
dynamical description exists. The projection is also called lumping,
aggregation, or reduction in various contexts, for example in Markov chains,
and connects micro to macro in multi-level systems. As a first setting we
consider systems whose evolution is described by bounded or unbounded linear
operators on Banach spaces and obtain conditions for lumpability using
semigroup theory. Time permitting, we will also present the problem from a dual
space point of view in the language of sun dual spaces. We will give several
examples for applications.

**Date: ****Thursday, October 20, 2016**

**Time: ****13:40**

**Place: ****Mathematics Seminar,
SA-141**

Tea and cookies will be served before the
seminar.