Bohr compactifications of groups and rings

Seminarium: 
Teoria modeli
Osoba referująca: 
Grzegorz Jagiella (University of Wrocław)
Data spotkania seminaryjnego: 
środa, 9. Październik 2019 - 16:15
Sala: 
603
Opis: 
(joint work with Jakub Gismatullin and Krzysztof Krupiński) Definable topological dynamics shows that the classical Bohr compactification of a discrete group $G$ can be seen as a special case of "definable" Bohr compactifications. In turn, the definable Bohr compactification of a definable group can be described in terms of its model-theoretic components. The calculation of such components for some classical matrix groups, such as $UT_n(R)$ for a commutative, unital ring $R$, naturally leads to the development of ring analogues to the components of groups. In my talk, I will give the precise definitions of ring components and develop their preliminary theory. I will then describe the components of the groups $UT_n(R)$ and use them to give the precise description of their definable Bohr compactifications, including classical Bohr compactifications of the groups $UT_n(\mathbb{Z})$, e.g. the discrete Heisenberg group.