**Eliana Bariga**will speak about Definably compact semialgebraic groups over real closed fields.

__Abstract:__

Semialgebraic groups over a real closed field can be seen as a generalization of the semialgebraic groups over the real field, and also as a particular case of the groups definable in an o-minimal structure.

In this talk, I will offer a description of the definably connected semialgebraic groups over a real closed field R through the study of their o-minimal universal covering groups and of their relationship with the R-points of some connected R-algebraic group.

I will show that the o-minimal universal covering group of a definably compact definably connected group definable in a sufficiently saturated real closed field R is an open subgroup of the o-minimal universal covering group of the R-points H (R) of some Zariski-connected R-algebraic group H.

This research is part of my PhD thesis at the University of Haifa, Israel and Universidad de los Andes, Colombia.

## Date:

Wed, 11/12/2019 - 11:00 to 13:00

## Location:

Ross building - Room 63