# Colloquium: Tuesday January 17, 2023. Speaker: Yatir Halevi (Haifa). Title: “Definably semisimple groups interpretable in p-adically closed fields”.

Our next Math colloquium talk will be in person next week on the 17th of January, in room 614, Science & Education building.

A zoom link for our meetings is:

https://us02web.zoom.us/j/83337601824

Speaker : Yatir Halevi (Haifa)

Date : Tuesday, 17th of January, 2023.

Time : 14:00

Title: Definably semisimple groups interpretable in p-adically closed fields.

Abstract: Identifying and characterizing the groups and fields one can define in

various first order structures has had multiple applications within
model theory and in other branches of mathematics. We focus here on
$p$-adically closed fields.

Let $\mathbb{K}$be a $p$-adically closed field (for example, $\mathbb{Q}_p$). We will discuss some recent results regarding interpretable groups and interpretable fields in $\mathbb{K}$:

1) Let $G$ be an interpretable group. If $G$is definably semisimple (i.e.
$G$has no definable infinite normal abelian subgroups) group, then
there exists a finite normal subgroup $H$such that $G/H$is definably
isomorphic to a $\mathbb{K}$-linear group.

2) Let $\mathbb{F}$be an interpretable field. Then $\mathbb{F}$ is definably isomorphic to a finite extension of $\mathbb{K}$.

No knowledge in model theory will be assumed, but some basic knowledge
in logic will help. (Joint work with Assaf Hasson and Ya’acov Peterzil)

Kol tuv,