Johan Lindberg: Equivariant sheaves and models of first-order theories

I will give an introduction to certain results in topos theory with focus on the representation theorems for Grothendieck toposes by Joyal and Tierney on the one hand and Butz and Moerdijk on the other. I will then discuss some applications of the latter to models of (fragments of) first-order theories and further properties of toposes of the so-called equivariant sheaves on topological categories.