17:00
I will speak about the CBP (canonical base property) for types of finite SU-rank. This property first appears in a paper by Pillay and Ziegler, who show that it holds for types of finite rank in differentially closed fields of characteristic 0, as well as in existentially closed difference fields. It is unknown whether this property holds for all finite rank types in supersimple theories. I will first recall the definition of a canonical base, and give some natural examples. I will then talk about a reduction of the problem (which allows one to extend the Pillay-Ziegler result to existentially closed fields of any characteristic), and finally derive some consequences of the CBP, in particular the UCBP, thus answering a question of Moosa and Pillay. If time permits, I will show an application of these results to difference
fields.