# Model Theory Seminar

### School of Mathematics, University of Leeds

All the seminars will be in MALL 2 and will be on Tuesdays at 2pm, with the exception of week 3 (see below).

### Autumn Term 2013

Week 3, Thursday 17th October at 1.30pm
Immi Halupczok
Model theory of valued fields and Poincaré series

This is the second talk of this little series. This time, I will speak about the model theory of henselian valued fields. More precisely, I will explain what kind of quantifier elimination one has and what this implies. Moreover, I'll present the Poincaré series associated to definable sets in $\mathbb{Q}_{p}$. A famous result from the 80s is that this Poincaré series is a rational function. This can be considered as a partial understanding of definable sets up to isometry.

I will also say a few words about how this is related to questions from Number Theory.