Topic:
There's a theorem by Denef (in: "the rationality of the Poincaré series associated to the p-adic points on a variety") which states that a quite big class of local zeta functions (somehow defined within $\mathbb{Q}_p$) are rational functions. There also exists a version of the theorem describing how the zeta functions depend on $p$. This has in particular been applied to obtain results about various zeta functions associated to groups, counting e.g., subgroups of given indices or representations of given dimensions. The goal of this seminar is to understand these things. In particular, we want to understand the paper by Hrushovski-Martin-Rideau.
Room:
usually 25.22.03.73
Dates and times:
Mon 11.9., 15:00: Basics of model theory (Alejandra)
Wed 13.9., 16:00: Quantifier elimination and Elimination of imaginaries (Matteo)
Fri 15.9., 15:00: Model theory of valued fields (Benjamin)
Mon 18.9., 14:00: Examples of elimination of imaginaries (David)
Wed 20.9., 15:00: Elimination of imaginaries in algebraically closed valued fields (Immi)
Thu 21.9., 15:00: Elimination of imaginaries in algebraically closed valued fields: the proof (Immi)
Fri 22.9., 15:00: Elimination of imaginaries in $\mathbb{Q}_p$ (Florian)
Wed 27.9., 15:00: Rationaliy results (Matteo)
Thu 5.10., 15:00, room 25.22.02.81: Applications to group zeta functions (Benjamin)