Thursday 25rd February, 2-3 pm

Speaker: Juan VIU SOS (Madrid)

**Title**: On zeta functions, weighted blow-ups and some applications for quasi-homogeneous surface singularities.

**Abstract**: The Denef-Loeser topological and motivic zeta functions are analytic invariants of holomorphic map germs $f:{\mathbb C}^n\to {\mathbb C}$, which are usually computed from embedded resolutions of $f$.

They codify some information about the topology of the Milnor fiber of the zero locus. More concretely, the Monodromy Conjecture predicts that any pole of these zeta functions is related with an eigenvalue of the monodromy at some point of $f^{-1}(0)$.

In this talk, we introduce some recent techniques that we have developed for the study of these zeta functions for $\mathbb{Q}$-divisors over orbifold varieties: a change of variables formula from relative canonical divisors, as well as a closed formula using compositions of weighted blowing-ups. Finally, we present some work in progress about applications on the study of the Monodromy Conjecture for quasi-homogeneous surface singularities.

This is a joint work Edwing LEON-CARDENAL (UNAM), Jorge MARTIN-MORALES (UNIZAR-CUD) y Wim VEYS (KU Leuven).