# The Cluckers-Veys conjecture on exponential sums

## Arithmétique

Lieu:
Salle Kampé de Fériet
Orateur:
Affiliation:
KU Leuven
Dates:
Jeudi, 7 Décembre, 2017 - 11:00 - 12:00
Résumé:

In 1978 Igusa introduced certain exponential sums for homogeneous polynomials in several variables. He conjectured upper bounds for these sums, expressed in terms of the numerical data of a resolution of singularities. Some cases of his conjecture have been solved, but the general case remains open. Recently, his conjecture has been generalised to nonhomogeneous polynomials by Cluckers and Veys. We prove the Cluckers-Veys conjecture for polynomials that have log-canonical threshold at most a half and this result implies Igusa's conjecture for homogeneous polynomials with the same restriction. This is joint work with Kien Nguyen.

In this talk I will introduce the sums that we are studying and discuss the different conjectures. I will also explain the relation between these sums and the Igusa zeta functions and shortly explain how we use this relation to prove our result.