My fields of research are Algebraic Geometry, Arithmetical Geometry and, more recently, Model Theory. During the last years, I worked mainly on Motivic Integration and its applications. For a quick introduction to that topic, see the papers What is motivic measure? (lecture at the 2004 Current Events Bulletin of the AMS published in the Bulletin of the American Mathematical Society) and Can p-adic integrals be computed? by Tom Hales, and also the notes Geometry of arc spaces by Jan Denef (Cambridge, août 2000). For a more recent survey, see the slides of my lecture at the 5-th European Congress of Mathematics Amsterdam, July 14 - 18, 2008 or those of my lectures at the Summer Institute in Algebraic Geometry Seattle, July 25 - August 12, 2005.
More recently, in collaboration with Ehud Hrushovski I have studied the topology of non-archimedean varieties. Our work was presented in 2012 by Antoine Ducros at Séminaire Bourbaki and in 2013 by Sam Payne at the 2013 Current Events Bulletin of the AMS.