Mini school/workshop on p-adic and motivic integration

September 21-22, 2018 

University of Geneva, Villa Battelle

Lecture series:

I. François Loeser:

Lecture 1: Motivic integration via constructible functions
I will introduce the approach to motivic integration developed with R. Cluckers via motivic constructible functions and will highlight some of the main applications
Lecture 2: Arc spaces, monodromy and vanishing cycles
 I will survey the many connections of arc spaces with mondromy and vanishing cycles (work with J. Denef, G. Guibert and M. Merle, E. Hrushovski)


II. Dimitri Wyss

p-adic integration along the Hitchin fibration
In my talks I will start by introducing the basic theory of p-adic integration on smooth varieties and explain how Batyrev used this to prove, that two birational Calabi-Yau varieties have the same Betti-numbers. I will then extend this theory to smooth and tame Deligne-Mumford stacks and present two applications that we found with Michael Groechenig and Paul Ziegler. The first is a proof of a conjecture of Hausel-Thaddeus, which states that suitably defined moduli spaces of SL_n and PGL_n Higgs bundles have the same (stringy) Hodge numbers. Secondly we give a new proof of Ngô's geometric stabilization theorem for any reductive group G, which implies the fundamental Lemma.
III. Tony Yue Yu
The Frobenius structure conjecture
The Frobenius structure conjecture is a conjecture about the geometry of rational curves in log Calabi-Yau varieties proposed by Gross-Hacking-Keel. It was motivated by the study of mirror symmetry. It predicts that the enumeration of rational curves in a log Calabi-Yau variety gives rise naturally to a Frobenius algebra satisfying nice properties. I will introduce the conjecture in the mini-course, and then explain how to use non-archimedean geometry to tackle the conjecture. We will study various properties of the moduli space of non-archimedean curves inside log Calabi-Yau varieties. If time permits, I will also introduce a new notion of skeletal curve which plays a special role in the theory. It is based on my joint work with S. Keel.


September 21, Friday

10:30 – 12:00 14:00  15:30 16:00  17:30

François Loeser Dimitri Wyss Tony Yue Yu
IMG-PRJ, Paris  IMG-PRJ, Paris Université de Paris-Sud, Paris

Lecture 1 Lecture 1 Lecture 1



September 22, Saturday

10:30 – 12:00 14:00 – 15:30 16:00 – 17:30

François Loeser Dimitri Wyss Tony Yue Yu
IMG-PRJ, Paris  IMG-PRJ, Paris Université de Paris-Sud, Paris

Lecture 2 Lecture 2 Lecture 2




Organizers: Tamas Hausel [tamas.hausel at], Zsolt Patakfalvi [zsolt.patakfalvi at], Andras Szenes (host)  [Andras.Szenes at]