**Wim Veys** (Leuven, Belgium)

*An Introduction to Motivic Integration and its Applications*

**Lecture 1: Spaces of jets and arcs**

number-theoretic pre-history: numbers of solutions of polynomial congruences;

spaces of jets and arcs, examples and properties;

Grothendieck ring of algebraic varieties.

**Lecture 2: Motivic integration**

motivic measure on non-singular and on singular varieties;

Kontsevich's completed Grothendieck ring;

motivic integrals;

Kontsevich's application: birationally equivalent Calabi-Yau manifolds have the same
Hodge numbers;

motivic volume.

**Lecture 3: Motivic and related zeta functions**

modification formula for the topological Euler characteristic;

motivic zeta functions;

topological zeta functions;

monodromy conjecture.

**Lecture 4: Batyrev's stringy invariants**

special singularities: terminal, canonical, log terminal, log canonical;

Batyrev's stringy Euler number and stringy E-function for log terminal singularities:
well defined using motivic integration;

applications;

stringy invariants for general singularities.

*References:*

2. M. Blickle: