Some Applications of p-adic Integration to Geometry and Arithmetics

In a broad sense, p-adic integration is the theory of integration on analytic manifolds over non-Archimedian locally compact fields, and is used in many different areas of mathematics.

This course has three "goal results" or motivating directions:
- Batyrev's theorem about equality of Betti numbers of two birationaly equivalent Calabi-Yau manifolds
- $p$-adic Igusa's zeta function \& Denef's formula and applications to singularity theory
- integration and Fourier analysis on Adèles and Idèles, with some applications to arithmetics.

Target group: Students in algebraic geometry and/or number theory.

Prerequisites: None

Evaluation: None

Teaching format: None

ECTS: 3 Year: 2024

Track segment(s):
Elective

Teacher(s):
Tanguy Vernet Loïs Faisant

Teaching assistant(s):
Mischa Elkner Lena Wurzinger