This series of 6 lectures introduces the key ideas of anabelian geometry, focusing on how arithmetic and geometric objects can be reconstructed from their associated Galois or fundamental groups. Starting with the arithmetic of the étale fundamental group and the example of the projective line minus three points, the series illustrates how discrete invariants, such as inertia and decomposition groups, can be recovered using group-theoretic methods.

The lectures then develop reconstruction techniques for fields and curves, including Uchida-style field reconstruction using tools from class field theory, as well as Tamagawa’s approach to the anabelian geometry of affine curves. The program concludes with topics in absolute and mono-anabelian geometry, covering methods for reconstructing p-adic fields, cyclotomic data, and invariants arising from p-adic Hodge theory.

One lecture is dedicated to explore how aspects of these ideas can be explored into Lean's formalized mathematical setting.

Lecturers: B. Collas (RIMS, JP), K. Sawada (RIMS, JP) & S. Tsujimura (RIMS, JP)

※ This event is part of the special year ``Arithmetic, Homotopy, and Geometry 2027-28''.