“ Wandering through fundamental groups and geometry under some non-archimedean flavors”
 
Speaker: Sylvain Gaulhiac (Kyiv School of Economics)
 
🗓When: February 18, 16:30–17:30
📍Where: KSE Dragon Capital Building, 3 M. Shpaka St., Room 4.07

Abstract:
Mathematicians like to associate a "fundamental group" to a geometric object X (for instance an algebraic variety). Some of you know the (absolute) Galois group of a field, or the topological fundamental group of a well-behaved topological space. The idea is always that the group classifies all the "coverings" of X. In algebraic geometry, it is also possible to define fundamental groups, and  a deep and difficult question in this context is the so-called "anabelian geometry": What geometric information about the object X does its fundamental group carry? Some results are known only in dimension zero (for a point) and in dimension 1 (for a curve).
 
After giving a very brief introduction to this subject, I will try to explain how a detour into some non-archimedean geometry can bring an interesting light to this topic, especially when the base field is algebraically closed. The talk will stay elementary, I will not assume the audience to be familiar with algebraic geometry, fundamental groups, anabelian theories nor with non-archimedean geometry. My goal will be to explain some general picture, and for this reason I will not enter into a lot of technical details.