ICTP ALGEBRAIC GEOMETRY SEMINAR - Wednesday, 26 April, at 14:00 (Ho Hai PHUNG)

[ICTP Math Section]

A L G E B R A I C  G E O M E T R Y   S E M I N A R


Wednesday, 26 April, at 14:00


Venue: Leonardo Building - Luigi Stasi Seminar Room

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Speaker: Ho Hai Phung (Institute of Mathematics, VAST, Hanoi)


Title: *Connections on algebraic schemes and their differential Galois 
groups *


Abstract: Connections on algebraic schemes generalize linear 
differential equations. Their study is motivated by Hilbert’s 21st 
problem and Galois theory of solving polynomial equations. Hilbert’s 
21st problem asks about a correspondence between linear differential 
equations on a punctured complex plane and representations of its 
fundamental group. This is nowaday known as the Riemann-Hilbert 
correspondence. Some geometric features of a connection are captured in 
its monodromy group, which relates to the fundamental group mentioned 
above and Galois' theory. This group is henceforth called the 
differential Galois group of the connection.
In my talk I will report about our recent works on connections over a 
family of smooth schemes parameterized by a curve and their differential 
Galois group.