Talk by Christian Maire (Math Colloquium)

 Christian Maire (University of Franche-Comte)

Title: The Theorem of Golod-Shafarevich in number theory

Abstract: For a finite group group of prime power order which can be defined minimally by d generators and r relations, the Golod-Shafarevich theorem asserts that r>d²/4. This has important consequences in number theory. After recalling the whole context, I will present a generalization of the GS theorem, and some new consequences of this generalized version. We will take the time to present the arithmetic objects, so that the lecture is intended for a general audience.