MATH 7310: Topics in Profinite Groups and Serre's Conjecture (Spring 2012)

Instructor: Martin Kassabov

MATH 7310 will not meet during the first week of classes. The first class is scheduled for January 31st.

In the 70's Serre conjectured that the topology of a finitely generated profinite group is uniquely determined by the group structure. I would like to go over the motivation of the conjecture (which will include an introduction to profinite groups) and explain the main ideas behind the proof of this conjecture by Nikolov and Segal. I might skip some technical steps in the proof which are essentially “uniform bounded generation type” results in finite simple groups. As usual in this area all results require that classification of finite simple groups.

Prerequisites: I will assume basic knowledge in group theory (mainly finite groups) and Galois theory. Equivalent of MATH 6310 and 6320 should be sufficient.