A human property (T) proof for highrank Aut(F_n)

Venue:
Geb 20.30, SR 2.058

Date:
07.12.2023
 Speaker:

Time:
15:45 Uhr

Abstract: Kazhdan's property (T) is an important rigidity property for groups. Typically, it is difficult to show that a given group satisfies property (T), and the proof that the automorphism groups of the free groups, Aut(F_{n}), have property (T) for n>=4 is an important result of recent years.
These proofs rely crucially on extensive computer calculations. We give a new proof that Aut(F_{n}) has property (T) for all but finitely many n that is inspired by the semidefinite programming approach but does not use the computer in any step. More specifically, we prove property (T) for a certain extension Γ_{n} of SAut(F_{n}) as n goes to infinity.