Microsoft is making sign-in more secure by phasing out text and phone call authentication for multi-factor authentication (MFA). These methods are easier for attackers to compromise. Instead, users will be required to switch to stronger authentication methods such as a passkey, using the Microsoft Authenticator mobile app, or other more secure options.
Apparently there are about 7,000 people in the university whose only MFA methods are the ones that will be withdrawn. Are you one of the 7,000?
We show that the group cohomology of simple connected Lie groups, and consequently their lattices and symmetric spaces, with L^p-coefficients vanishes below the rank. This confirms a conjecture of Gromov in the special case of the coefficient module L^p(G). We relate the vanishing of L^1-cohomology to a fixed-point theorem and confirm a conjecture of Farb. Farb conjectured a fixed point property for actions of lattices in such groups on CAT(0) cell complexes of dimension lower than the rank.
In this talk, I will give a short introduction to group cohomology and discuss ideas from the proofs of both results. This talk is based on joint work with Saar Bader, Uri Bader, and Roman Sauer.
