- Series
- CDSNS Colloquium
- Time
- Friday, April 15, 2022 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Remote via Zoom
- Speaker
- Bassam Fayad – University of Maryland – bassam@umd.edu – https://www-math.umd.edu/people/faculty/item/1607-bassam.html
- Organizer
- Alex Blumenthal
Please Note: Zoom link: https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09
In which cases and ways can one perturb the action on the torus of a commuting pair of $SL(n, \mathbb Z)$ matrices?
Two famous manifestations of local rigidity in this context are: 1) KAM-rigidity of simultaneously Diophantine torus translations (Moser) and 2) smooth rigidity of hyperbolic or partially hyperbolic higher rank actions (Damjanovic and Katok). To complete the study of local rigidity of affine $\mathbb Z^k$ actions on the torus one needs to address the case of actions with parabolic generators. In this talk, I will review the two different mechanisms behind the rigidity phenomena in 1) and 2) above, and show how blending them with parabolic cohomological stability and polynomial growth allows to address the rigidity problem in the parabolic case.
This is joint work with Danijela Damjanovic and Maria Saprykina.