- Series
- Job Candidate Talk
- Time
- Thursday, January 25, 2024 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 006; Zoom streaming available
- Speaker
- Asaf Katz – U Michigan – asaf.katz@gmail.com – https://sites.google.com/view/asafkatz
- Organizer
- Alex Blumenthal
Please Note: Zoom link: https://gatech.zoom.us/j/98245747313?pwd=RmFtcmlWYjBncXJTOU00NFMvSVNsZz09 Meeting ID: 982 4574 7313 Passcode: SoM
Abstract: Classifying the invariant measures for a given dynamical system represents a fundamental challenge.
In the field of homogeneous dynamics, several important theorems give us an essentially complete picture. Moving away from homogeneous dynamics — results are more difficult to come by. A recent development in Teichmuller dynamics — the celebrated magic wand theorem of Eskin–Mirzakhani, proved by their factorization technique gives one such example.
I will explain an implementation of the factorization technique by Eskin–Mirzakhani in smooth dynamics, aiming to classify u-Gibbs states for non-integrable Anosov actions. Moreover, I will try to explain some applications of the theorem, including a result of Avila–Crovosier–Eskin–Potrie–Wilkinson–Zhang towards Gogolev’s conjecture on actions over the 3D torus.