Diophantine analysis of Markoff type surfaces
Hot Topics: Interactions between Harmonic Analysis, Homogeneous Dynamics, and Number Theory March 03, 2025 - March 07, 2025
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
We review the rudiments of a diophantine theory of affine Markoff cubics. These enjoy an action of the mapping class group on p-adic integral points thanks to their realization as the character variety of the once punctured torus. This provides a powerful tool making them one of the few families of affine log K_3's whose integral points can be studied. We highlight recent advances and some applications.