Peter Sarnak: Integer points on affine cubic surfaces (NTWS 016)
Channel: Number Theory Web Seminar
Date: 12/04/2023

Abstract: The level sets of a cubic polynomial in four or more variables tends to have many integer solutions, while ones in two variables a limited number of solutions. Very little is known in case of three variables. For cubics which are character varieties (thus carrying a nonlinear group of morphisms) a Diophantine analysis has been developed and we will describe it. Passing from solutions in integers to integers in say a real quadratic field there is a fundamental change which is closely connected to challenging questions about one-commutators in SL_2 over such rings.

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date:
Thursday, June 25, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm China Standard Time)
Friday, June 26, 2020 (1am AEST, 3am NZST)

The recording experienced a technical glitch around minute 46.