Umberto Zannier: Bounded generation in linear groups and exponential parametrizations (NTWS 154)
Channel: Number Theory Web Seminar
Date: 2023-05-19

Abstract: In fairly recent joint work with Corvaja, Rapinchuk, Ren, we applied results from Diophantine S-unit theory to problems of “bounded generation” in linear groups: this property is a strong form of finite generation and is useful for several issues in the setting. Focusing on “anisotropic groups” (i.e. containing only semi-simple elements), we could give a simple essentially complete description of those with the property. More recently, in further joint work also with Demeio, we proved the natural expectation that sets boundedly generated by semi-simple elements (in linear groups over number fields)  are “sparse”. Actually, this holds for all sets obtained by exponential parametrizations. As a special consequence, this gives back the previous results with a different approach and additional precision and generality.

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

Original air date: 
Thursday, December 22, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, December 23, 2022 (12am CST, 3am AEDT, 5am NZDT)