## Geometry Seminar - Abstracts

### Talk

Tuesday 4 June 2024, 16:00 - 17:00 in HG00.310

**Aaron Levin** (Michigan State)

*Greatest common divisors in Diophantine approximation*

### Abstract

In 2003, Bugeaud, Corvaja, and Zannier gave an upper bound for the
greatest common divisor \(\mathrm{gcd}(a^n-1,b^n-1)\), where a and b are fixed integers and
n varies over the positive integers. In contrast to the elementary statement of
their result, the proof required deep results from Diophantine approximation. I
will discuss a higher-dimensional generalization of their result and some
recent related results.

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