## Student Algebra & Combinatorics

•  Zheng Xiao, MSU
•  Recent results of GCD problems on almost $S$-units and recurrences
•  10/07/2019
•  4:30 PM - 5:30 PM
•  C517 Wells Hall

The GCD problem is one of the major problems in Diophantine Geometry. Corvaja, Zannier and Bugeaud first gave a fundamental result on GCD of integers powers and then generalized to rational numbers and algebraic numbers by many mathematicians. In this talk I will introduce recent GCD results on $S$-units due to Levin and generalize to almost $S$-units. I will give the definition of almost units and present the main theorem of GCD on multivariable polynomials, which is lead to a result about recurrence sequences. If time allows, I will also introduce Silverman’s generalized GCD along the blow up of a closed subscheme and apply to abelian surface case and its connection to Vojta’s conjecture.

## Contact

Department of Mathematics
Michigan State University