Geometry and Analysis on Groups Research Seminar

"Geometry and Analysis on Groups" Research Seminar

Time: 20.11.03, 15:00–17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: The Diophantine problem in commutative rings, solvable groups, and classical matrix groups
Speaker: Albert Garreta (UPV / EHU)
Abstract: The Diophantine problem in a group or ring G is decidable if there exists an algorithm that given a finite system of equations with coefficients in G decides whether or not the system has a solution in G. I will overview recent developments that have been made in regards to this problem in the area of commutative rings, solvable groups, and classical matrix groups. For large classes of such rings and groups the situation is completely clarified modulo a big conjecture in number theory. This includes the class of all finitely generated commutative rings (with or without unit), all finitely generated nilpotent groups, and matrix groups such as GL (n, R), SL (n, R), T (n, R), etc where R is a finitely generated commutative ring.

The talk is based on joint results with Alexei Miasnikov and Denis Ovchinnikov, and further on results of Alexei Miasnikov and Mahmood Sohrabi.