In 1900 Hilbert posed the problem for finding an algorithm according to which the integral solvability of a diophantine equation in any number of unknowns would be found. After 70 years, a young Russian mathematician, Yuri Matiyasevich, completed the last and the most important step for the proof of undecidability of this problem and opened the way how this decidability result would lead to a big number of definability problems.
I will begin my talk with a quick sketch of the proof of the undecidability of Hilbert's Tenth Problem. After that I will show how this problem can be generalized to any ring and turn into a definability problem. Finally I will prove the undecidability of the problem for the ring of matrices over an integral domain for which the problem is undecidable.
To volunteer to give a talk, or for any other questions regarding this schedule, contact Sara Miller