Speaker: Dr. Alexei J. Kanel-Belov, Bar Ilan University

Title: Algorithmical unsolvability in algebraic geometry and algebra

Abstract: The talk is devoted to algorithmical questions in algebraic geometry and algebra. Let $M$ be an algebraic variety. Does there exist an embedding of an affine line into $M$? We prove that this question is algoritmically unsolvable. It is well known that if ideal of relation has finite Groebner basis then there is an obvious algorithm to check if an element is equal to 0 or not. However, existence of zero divisors is no the case. We shall discuss an isomorphism problem of algebric varieties.