ACC Seminar: Diophantine Problems in Wreath Products of Groups

Refreshments will be served at 4:00 PM.

ABSTRACT

The Diophantine problem in a group G, shortly DP(G), is decidable if there is an algorithm which, when given a finite system of group equations with coefficients in G, decides whether the system has a solution in G. I will describe some results on undecidability of the Diophantine problem in wreath products of groups. The focus will be on the undecidability of DP(G), where G is the wreath product of two free abelian groups of finite rank. The proof is accessible to graduate students, and I will present it in detail. At the end, I will discuss the related open problems.

BIOGRAPHY

Alexei Miasnikov is a Distinguished Research Professor of Mathematics at Stevens Institute of Technology. A world-class mathematician and leading international expert in geometric and algorithmic group theory, model theory, computer science, and cryptography, Alexei has received numerous awards and honors. In 2012, he was selected as an Inaugural Fellow of the American Mathematical Society for his outstanding research contributions to the Mathematical Sciences. He was invited to speak at the 2014 International Congress of Mathematicians for his research on the model theory of groups. In 2016, Alexei received the prestigious Malcev Prize from the Russian Academy of Sciences for his lifetime achievements, particularly his solution for Tarski’s problem on the elementary theory of free groups. His other international honors and awards include the Microsoft Research Fellow Award, the Marsden Fund Award, numerous NSF awards, and his former position as Canada Research Chair at McGill University.

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