Seminario teoría de grupos UAM-ICMAT

Miercoles 9 de Octubre, 12:30, Aula 520 UAM

Albert Garreta (UPV/EHU)

Title: Equations and first-order theory of one-relator monoids and of word-hyperbolic monoids.

Abstract:

First we will introduce the classes of word-hyperbolic monoids and of one-
relator monoids, and we will compare these to their group theoretic counter-
parts. We will also provide a broad overview on the topics of first-order theory
and Diophantine problems in groups and monoids, paying special attention
to their algorithmic aspects. We will then proceed to discuss the decidability
of different fragments of the first-order theory in word-hyperbolic monoids
and one-relator monoids. In particular we will prove in an informal manner
that in many of these one can encode (by means of systems of equations)
the longstanding open problem of word equations with length constraints. A
consequence of this result is that these monoids have undecidable positive
AE-theory. This is joint work with Robert D. Gray.