Matteo Cavaleri (Unicusano U, Rome): Approximations and computations in infinite groups

Research Project:

Sofic groups were introduced by Gromov as a common generalization of amenable and residually finite groups. For both these classes, algorithmic problems have been studied; for example, the solvability of the word problem for residually finite, finitely presented groups, and the (non)-subrecursivity of the Folner function for certain amenable groups. 

The project aims at investigating soficity, amenability and related properties of finitely generated groups, from an algorithmic point of view. Classical algorithmic decision problems, such as word problem, conjugacy problem, isomorphism problem, are related with the algebraic structure and in particular are related with the quantification of appropriate algebraic properties.

There are different ways to define computability of the approximations and, even if the mere existence characterizes the same class of groups, when we ask for an effective construction we have many different behaviours, proved in relation with the subrecursivity of the growth of the approximations, the word problem and the generic word problem. During my stay at ESI, I plan to deepen results in the amenable setting and to explore variations of amenability and soficity.

Coming soon.

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At a glance
Junior Research Fellow
July 15, 2018 — Sept. 15, 2018