Recent zbMATH articles by "Flannery, Dane Laurence"https://zbmath.org/atom/ai/flannery.dane-l2024-03-13T18:33:02.981707ZWerkzeugExperimenting with symplectic hypergeometric monodromy groupshttps://zbmath.org/1528.200882024-03-13T18:33:02.981707Z"Detinko, A. S."https://zbmath.org/authors/?q=ai:detinko.alla-s"Flannery, D. L."https://zbmath.org/authors/?q=ai:flannery.dane-l"Hulpke, A."https://zbmath.org/authors/?q=ai:hulpke.alexanderThe authors have worked over the past 8 or 9 years on computer-aided algorithms in linear groups -- specifically, arithmetic groups. One of the properties they exploit is that of strong approximation. One has such strong approximation properties for thin groups (certain Zariski dense subgroups) also which may not be arithmetic (in the Zariski closure). It is generally difficult to determine when a Zariski dense subgroup is arithmetic and when it is thin. The authors' computational methods also depend on the congruence subgroup property. In the paper under review, the authors work with symplectic hypergeometric monodromy groups. They extend their computational methods to these families and compute the arithmetic closure of these groups. As a byproduct, they are able to also deduce arithmeticity in some cases.
Reviewer: Balasubramanian Sury (Bangalore)