Quantifying Residual Finiteness and LERF-ness in Terms of Geometric Data

Priyam Patel (Rutgers)

Abstract: This talk will begin by defining residual finiteness (RF) and locally extended residual finiteness (LERF) for groups, followed by a brief history of the results that study the connection between these algebraic properties and the fundamental groups of surfaces and 3-manifolds. We will then describe what it means to quantify these group properties and present the results that quantify RF-ness and LERF-ness of hyperbolic surface groups in terms of geometric data. If time permits, we will conclude with an overview of similar techniques used to quantify residual finiteness for particular hyperbolic 3-manifold groups.