Gal Binyamini of the Institute for Advanced Study presents a research seminar on the o-minimal structures R_LN and R_{LN,exp}, which carry an effective form of the finiteness property central to o-minimality. He explains how R_{LN,exp} extends beyond the classical theory of Pfaffian functions by containing period integrals for arbitrary algebraic families, a structure whose existence Khovanskii conjectured in weaker form in the 1980s. Binyamini walks through the formal definition of the structure and draws on hyperbolic geometry, commutative algebra, and differential equations to show how effective bounds on complexity are derived. The talk is aimed at specialists following the IAS Special Year seminar series, assuming familiarity with o-minimality and model theory, and focuses on the technical machinery linking geometric finiteness to concrete numerical estimates.