Explore a comprehensive mathematics colloquium on deformations of the cohomology ring of moduli spaces. Delve into the study of representation spaces of fundamental groups of Riemann surfaces, examining their various incarnations in algebraic geometry, differential geometry, and physics. Investigate the rich history of cohomology rings in these spaces and discover how Instanton Floer homology and quantum cohomology provide natural deformations to ring structures. Learn about the challenges in describing deformations when surfaces have punctures and gain insights into computing these complex families of deformations. Benefit from the speaker's expertise as they review contributions from mathematicians and physicists in this multifaceted field of study.