Explore stationary measures for Fuchsian groups and related contexts in this research talk by Vaibhav Gadre, part of the Geometry in Groups program at the International Centre for Theoretical Sciences. Delve into an important topic within geometric group theory, a rapidly growing field with connections to geometry, topology, dynamics, analysis, and probability. Learn from an expert researcher during this 46-minute presentation, which contributes to the program's goals of increasing exposure to active areas in geometric group theory and strengthening research networks. Gain insights into this specialized area of mathematics alongside other talks and minicourses by eminent researchers, fostering a collaborative and inclusive learning environment for mathematicians from diverse backgrounds.