Explore the fascinating world of random manifolds in this 50-minute lecture by Tsachik Gelander at the International Centre for Theoretical Sciences. Delve into the insights gained from studying random geometric structures as part of the program on Zariski Dense Subgroups, Number Theory, and Geometric Applications. Discover how examining random manifolds contributes to our understanding of algebraic and differential geometry, combinatorics, and related fields. Learn about the intersection of number theory, algebraic groups, and geometry, and how these concepts apply to various mathematical problems. Gain exposure to cutting-edge research topics such as fake projective planes, isospectral spaces, and expanding graphs. Engage with advanced mathematical concepts and explore their applications in topology and mathematical physics.