Explore a groundbreaking lecture on exotic manifolds, focusing on Spherical Duality and Torus Links. Delve into the construction of homotopy spheres in dimension 7 supporting O(3)-actions and their connection to O(1)-actions on Brieskorn 3-spheres. Discover how these constructions relate to algebraic curves in P^2, offering new insights into exotic spheres and "homotopy Hopf manifolds." Examine the concept of spherical duality as a generalization of T-duality in mirror symmetry. Learn about ongoing research in this field, presented by Leonardo Cavenaghi from UNICAMP, in collaboration with Ludmil Katzarkov (UMiami) and Lino Grama (Unicamp).