Milnor Spheres via Spherical T-duality and Generalized Log Transform

This lecture explores the interplay between Spherical T-duality, exotic spheres, and the generalized log transform, revealing new connections in geometric topology and complex geometry. Discover how Spherical T-duality generalizes classical T-duality by replacing the circle group U(1) with the 3-sphere S³ or SU(2), relating SU(2)-bundles equipped with degree-7 cohomology cocycles. Examine a striking class of examples involving 7-dimensional homotopy spheres Σ⁷, whose product with S¹ exhibits distinct holomorphic structures under spherical T-duality, contrasting with classical Hopf manifolds such as S³ × S¹. Learn about the generalized log transform, which extends classical 4-dimensional elliptic fibration techniques to higher dimensions. When applied to 8-dimensional homotopy Hopf manifolds, this approach reveals structural parallels with lower-dimensional cases, shedding light on singularities and complex structures. This presentation covers joint work with Leonardo Cavenaghi and Ludmil Katzarkov.