New Look at Milnor Spheres - Geometric Topology and Complex Geometry

Watch a 47-minute mathematics lecture exploring the fascinating connections between Spherical T-duality, exotic spheres, and the generalized log transform in geometric topology and complex geometry. Delve into how Spherical T-duality extends classical T-duality by replacing the circle group U(1) with the 3-sphere S^3 or SU(2) group, examining their relationships with SU(2) bundles and degree-7 cohomology cocycles. Learn about 7-dimensional homotopy spheres Σ^7 and their product with S^1, discovering distinct holomorphic structures transported through spherical T-duality in contrast to classical Hopf manifolds. Explore the generalized log transform as an extension of classical techniques from 4-dimensional elliptic fibrations to higher dimensions, and understand its application to 8-dimensional homotopy Hopf manifolds, revealing new insights into singularities and complex structures through collaborative research with Leonardo Cavenaghi and Ludmil Katzarkov.