Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

Explore the intricate relationship between hyperbolic geometry and homology cobordism in this Stony Brook Mathematics Colloquium talk. Delve into the three-dimensional homology cobordism group, a fundamental concept in low-dimensional topology. Learn about the challenges in understanding its structure and the interplay with hyperbolic geometry. Discover how monopole Floer homology, a sophisticated invariant of three-manifolds derived from Seiberg-Witten equations, can be applied to investigate properties of subgroups within the homology cobordism group. Focus on hyperbolic homology spheres that meet specific geometric constraints of Riemannian and spectral nature. Gain insights into this complex topic as presented by Francesco Lin from Columbia University in this hour-long lecture that bridges advanced mathematical concepts in topology and geometry.