Ẑ-Invariants and Universal Abelian Cover

Explore the concept of Ẑ-invariants and Universal Abelian Cover in this 47-minute lecture by Josef Svoboda from the University of Miami. Delve into the study of invariants for plumbed 3-manifolds that are rational homology spheres, focusing on their universal abelian covers and associated analytic invariants. Learn how these covers relate to isolated singularities and their impact on monodromy, spectrum, and Poincaré series. Discover the application of this perspective to investigate (GPPV) Ẑ-invariants, with insights from ongoing research conducted in collaboration with S. Gukov, L. Katzarkov, and K.S. Lee. Follow the presentation through key topics including notation, partition functions, examples, and speculation, concluding with a Q&A session to deepen understanding of this complex mathematical subject.