Talks
Title: Chern-Simons Theory for 3-ManifoldsAbstract: We review the Chern-Simons theory for 3-manifolds. The talk will start with a gentle introduction to principal bundles and their connections, and reach the definition and properties of the Chern-Simons 3-form and invariant. We will also discuss holonomy representation and the case of hyperbolic 3-manifolds.Title: The Renormalization of Volume and the Chern-Simons Invariant for Hyperbolic 3-ManifoldsAbstract: For hyperbolic 3-manifolds, many interesting results support a deep relationship between volume and the Chern-Simons invariant. In this talk, we consider noncompact hyperbolic 3-manifolds having infinite volume. For these manifolds, there is a well-defined invariant called the renormalized volume which replaces classical volume. We will renormalize the Chern-Simons invariant and discover a close relationship with the renormalized volume.
Title: The renormalization of volume and Chern-Simons invariant for hyperbolic 3-manifoldsAbstract: For hyperbolic 3-manifolds, there are interesting results supporting a deep relationship between hyperbolic volume and the Chern-Simons invariant. For noncompact hyperbolic 3-manifolds having infinite volume, specifically convex-cocompact hyperbolic 3-manifolds, there is a well-defined invariant called the renormalized volume which replaces classical volume. In this talk, we renormalize the Chern-Simons invariant for convex-cocompact hyperbolic 3-manifolds and discover a close relationship with the renormalized hyperbolic volume. It reveals a connection to Weitzenböck geometry and introduces a complex-valued quantity related to mean curvature.
Title: The Renormalization of Volume and Chern-Simons Invariant for Hyperbolic 3-ManifoldsAbstract: For hyperbolic manifolds, many interesting results support a deep relationship between hyperbolic volume and the Chern-Simons invariant. In this talk, we consider noncompact hyperbolic 3-manifolds having infinite volume. For these manifolds, there is a well-defined invariant called the renormalized volume which replaces classical volume. The talk will start from a gentle introduction to hyperbolic geometry and reach the renormalization of the Chern-Simons invariant, which has a close relationship with the renormalized hyperbolic volume.
Title: The Renormalization of Volume and Chern-Simons Invariant for Hyperbolic ManifoldsAbstract: In this talk, we consider geometric invariants on noncompact hyperbolic 3-manifolds. The talk consists of three parts: the renormalization of volume for hyperbolic 3-manifolds having infinite volume, a brief introduction to Chern-Simons invariant, and its renormalization for hyperbolic 3-manifolds.