Knot Invariants from Finite Dimensional Integration

Explore the concept of "I-Type Knot Invariants" in this comprehensive lecture by Dror Bar-Natan at ICBS2024. Delve into the computation of knot invariants from knot diagrams using finite dimensional integration techniques. Learn how these invariants are calculated by integrating the exponential of a perturbed Gaussian Lagrangian, which is a sum of locally defined quantities over diagram features. Discover why these invariants are considered the strongest known per CPU cycle and their advantages over infinite dimensional constructions. Examine the algebraic nature of these integrals and their departure from traditional analytical approaches. Gain insights into the rigorous mathematical foundations of this method and its implications for knot theory.