Explore the intricacies of fractional Laplacians in this 42-minute lecture by Alexander I. Nazarov, presented by the International Mathematical Union. Delve into the CS-extension and examine the restricted Dirichlet fractional Laplacian for & E (-1,0). Compare various fractional Laplacians in terms of quadratic forms and analyze the spectral Dirichlet and Neumann fractional Laplacians. Follow along as Nazarov presents proofs for Theorems 1, 2, and 3, and encounter a thought-provoking counterexample. Gain a deeper understanding of this complex mathematical concept through a comprehensive exploration of its diverse forms and applications.