Explore an in-depth lecture on mirror symmetry for character varieties and field theory, presented by Sergey Galkin at the International Centre for Theoretical Sciences. Delve into the construction of mirrors for moduli spaces of SU(2) character varieties on Riemann surfaces, using mirrors for projective threespaces as building blocks. Discover how this construction allows for rapid computation of periods across all genera and leads to the creation of oscillatory integrals satisfying the gluing axiom of topological field theory. Examine the relationship between the mirror construction and a conjecture on decomposing derived categories of coherent sheaves on moduli spaces of stable rank 2 bundles. Throughout the lecture, encounter key concepts such as the Ginzberg-Landau model, 3-valent graphs, classical periods, random walks on lattices, Newton polytopes, homological mirror symmetry, and quantum periods. Gain insights into the mathematical foundations and implications of this research, including its connections to singularity theory, algebraic geometry, and topological field theory. Read more