Title: “Sparse random matrices, statistical field theory and supersymmetry”

Abstract: Solving problems arising from large, sparse random matrices (such as finding their eigenvalue densities) presents substantial challenges for mathematically rigorous techniques revolving around the method of moments and free probability. At the same time, such problems were effectively treated in the physics literature as early as the 1980s using heuristic methods typical of quantum/statistical field theory: functional integrals, integrals over anticommuting variables, and saddle point estimates. The saddle point problems that emerge are typically in the form of nonlinear integral equations of the Hammerstein type with Bessel kernels. I will give a pedagogical overview of these methods leading to a few concrete applications to sparse random matrix problems in my own recent works.