Watch a technical lecture from the Arithmetic Quantum Field Theory Conference where Alejandra Castro explores the relationship between modular forms and black hole entropy, focusing specifically on weak Jacobi forms. Discover how constraints on polar states influence the asymptotic growth of non-polar states and their implications for gravitational path integrals. Learn about the UV/IR connection linking black hole microstate counting to modular forms, gaining insights into the microscopic interpretation of logarithmic corrections to supersymmetric black hole entropy and their relevance to AdS_3/CFT_2 consistency conditions. Delve into how modular symmetry in counting formulae enables precise matching between Bekenstein-Hawking entropy of supersymmetric black holes and Cardy's formula for asymptotic state growth.