Lectures related to Pentagonal Number Theorem and Jacobi Identity

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores differentiating under the integral sign and continuity of functions in integrals.

Explores the properties and transformations of theta functions, including modular forms and lattice levels.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Covers weak derivatives, their properties, and applications in functional analysis.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.