Lectures related to Meromorphic Differentials and Modular Forms

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.

Covers the basics of finite fields, including arithmetic operations and properties.

Explains bases and dimension in vector spaces, covering generative and free families, isomorphism, and key theorems.

Explores holomorphic maps, ramification points, and the genus of a modular curve.

Covers the definition of vector spaces, subspaces, and linear combinations of vectors.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explains kernel, image, and linear maps, illustrating concepts with examples.

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