Lectures related to Theta functions: Properties and Transformations

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

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

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

Covers the properties and applications of modular forms and discusses equidistribution and modularity.

Covers functions, including even and odd functions, periodicity, and function operations.

Explores sub/super harmonic functions and their applications in a theoretical context.

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

Explores real functions, covering parity, periodicity, and polynomial functions.

Covers the properties of harmonic functions and the concept of mollification.

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

Covers the analysis of functions, composition, and mathematical induction.

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.

Covers the Petersson inner product and Hecke operators in modular forms theory, exploring their definitions and properties.

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Explores differentiating under the integral sign and conditions for differentiation, with examples and extensions to functions on open intervals.

Covers the definitions and notations related to functions.

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

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.