Lectures related to Analytic continuation

Laplace Transform: Analytic Continuation

Covers the Laplace transform, its properties, and the concept of analytic continuation.

Covers the analytical extension of the Gamma function to real and complex numbers, discussing properties and convergence.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Singular Vectors in Liouville CFT: Representation Theory Insights

Covers singular vectors in Liouville CFT, focusing on representation theory and their implications in mathematical physics.

Cauchy-Hadamard Theorem

Explores the Cauchy-Hadamard theorem on convergence radius of power series and real analytical solutions.

Primes in arithmetic progressions (II), and Gamma functions

Explores the existence of primes in arithmetic progressions and the properties of the Euler gamma function.

Analytic Continuation and Uniqueness of Holomorphic Functions

Covers the concept of analytic continuation and the uniqueness of holomorphic functions, including the extension of holomorphic functions and the properties of entire and meromorphic functions.

Analytical Solutions: EDO

Explores the analytical solutions of ordinary differential equations, emphasizing the identification and solving process for various EDO types.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Spectral Expansion: Eisenstein Series

Covers the spectral expansion of Eisenstein series and the properties of hyperbolic surfaces.

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Harmonic Oscillations: Superposition

Explores the principle of superposition for harmonic oscillations and provides geometric interpretations and examples.

Electrostatics and Green's Functions: Mathematical Methods

Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.

Harmonic Oscillator: Analytic Continuation and Integration

Covers the harmonic oscillator, analytic continuation, integration, and classical trajectories.

Maximum Principle in Harmonic Functions

Explores the maximum principle in harmonic functions and its implications for uniqueness and bounds on solutions.

Calculus of Variations

Covers topics in Calculus of Variations, including regularity results and implicit function theorems.

Monodromy Conjecture

Explores the Monodromy Conjecture, discussing its origins, implications, and conditions for convergence in mathematical contexts.

L-values and Extensions

Explores de Rham theory, L-values, and extensions, including special value formulas and examples related to Hecke characters and modular forms.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Complex Integration: Fourier Transform Techniques

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.