Lectures related to Eisenstein Series and Spectral Decomposition

Representation Theory: Actions and Invariants

Covers the representation theory of groups, focusing on actions and invariants.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Conformal Blocks: Functions on Moduli Spaces

Covers conformal blocks and their significance in complex structures and moduli spaces.

Unitary Minimal Models: Representation Theory Insights

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Structure of Algebras

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Spectral Estimation Methods

Explores parametric spectrum estimation methods, including line and smooth spectra, and delves into heart rate variability analysis.

Spectral Analysis: Hyperbolic Surfaces

Explores the spectral analysis of hyperbolic surfaces through the trace formula and its applications in understanding geometric and spectral properties.

Density Theorem: Endomorphisms of Simple Modules

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Monster Group: Representation

Explores the Monster group, a sporadic simple group with a unique representation theory.

Eisenstein Series: Decomposition and Unitarizability

Covers the decomposition of Eisenstein series into orthogonal components and the unitarizability of certain representations.

Signal Processing: Basics and Spectral Analysis

Covers the basics of signal processing, linear estimation, and digital filters.

Wave Patterns and Spectral Analysis

Explores wave patterns, Fourier transforms, group velocity, and Gaussian spectra in hydrodynamics.

Segal CFT: Hilbert Space Applications

Covers the applications of Segal's Conformal Field Theory in Hilbert spaces.

Statistical Signal Processing for Wireless Communications

Covers statistical signal processing tools for wireless communications, including spread spectrum, spectral analysis, ultra-wide band communications, and heart rate variability analysis.

Spectral Analysis: Integrated Spectrum and Autocovariance

Explores spectral analysis, integrated spectrum, autocovariance, estimation, and convergence in time series models.

Representation Theory: Finite Subgroups of SU(2)

Explores representation theory and character theory of finite groups, including scalar product and McKay graph.

Estimation & Spectral Analysis in Time Series

Covers the estimation of time series models and spectral analysis in depth.

Singular Vectors in Liouville CFT: Representation Theory Insights

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

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Signals and Systems I: Fourier Transform and Spectral Analysis

Explores Fourier series, energy calculation, functional spaces, correlation spectra, and spectral density in signals and systems.