Lectures related to Unitary representation

Kirillov Paradigm for Heisenberg Group

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Generators of Groups

Explains the concept of generators of groups and their mathematical properties.

Spherical Hecke Algebra: Irreps and Eigenspaces

Covers the spherical Hecke algebra and finite-dimensional unitary representations.

Unitary Minimal Models: Representation Theory Insights

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

Eisenstein Series: Decomposition and Unitarizability

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

Unitary Operators: Translation and Transformation

Explores unitary operators for translation and transformation in quantum mechanics.

Scattering Amplitude and Optical Theorem

Covers the introduction of scattering amplitude, optical theorem, and unitary operators in quantum mechanics.

Hilbert Space: State, Evolution, Measurement

Introduces Hilbert space as a big place where quantum systems evolve with unitaries.

Extension of Linear Transformations

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Quantum Mechanics: Spectral Basis and Schrödinger Equation

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.

Stone-von Neumann Theorem

Explores the Stone-von Neumann Theorem and unitary operators on Hilbert spaces.

Spectral Analysis: Hyperbolic Surfaces

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

Unitary Representations: Schur's Lemma

Explains Schur's Lemma on unitary representations and their irreducibility and invariance properties.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Shor's factoring algorithm: Quantum Phase Estimation

Covers Shor's factoring algorithm and the link between order finding and factoring.

Linear Algebra: Quantum Mechanics

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

Quantum Physics I

Explores quantum state evolution, unitary operators, Heisenberg representation, spin precession, and observable averages.

Linear Algebra: Quantum Mechanics

Covers the application of linear algebra concepts to Quantum Mechanics, including spectral theorem and Brillouin zone.

Quantum Physics I

Introduces quantum physics postulates, measurement principles, and operator transformations between bases.

Deutsch Josza algorithm

Covers the Deutsch-Josza algorithm, a quantum algorithm solving problems with a single query to an oracle.