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- 2013/2014 PSI Lectures

Watch recorded courses from 2013/2014 PSI Lecture Series

**Welcome PSI 2013/14**

**Complex Analysis - Tibra Ali**

- Lecture 1 - Review of the basics of complex numbers, geometrical interpretation in terms of the Argand-Wessel plane. DeMoivre's theorem and applications. Branch points and branch cuts
- Lecture 2 - Cauchy-Riemann equations. Holomorphic functions and harmonic functions. Contour integration
- Lecture 3 - Cauchy's integral theorem. integral formula. Taylor and Laurent series. Singularities. Residue theorem
- Lecture 4 -Applications of the residue theorem. Semi-circular contours. Mouse hole contours. Keyhole integrals

**Algebra - Anna Kostouki**

- Lecture 1 - Lie Algebra (vector space, dual basis, matrix representations), the groups Cn and Sn.
- Lecture 2 - The groups O(n), SO(n), U(n), SU(n); Lie groups and Lie algebras; structure constants
- Lecture 3 - Lie algebras: the Adjoint representation, compact, simple and semi-simple Lie Algebras; highest-weight representations of su(2).
- Lecture 4 - The Cartan subalgebra, roots and weights, rank-2 and higher algebras

**Distributions & Special Functions - Dan Wohns**

- Lecture 1 - Distribuitions, Test functions, Derivatives of distributions, Multiplication of distributions with functions
- Lecture 2 - Composition of distributions with functions, Orthogonal functions, Sturm-Liouville theory, Parseval's Theorem, Orthogonal polynomials
- Lecture 3 - Orthogonal polynomials, gamma function, Zeta function, Hypergeometric functions
- Lecture 4 - Asymptotic Series, Stirling's approximation, Saddle point method

**Variational Calculus & Gaussian Integrals - Denis Dalidovich**

- Lecture 1 - One-dimensional and multi-dimensional Gaussian integrals. Averages with the gaussian weight, Wick's theorem
- Lecture 2 - Imaginary Gaussian Integrals. Grassman variables, definitions. Gaussian Integrals with Grassman variables
- Lecture 3 - Functionals and functional derivatives. Euler-Lagrange equations
- Lecture 4 - Noether's theorem. Functionals and Euler-Lagrange equations for continuous systems; energy-momentum tensor

**Integral Transforms & Green's Function - David Kubiznak**

- Lecture 1 - 1d Boundary value problem, Poisson's equation, Green's identities, Method of image
- Lecture 2 - Fourier transform, Cauchy problem and diffusion equation, FT in quantum mechanics
- Lecture 3 - Classical electrodynamics, wave equation, Retarded potentials, Feynman-Wheeler theory
- Lecture 4 -Scalar field, Functional Integral, Propagator, Degrees of freedom in gauge theories

**Quantum Mechanics - Agata Branczyk**

- Lecture 1 - The wavefunction, Momentum and the time-independent Schroedinger equation
- Lecture 2 - Schroedinger equation in 3D and angular momentum
- Lecture 3 - Angular momentum and mixed states
- Lecture 4 - Quantum state tomography and teleportation

**Computational Methods in Physics - Erik Schnetter**

**QFT 0 - Freddy Cachazo**

**Student Presentations**

**Relativity - Neil Turok**

- Lecture 1 - Maxwell's theory in relativistic notations
- Lecture 2 - Lorentz transformations, Time dilatation, Length contraction, Spacetime diagrams, E=mc^2
- Lecture 3 - Relativistic mechanics, Newton's bucket vs. Einstein's elevator, Principle of equivalence
- Lecture 4 Lecture 4b- Geodesic equation, Newtonian limit, Gravitational redshift, Classical field theory, Manifolds
- Lecture 5 - Manifolds, Tensors, Connection
- Lecture 6 - Metric, Equivalence principle
- Lecture 7 - De Sitter space, Connection, Torsion, Metricity
- Lecture 8 - Particle in curved spacetime, Parallel transport, Geodesics, Noether symmetries
- Lecture 9 - Geodesic deviation, Riemann tensor and its symmetries, Weyl tensor
- Lecture 10 - Bianchi identities, Perfect fluid, Newtonian limit, Einstein's equations
- Lecture 11 - Cosmological principle, Maximally symmetric spaces, FRW metric
- Lecture 12 - Friedmann's equations and their solutions, Einstein's static Universe, Dark matter and dark energy
- Lecture 13 - Schwarzschild black hole solution
- Lecture 14 - Light and Particle motion in Schwarzschild geometry, Perihelion precession, Light bending
- Lecture 15 - Journey into a black hole: from Schwarzschild to Kruskal

**Quantum Theory - Joseph Emerson**

- Lecture 1 - Motivations and axioms of quantum theory
- Lecture 2 - Axioms continued. Density matrix. The Schroedinger and the Heisenberg Pictures
- Lecture 3 - Composite and Entangled Systems. Dual Space
- Lecture 4 - Subsystems and Partial Trace. Schmidt Decomposition.
- Lecture 5 - Partial criteria for Entanglement. Von Neumann Entropy
- Lecture 6 - Mixed State Entanglement
- Lecture 7 - Purification theorem. Measurement. Generalized measurement. Von Neuman's model of indirect measurement
- Lecture 8 - Generalized measurement. Preparations/Measurements/Transformations. Stinespring dilatation theorem.
- Lecture 9 - Generalized transformations. Classical state update rule. Quantum state update rule.
- Lecture 10 - Leuder's - von Neuman postulate. Measurement decoherence. Neumark's theorem.
- Lecture 11 - State update rule under generalized measurement. Lueder's rule. Fault-tolerant threshold theorem. Dirac's idea: Poisson bracket (QM&CM)
- Lecture 12 - Bell's inequality and nonlocality. Einstein-Polosky-Rosen paradox.
- Lecture 13 - Bell's theorem and nonlocality. Nonlocal games.
- Lecture 14 - Infinite dimensions (rigged Hilbert space). Path integrals. Continuous-time open system dynamics.
- Lecture 15 - Concepts in quantum information. Complexity classes. Quantum simulation. Circuit model of quantum computation.

**QFT1 - Freddy Cachazo**

- Lecture 1 - Classical field theory
- Lecture 2 - Hamiltonian quatization of scalar field theory. Vacuum energy.
- Lecture 3 - Quantization of Klein-Gordon field continued. The Feynman propagator. Noether's theorem.
- Lecture 4 - Energy-momentum tensor. Lorentz transformation and conserved charges. Interacting field theories. Irrelevant, relevant and marginal couplings. Fundamental assumptions of Perturbation theory.
- Lecture 5 - Two point function in the interacting theory. Time ordering and the Dyson series. The vacuum.
- Lecture 6 - Review of week 1. Normal ordering and Wick's theorem. Feynman diagrams and symmetry factors. Feynman rules. Cancelation of vacuum bubbles.
- Lecture 7 - Review of the previous lecture. Momentum space two point function. Momentum space Feyman rules. One particle irreductible diagrams. Resummation of the perturbation series. Structure of the particles states in the exact theory. Base mass and physical mass.
- Lecture 8 - Cross sections. The LSZ reduction formula. Dimensional regularization.
- Lecture 9 - Covariant quantization of Maxwell's theory.
- Lecture 10 - Feynman rules for scalar nucleon-meson theory. Decay amplitudes. Scalar electrodynamics.
- Lecture 11 - Left handed and right handed spinor representations of the Lorentz group. The Weyl equations. The Dirac equation. Clifford algebra.
- Lecture 12 - Quantization of the Dirac field.

**Statistical Mechanics - Anton Burkov**

- Lecture 1 - Introduction to phase transitions, the Ising model, Mean Field Theory
- Lecture 2 - Critical exponents α, β, γ, δ out of MFT, Hubbard Stratonovich Transformation
- Lecture 3 -Spin-spin correlation function; calculation in the functional integral formalism and in MFT
- Lecture 4 - Calculation of the correlation function in the MFT through Fourier transform; Fluctuations
- Lecture 5 - Corrections in Cv from fluctuations, Ginzburg criterion, Landau-Ginzburg theory
- Lecture 6 - Wilsonian RG: fast and slow modes
- Lecture 7 - Calculation of the first cumulant; the Gaussian F.p.; Feynman diagrams
- Lecture 8 - Calculation of the 2nd cumulant; Wilson Fisher F.P.; linearized flow around the Gaussian F.P.
- Lecture 9 - Linearized flow around fixed points; calculation of critical exponents from RG
- Lecture 10 - Mermin-Wagner theorem, lower critical dimension
- Lecture 11 - Results of 2+ε expansion; Topological order in d=2
- Lecture 12 - Electrostatic analogy, Duality transformation of the XY model
- Lecture 13 - RG for the sine-Gordon model

**QFT2 - Francois David**

- Lecture 1 - Euclidean time, Path integrals, Relation between Euclidean field theory and statistical mechanics
- Lecture 2 - Operators and correlation functions in the path integral formalism, Free scalar field, Functional integration using spacetime discretization
- Lecture 3 - Free scalar field propagator, Wick's theorem
- Lecture 4 - Quantization of φ4 theory, COrrelation functions
- Lecture 5 - Structure of perturbative expansion, Effective action
- Lecture 6 - One-loop effective action, Kallen-Lehmann spectral representation
- Lecture 7 - Renormalization of φ4 theory at one loop with D=4
- Lecture 8 - Perturbative renormalization, Beta function
- Lecture 9 - Wilsonian renormalization
- Lecture 10 - Wilsonian renormalization of scalar field theory at one loop in the local potential approximation
- Lecture 11 - Grassman variables, Berezin calculus, Fermionic functional integrals
- Lecture 12 - Non-abelian gauge theory, Gauge fixing
- Lecture 13 - Quantization of non-abelian gauge theory, Gauge fixing
- Lecture 14 - Faddeev-Popov determinant, Ghosts
- Lecture 15 - Feynman rules for non-abelian gauge theory, Renormalization of non-abelian gauge theory

**Condensed Matter - Anushya Chandran, Roger Melko, Xiao-Gang Wen**

- Lecture 1 - Introduction to Condensed Matter, Order and symmetry, Crystal Lattices, symmetries, reciprocal space
- Lecture 2 - Reciprocal lattice vectors and first Brillouin zone, Bloch's theorem; Phonons in 1D chains, dispersion, acoustical and optical modes
- Lecture 3 - Quantum mechanics of lattice vibrations, Einstein model, heat capacity at high and low temperatures
- Lecture 4 - Bose-Einstein condensation for non-interacting bosons, critical temperature. Magnons and spin waves: 1D ferromagnetic Heisenberg chain, quantum mechanical treatment
- Lecture 5 - Specific heat and thermal dependence of magnetization in ferromagnets. Fermi gas: Fermi energy, density of states and specific heat
- Lecture 6 - Particle hopping on a lattice, multi-band cases
- Lecture 7 - Review of Lagrangian and Hamiltonian formalisms; particle in electromagnetic field; quantum motions
- Lecture 8 - Classical equations of motion following from a hopping Hamiltonian on a lattice; multi-band case
- Lecture 9 - Conductivity as follows from quasi-classical approach. Quantum Boltzmann approach, distribution funtion, Hall conductivity
- Lecture 10 - Quantized Hall conductance in insulators, Chern numbers. Introduction to topological classification of gapped phases of non-interacting fermions.
- Lecture 11 - Non-interacting Fermi gas, properties of metals. Interacting fermions, Fermi-liquid, Hartree-Fock approximation
- Lecture 12 - Landau Fermi-liquid theory; quasiparticles and their lifetime.
- Lecture 13 - Excitations and specific heat in Landau Fermi-liquid. Classical charged particle in magnetic field; quantum dynamics of an electron in magnetic field.
- Lecture 14 - Integer Quantum Hall effect: role of disorder and semi-classical percollation picture; edge states
- Lecture 15 - Fractional Quantum Hall effect, Laughlin wave functions, properties of Quantum Hall states

**Standard Model - Paul Langacker**

- Lecture 1 - Historical background on particle physics
- Lecture 2 - Introduction to SM and QED
- Lecture 3 - Lie groups
- Lecture 4 - Global symmetries of strong interactions and the Eightfold way. Chiral symmetry
- Lecture 5 - Spontaneous symmetry breaking and Goldstone's theorem
- Lecture 6 - Nonabelian gauge theories and Feynman Rules. QCD.
- Lecture 7 - Aspects of QCD
- Lecture 8 - Weak interactions. Fermi Theory
- Lecture 9 - Semi-leptonic decays in Fermi Theory
- Lecture 10 - SU(2) X U(1) theory of weak interactions
- Lecture 11 - Spontaneous symmetry breaking of SU(2) X U(1)
- Lecture 12 - CKM matrix and CP violation
- Lecture 13 - Unitarity triangle and Higgs production

**Gravitational Physics - Ruth Gregory**

- Lecture 1 - Manifolds and Tensors
- Lecture 2 - Differential Forms, Exterior and Lie Derivatives
- Lecture 3 - Lie Derivative contd, Killing vectors, Connections and Curvature, Cartan's Equations of Structure
- Lecture 4 - Applying Cartan: spherically symmetric, static solutions
- Lecture 5 - The casual structure of spacetime
- Lecture 6 - The Einstein-Hilbert action (and beyond)
- Lecture 7 - Gravity and non-perturbative field theory
- Lecture 8 - Geometry of Submanifolds
- Lecture 9 - Applications of Gauss-Codazzi, Israer Equations, Gibbons-Hawking Term
- Lecture 10 - Black Hole Thermodynamucs, Euclidean Magic
- Lecture 11 - Kaluza-Klein Theory
- Lecture 12 - Higher Dimensional Black Holes: KK Black Holes, Magnetic Monopole, SUGRA Solutions
- Lecture 13 - Perturbation Theory, Gregory-Laflamme Instability of Black String
- Lecture 14 - Acceleration & Gravity: C-Metric, Cosmic Strings
- Lecture 15 - Gravitational Instantons

**Foundations of Quantum Mechanics - Lucien Hardy**

- Lecture 1 - Basic elements of interferometry, Mach-Zehnder interferometer, Elitzur-Vaidman bomb tester, quantum errasure, Hardy's paradox.
- Lecture 2 - Axioms for pure state Quantum Theory; No-cloning theorem; Quantum Zeno effect
- Lecture 3 - Quantum optical interferometry, singles modes and coherent states; Hong-Ou-Mandel effect.
- Lecture 4 - Zou-Wang-Mandel experiment; Einstein's comments at the 1927 Solvay conference; Einstein-Podolsky-Rosen paradox
- Lecture 5 - The Harrigen-Spekkens classification scheme of ontological models; interpretations flow-chart
- Lecture 6 - The de Broglie-Bohm model; measurements and non-locality of the model
- Lecture 7 - The many-worlds interpretation of quantum mechanics: axioms, consequences and crtiticism
- Lecture 8 - Collaps models of quantum mechanics, GRW model
- Lecture 9 - Psi-epistemic models; the ontological excess baggage theorem
- Lecture 10 - Toy models based on the balanced model principle, Contextuality
- Lecture 11 - Epistemic vs. ontic interpretations of the wavefunction and the Pussey-Barrett-Rudolph theorem proving the reality of the wavefunction
- Lecture 12 - Rob Spekken's approach to non-contextuality; Generalized probability theories
- Lecture 13 - Quantum circuits and measurements, the property of convexity
- Lecture 14 - Quantum circuits: tomographic locality and Wooters hierarchy. Reasonable postulates for quantum theory
- Lecture 15 - The shape of quantum state space and the Fuchs approach

**Condensed Matter - Alioscia Hamma**

- Lecture 1 - The notion of a quantum phase transition, universality, dynamical critical exponent, types of phase transitions and level crossing
- Lecture 2 - Quantum Ising Moel: spontaneous symmetry breking and dephasing. Transfer matrix method in one dimension
- Lecture 3 - Mapping between classical and quantum Ising models, scaling limit
- Lecture 4 - The method of duality in the study of 1D quantum Ising model. Orthogonality catastrophe. Fidelity between the states.
- Lecture 5 - Quantum geometric tensor. quantum XY-model, Berry curvature
- Lecture 6 - Locality in quantum many-body physics; Lieb-Robinson bounds
- Lecture 7 - Lieb-Robinson bounds: bounds on correlation functions and Lieb-Mattis-Schultz theorem
- Lecture 8 - Quasi-adiabatic connectivity; Lattice gauge theory
- Lecture 9 - Elitzur's theorem. Quantum phase transitions without symmetry breaking
- Lecture 10 - Quantum lattice Z_2 gauge theory: ground states, duality
- Lecture 11 - Discrete gauge theory; Kitaev's toric code: states classification
- Lecture 12 - Kitaev's toric code: string operators, emergent fermions
- Lecture 13 - Topological order, entanglement, memory
- Lecture 14 - Topological order, entanglement, memory (continued); Equilibration

**String Theory - Davide Gaiotto**

- Lecture 1 - Introduction to perturbative String Theory
- Lecture 2 - Free scalar field on the world-sheet
- Lecture 3 - The bosonic string spectrum
- Lecture 4 - BRST Quantization
- Lecture 5 - The central charge and the Weyl anomaly
- Lecture 6 - BRST quatization of the string, ghosts
- Lecture 7 - BRST quantization contd; the state-operator correspondence
- Lecture 8 - Vertex operators
- Lecture 9 - Scattering amplitudes
- Lecture 10 - Strings in background fields; T-duality
- Lecture 11 - D-branes as sources of closed strings
- Lecture 12 - Open strings, boundary conditions
- Lecture 13 - Super-particle world line formalism; Introduction to the superstring
- Lecture 14 - Superstrings

**Cosmology - Latham Boyle**

- Lecture 1 - Review of standard model
- Lecture 2 - Maximally Symmetric Spaces
- Lecture 3 - FRW Spacetime: Metric, Hubble's Law, Cosmological Redshift
- Lecture 4 - FRW Spacetime: Horizons, Dynamics, Standard Cosmological Model
- Lecture 5 - Thermodynamics in expanding spacetime
- Lecture 6 - BBN & CMB
- Lecture 7 - Dark matter
- Lecture 8 - Cosmological constant problem, modified gravity
- Lecture 9 - Baryogenesis
- Lecture 10 - Inflation
- Lecture 11 - QFT in curved spacetime, Unruh
- Lecture 12 - Euclidean trick: temperature of the Sitter horizon, Primordial perturbations & Inflation
- Lecture 13 - Inflation and perturbation

**Beyond the Standard Model - Robert Mann**

- Lecture 1 - Review of Gauge Theories
- Lecture 2 - Introduction to anomalies
- Lecture 3 - Abelian and Non-abelian anomalies
- Lecture 4 - Implications of the Anomaly
- Lecture 5 - Path integral Derivation of the Anomaly
- Lecture 6 - Topological Aspects of Abelian Anomalies
- Lecture 7 - Topological Aspects of Non-Abelian Anomalies
- Lecture 8 - Index Theorems and Characteristic Classes
- Lecture 9 - Index Theorems and Characteristic Classes (continued), Introduction to Instantons
- Lecture 10 - Introduction to Instantons (continued)
- Lecture 11 - The Theta Vacua
- Lecture 12 - Implications of Instantons
- Lecture 13 - Introduction to Magnetic Monopoles

**Quantum Gravity - Bianca Dittrich**

- Lecture 1 - Introduction to Quantum Gravity, Einstein-Hilbert Action
- Lecture 2 - Triads, Spin Connection, 3D Gravity
- Lecture 3 - Platini Action and its Symmetries, B-F Theory
- Lecture 4 - Canonical Analysis and Gravity Hamiltonian
- Lecture 5 -Systems with first class constraints, Constraint algebra
- Lecture 6 - Parametrized particle and its quantization
- Lecture 7 - Towards quantizing gravity, SU(2) gymnastics
- Lecture 8 - Holonomies, Fluxes and their Poisson Algebra
- Lecture 9 - Quantizing one edge
- Lecture 10 - SU(2) gymnastics: Haar measure & Peter-Weyl theorem
- Lecture 11 - Action of fluxes, Length operator
- Lecture 12 - Solving the Gauss constraint
- Lecture 13 - Tetrahedra: Solving the flatness constraint
- Lecture 14 - Lightning review of 3+1 LQG

**Quantum Information - Andrew Childs**

- Lecture 1 - qubits, unitary operations and quantum protocols (superdense coding and teleportation)
- Lecture 2 - Circuits, reversible computation, and universality
- Lecture 3 - universality cont., DiVincenzo criteria, nonlinear optics, survey of implementations
- Lecture 4 - the Church-Turing thesis, efficiency, strong Church-Turing thesis, complexity classes, black boxes
- Lecture 5 - introductory quantum algorithms: Deutch-Jozsa and Simon's problem
- Lecture 6 - the quantum Fourier transform and phase estimation
- Lecture 7 - factoring, RSA, Shor's algorithm and order finding
- Lecture 8 - searching algorithms
- Lecture 9 - open quantum systems
- Lecture 10 - distance measures and entropy
- Lecture 11 - compression
- Lecture 12 - error correction
- Lecture 13 - stabilizer codes and fault tolerance
- Lecture 14 - quantum key distribution

**Quantum Information - David Cory**

- Lecture 1 - Basics of Neutron Interferometry (NI) without spin
- Lecture 2 - Basics of NI with spin
- Lecture 3 - Discussion of Tutorial 1, Incoherence and Decoherence in NI
- Lecture 4 - Noise in NI

**Condensed Matter - Guifre Vidal**

- Lecture 1 - Fermionic systems with quadratic Hamiltonians
- Lecture 2 - Overview of the course; Quantum spin chains; Tensor product and graphical notation
- Lecture 3 - MATLAB session I -- Quantum spin chains, exact diagonalization
- Lecture 4 - MATLAB session II -- Quantum spin chain by power method
- Lecture 5 - MATLAB session III -- Diagonalizing quadratic Hamiltonians
- Lecture 6 - Basics of Entanglement: Definition, Schmidt decomposition, measure of entanglement. Shanon, von-Neumann and Renyi entropies
- Lecture 7 - MATLAB session IV -- Entanglement in quantum spin chain
- Lecture 8 - MATLAB session V -- Entanglement in systems with free fermions
- Lecture 9 - Boundary law -- scaling of entanglement in systems of free fermions and toy model
- Lecture 10 - Entanglement as a theoretical tool: universality and entanglement spectrum
- Lecture 11 - Basics of tensor networks -- definitions, notations, computational cost.
- Lecture 12 - Matrix product states: efficient manipulations.
- Lecture 13 - Matrix product states: entanglement entropy and ground states of gapped systems
- Lecture 14 - Multi-scale entanglement renormalization ansatz (MERA) and tree tensor networks (TTN)
- Lecture 15 - Projected entangled-pair states (PEPS), branching MERA and applications of tensor networks

**String Theory - Andrei Starinets**

- Lecture 1 - Introduction
- Lecture 2 - Example of dualities
- Lecture 3 - Black hole thermodynamics
- Lecture 4 - Black hole thermodynamics contd
- Lecture 5 - Elements of string theory: type IIB SUGRA eom
- Lecture 6 - Elements of string theory contd: SUGRA action and black brane solns
- Lecture 7 - More on Dp-branes, N=4 SYM as the low energy effective theory for D3-branes.
- Lecture 8 - "Constructing" gauge-string duality
- Lecture 9 - "Constructing" gauge-string duality contd.
- Lecture 10 - Thermodynamics of N=4 SYM
- Lecture 11 - Scalar field in AdS5 (Euclidean propagator)
- Lecture 12 - Scalar field in AdS5 (Lorentzian propagator)
- Lecture 13 - BF bound, normalizable modes, quasinormal spectrum
- Lecture 14 - Elements of hydrodynamics
- Lecture 15 - Holographic calculation of transport coefficients

**Particle Theory - Brian Shuve**

- Lecture 1 - Dark Matter: Evidence, hypothesis and challenges.
- Lecture 2 - FRW universe and equilibrium thermodynamics.
- Lecture 3 - Departure from equilibrium and the Boltzmann equation.
- Lecture 4 - Thermal relics, solving the Boltzmann equation and the WIMP miracle.
- Lecture 5 - Thermal freeze-out, general implications of WIMP models, variations on thermal freeze-out.
- Lecture 6 - Resonant enhancement and coannihilation. Introductin to direct detection.
- Lecture 7 - Spin independent scattering.
- Lecture 8 - Spin dependent scattering. Experimental status of direct detection.
- Lecture 9 - Indirect detection.
- Lecture 10 - Non-thermal dark matter. Freeze in.
- Lecture 11 - Vacuum misalignment. QCD axion as DM.
- Lecture 12 - Introduction to Baryogenesis. Sakharov conditions.
- Lecture 13 - Baryogenesis in the standard model.

**Cosmology - Matt Johnson**

- Lecture 1 - Introduction, FRW metric, Perfect fluids
- Lecture 2 - FRW universe, Newtonian theory of perturbations
- Lecture 3 - Growth of structure in Newtonian theory
- Lecture 4 - Metric perturbations and coordinate transformations
- Lecture 5 - Einstein's equations in a perturbed universe, Boltzmann equation
- Lecture 6 - Photons, Boltzmann equation
- Lecture 7 - Boltzmann equation, Baryon acoustic oscillations
- Lecture 8 - Primordial perturbations
- Lecture 9 - Scalar power spectrum
- Lecture 10 - Spectral tilt, Running
- Lecture 11 - Non-gaussianities
- Lecture 12 - Stochastic Eternal Inflation
- Lecture 13 - Vacuum Decay

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