# 2012/2013 PSI Lectures

Watch recorded courses from 2012/2013 PSI Lecture Series

## VIEW TABS FOR DIFFERENT LECTURES IN 2012/2013YEAR

Welcome PSI 2012/13 - Part 1, Part 2

Algebra - Anna Kostouki

• Lecture 1 - Linear Algebra: Vector spaces, basis, scalar product, linear operators, matrix representations
• Lecture 2 - Group theory: Finite groups (cyclic and permutation groups), rotational groups
• Lecture 3 - Group Theory contd: O(3) and SO(3), U(n) and SU(n), Lorentz and Poincare groups
• Lecture 4 - Tangent and cotangent space, vectors and tensors, Clifford algebras, Grassman algebras.

Student Presentations

Special Functions and Differential Equations - Dan Wohns

• Lecture 1 - Distributions: test functions, Dirac delta function, Derivatives of distributions, Multiplication of distributions by functions
• Lecture 2 - Solution Methods: Reduction of order, Variation of parameters, Power series method, WKB approximation
• Lecture 3 - Orthogonal Functions - Sturm-Liouville theory, Parseval's theorem, Orthogonal polynomials
• Lecture 4 - Special Functions and Complex Variables: Gamma function, Stirling's approxximation, Saddle point method, Zeta function

Calculus of Variation and Gaussian Integrals - Lilia Anguelova

• Lecture 1 - Gaussian integrals in one dimension; Multi-dimensional Gaussian integrals; Averages with Gaussian weight
• Lecture 2 - Wick's theorem; Imaginary Gaussian integrals; Gaussian integrals with Grassmann variables
• Lecture 3 - Functionals; Functional derivatives, Euler-Lagrange equations; Lagrangian Mechanics
• Lecture 4 - Noether's theorem; Euler-Lagrange equations for continuous systems; Energy-momentum tensor; Constrained variations

Integral transforms & Green's Functions - David Kubiznak

• Lecture 1 - Green's functions, BVP, Poisson's equation, Green's identities, Method of images
• Lecture 2 - Fourier transform, diffusion equation, heat kernel, FT in quantum mechanics
• Lecture 3 - Maxwell's equation, Wave equation, Retarded Potentials, Feynman-Wheeler theory
• Lecture 4 - Functional integral, Propagator, Degrees of freedom in gauge theories

Condensed Matter 101 - Denis Dalidovich

• Lecture 1 - Basic models of condensed matter; thermodynamics of free electron gas
• Lecture 2 - Second quantisation; thermodynamics of free boson gas
• Lecture 3 - Crystal lattices and Bloch's theorem
• Lecture 4 - Motion in a periodic potential; tightly bound electrons

Mathematica - Pedro Vieira

Ising Model - John Berlinsky

Relativity - Michael Duff

• Lecture 1 - Motivation: Special relativity vs Newtonian Gravity
• Lecture 2 - Equivalence Principle, Coordinate Transformations
• Lecture 3 - General Covariance, Geodesic Equation, Tensors
• Lecture 4 - Tensor Algebra, Tensor Densities, Covariant Derivative
• Lecture 5 - Curvature Tensor and its Properties, Conditions for Flatness
• Lecture 6 - Geodesic Deviation, Einstein's Equations
• Lecture 7 - Solutions of Einstein's Equations: Schwarzschild Metric
• Lecture 8 - Charged Black Hole (Reissner-Nordstrom solution); Rotating Black Hole (Kerr Solution)
• Lecture 9 - Experimental Tests of GR: Precession of Perihelion, Deflection of Light
• Lecture 10 - Experimental Tests of GR: Precession of Perihelion, Deflection of Light
• Lecture 11 - Lagrangian Formulation, Einstein-Hilbert action
• Lecture 12 - Coupling Gravity to Matter: Scalar Field, Maxwell Field
• Lecture 13 - Brans-Dicke Theory, Vierbein Formalism
• Lecture 14 - Kaluza-Klein Theory, Supergravity
• Lecture 15 - Cosmology: Friedmann-Robertson-Walker Metric

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 - The Von Neumann Equation. Composite and Entangled Systems.
• Lecture 4 - Subsystems and Partial Trace. Schmidt Decomposition. Von Neumann Entropy.
• Lecture 5 - Partial criteria for Entanglement. Positive Partial Transpose (PPT). Sequential Measurement and Collapse. Von Neumann model of a measurement.
• Lecture 6 - Abstract model of von Neumann measurement. Decoherence.
• Lecture 7 - Interpretational controversy surrounding the collapse of the wave function. EPR Paradox.
• Lecture 8 - Dirac's abstract formulation of quantum and classical mechanics in terms of the Poisson braket and the commutator.
• Lecture 9 - Bell's inequalities. CHSH inequality. Hidden variables.
• Lecture 10 - Final comments relating to Bell's theorem. Infinite dimensional Hilbert Spaces. Self-adjoint operators on infinitte dimensional Hilbert Spaces.
• Lecture 11 - Infinite dimensions continued. Markov processes and classical path integrals. The Feynman path integral.
• Lecture 12 - The Feynman path-integral continued. Open quantum systems. Kraus operators.
• Lecture 13 - The optical Bloch equations. NMR and the Bloch equations.
• Lecture 14 - The Rotating Wave Approximation. Continuos Models of Markovian Open Systems and Dynamics [The Lindblad Formalism].
• Lecture 15 - Concepts and Examples from Quantum Information. Quantum Circuts. factoring. Quantum Teleportation.

Quantum Field Theory I - Konstantin Zarembo

• Lecture 1 - Particles and Second Quantization, Bose Condensation
• Lecture 2 - Part 1 Part 2 - Phonons, Debye Theory
• Lecture 3 - Part 1 Part 2 - Klein-Gordon field, Conservation Laws, Noether's Theorem
• Lecture 4 - Part 1 Part 2 - Quantization of Klein-Gordon field, Heisenberg Representation, Dirac's Equation
• Lecture 5 - Part 1 Part 2 - Spinors and Spin, Dirac Conjugation
• Lecture 6 - Part 1 Part 2 - Dirac Lagrangian, Solutions of Dirac Equation, Quantization, Weyl Fermions, Helicity
• Lecture 7 - Part 1 Part 2 - Electromagnetic Field: Gauge Symmetry, EM Waves, Quantization
• Lecture 8 - Part 1 Part 2 - Quantum Electrodynamics, Dimensional Analysis and Perturbation Theory
• Lecture 9 - Part 1 Part 2 - Idea of Renormalization, Green's Functions, Wick's Theorem
• Lecture 10 - Part 1 Part 2 - Feynman Propagator, Feynman Diagrams
• Lecture 11 - Part 1 Part 2 - Scattering Amplitudes, Perturbation Theory in QED
• Lecture 12 - Part 1 Part 2 - Scattering of Electrons, Coulomb Law from QED, Yukawa Interactions
• Lecture 13 - Part 1 Part 2 - Cross Sections and Decay Rates
• Lecture 14 - Part 1 Part 2 - Examples of QED Calculation, QFT: Summary& Future Directions

Condensed Matter - Assa Auerbach

• Lecture 1 - From Hubbard Model to Heisenberg Model: Superexchange
• Lecture 2 - From Hubbard Model to Heisenberg Model: Brillouin-Wigner renormalization
• Lecture 3 - Coherent states for spins
• Lecture 4 - Spin coherent state path integral
• Lecture 5 - Spin wave theory from spin coherent path integral
• Lecture 6 - Field theory for quantum antiferromagnets; non-linear sigma-model
• Lecture 7 - Spontaneously broken symmetry
• Lecture 8 - Negative U Hubbard Model; particle-hole canonical transformation
• Lecture 9 - x-xz model; superconducting charge density wave and supersolid phases
• Lecture 10 - Field operators and boson coherent states
• Lecture 11 - Persistent currents and flux quantization
• Lecture 12 - Meissner effect, statics of vortices, Magnus force
• Lecture 13 - Motion of vortices; vortex lattice

Quantum Field Theory II - 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, quantization of the free scalar field using functional integrals
• Lecture 3 - Free scalar field: Functional integration using spacetime discretization, Correlation functions
• Lecture 4 - Free scalar field propagator, Quantization of φ4 theory
• Lecture 5 - Structure of perturbative expansion, Effective action
• Lecture 6 - Effective action continued
• Lecture 7 - Kallen-Lehman spectral representation, Mass renormalization of φ4 theory
• Lecture 8 - Coupling constant renormalization of massless φ4 theory
• Lecture 9 - Renormalization group
• Lecture 10 - Grassman variables, Berezin calculus, Fermionic Path integrals
• Lecture 11 - Non-abelian gauge theory
• Lecture 12 - Yang-Mills action, Coupling to matter, Feynman rules
• Lecture 13 - Gauge fixing
• Lecture 14 - Faddeev-Popov determinant, ghosts, Feynman rules, Yang-Mills beta function
• Lecture 15 - Wilsonian renormalization, Renormalization of non-abelian gauge theory

Statistical Mechanics - John Berlinsky

• Lecture 0 - Ising Model
• Lecture 1 - Introduction to phase transitions, Spatial Correlation Functions
• Lecture 2 - Correlations and susceptibility, Critical exponents, Mean Field Theory & Landau theory
• Lecture 3 - Vector order parameters, Spatially varying fields
• Lecture 4 - Spin-spin correlation function in MFT, Scaling & Power laws
• Lecture 5 - Two-parameter scaling, relations among critical exponents, Kadanoff length scaling
• Lecture 6 - Ginzburg criterion, Gaussian model
• Lecture 7 - Gaussian model: partition function, free energy, internal energy, specific heat, critical region
• Lecture 8 - The renormalization group idea> Block spin renormalization for the 1-d Ising Model
• Lecture 9 - Block spin renormalization in d>1
• Lecture 10 - General RG theory; flows in the space of many couplings, scaling variables
• Lecture 11 - The ε expansion; the Gaussian model and the  uσ4 model
• Lecture 12 - RG flow for model  uσ4 continued; Wilson-Fisher fixed point
• Lecture 13 - Exponents from the ε expansion; corrections to scaling

Standard Model - Mark Wise

• Lecture 1 - Phase spaces for decay widths and cross-sections
• Lecture 2 - Differential cross-sections and invariant amplitude: e^-e^+ to mu^- mu^+. The standard model gauge group. The Higgs doublet
• Lecture 3 - Spontaneous symmetry breaking and massive gauge bosons
• Lecture 4 - The particle content of the standard model. Yukawa couplings. The CKM matrix.
• Lecture 5 - Interactions of gauge bosons with fermions. Interactions of the Higgs boson with fermions. Muon decay.
• Lecture 6 - Muon decay continued. Renormalization of QED. Dimensional reguralization.
• Lecture 7 - Computation of counterterms in QED
• Lecture 8 - Beta function for the electromagnetic coupling constant. Renormalization of QCD. Asymptotic freedom.
• Lecture 9 - Applications of asymptotic freedom. Charmonium and bottomonium.
• Lecture 10 - Structure functions. Proton + proton to Z + X.
• Lecture 11 - Higgs decay into gluons.
• Lecture 12 - Renormalization of bottom mass. Chiral Lagrangian.
• Lecture 13 - Chiral perturbation theory. Light meson masses.
• Lecture 14 - Decay of pi minus. Application of chiral perturbation theory: The atmospheric neutrino problem. Discrete symmetries.
• Lecture 15 - Discrete symmetries continued. The PSI song. CP violation in the Standard Model. The CKM matrix and the unitarity triangle.

String Theory - Barton Zwiebach

• Lecture 1 - Review of Ralativity, Light cone coordinates, Compactification
• Lecture 2 - Orbifolds, Nonrelativistic sting, Relativistic point particle
• Lecture 3 - Relativistic strings, Nambu-Goto action
• Lecture 4 - Boundary conditions: D-branes, Static gauge, String in rest, Transverse velocity
• Lecture 5 - String parametrization, equations of classical motion and constraints
• Lecture 6 - Symmetries and conserved momentum and Lorentz charges. general gauges.
• Lecture 7 - Equations of motion for free open strings, light-cone solutions, Virasoro operators.
• Lecture 8 - Light cone fields, Point particle quantization
• Lecture 9 - Quantization of point particle in light cone gauge, Momentum and Lorentz generators
• Lecture 10 - Quantization of an open string I
• Lecture 11 - Quantization of an open string II: critical dimension, tachyon, Maxwell field
• Lecture 12 - Quantization of a closed string; Virasoro operators, graviton, dilaton
• Lecture 13 - Strings on R^1/Z_2 orbifold. Action for fermionic strings.
• Lecture 14 - Quantizing superstrings: NS and R sectors, Spacetime fermions.
• Lecture 15 - Overview of superstring theories, D-branes

Foundations of Quantum Mechanics - Rob Spekkens

• Lecture 1 - What's the problem? The realist strategy. The quantum measurement problem.
• Lecture 2 - The operational strategy. Operationalism vs realism.
• Lecture 3 - The most general preparations. The most general measurements.
• Lecture 4 - The most general types of transformations.
• Lecture 5 - A framework for convex operational theories. Operational classical theory. Operational quantum theory. Real vs complex field.
• Lecture 6 - Recasting the òrthodox`interpretation as a realist model. Realism via hidden variables. Psi-ontic vs psi-epistemic models
• Lecture 7 - Evidence in favour of psi-epistemic hidden variable models. Restricted Liouville mechanics. Restricted statistical theory of bits.
• Lecture 8 - Bell's theorem.
• Lecture 9 - Non-locality in more depth.
• Lecture 10 - Contextuality
• Lecture 11 - Generalized notions of non-contextuality.
• Lecture 12 - The deBroglie-Bohm interpretation.
• Lecture 13 - The deBroglie-Bohm interpretation continued.
• Lecture 14 - Dynamical Collapse theories.
• Lecture 15 - The Everett interpretation.

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 - Examples: Gravitational Wave Spacetime, Warped Compactification
• Lecture 5 - The physics of curvature: accelerations vs gravity, geodesics in Schwarzschild
• Lecture 6 - Derivation of Black Hole solutions: Schwarzchild, (A)dS Black Holes, Euclidean Black Holes and Hawking Temperature
• Lecture 7 - Lagrangians, Einstein-Hilbert Action, Energy-Momentum Tensors, Energy Conditions
• Lecture 8 - Domain wall solution, Cosmic string solutions
• Lecture 9 - Jordan-Brans-Dicke modified gravity, Jordan & Einstein frames
• Lecture 10 - Kaluza-Klein Theory, KK Black Holes
• Lecture 11 - Gauss-Codazzi formalism, Geometry of submanifolds
• Lecture 12 - Applications of Gauss-Codazzi, Gibbons-Hawking term, Israel equations
• Lecture 13 - Penrose Diagrams, Properties of BHs
• Lecture 14 - Cosmic Censorship, (In)Stability of Black Holes
• Lecture 15 - Gravity and String Theory, D-Branes, properties of AdS

Quantum Gravity - Bianca Dittrich

• Lecture 1 - Einstein-Hilbert action, Einstein's theory in 3D
• Lecture 2 - Tetrad formalism: vielbeins, spin correction, torsion and cur
• Lecture 3 - First-order formalism, Symmetries of 3D gravity action
• Lecture 4 - Hamiltonian analysis, Canonical variables for gravity, Totally constraint system
• Lecture 5 - Constraints, Gauge transformations and constraint algebra
• Lecture 6 - Phase space of systems wuth gauge symmetry, Dirac observables, Parametrized particle
• Lecture 7 - Quantization of parametrized particle I
• Lecture 8 - Quantization of parametrized particle II
• Lecture 9 - SO(3), SU(2), and Holonomy
• Lecture 10 - Holomonies, Fluxes and their Poisson algebra
• Lecture 11 - Outline of Quantization, SU(2) gymnastics
• Lecture 12 - Hilbert Space for One Edge, Action of Fluxes, Lenght Quantized
• Lecture 13 - Solving the Gauss Constraint, Intertwiner

Condensed Matter - Dmitry Abanin, Alioscia Hamma

• Lecture 1 - The notion of a quantum phase transition: ground state energy, phase diagram. Quantum Ising Model in 1D, duality
• Lecture 2 - Universality in critical phenomena and scaling
• Lecture 3 - Quantum to classical mapping.
• Lecture 4 - Exact spectrum of transverse Ising model and correlation functions.
• Lecture 5 - Quantum Information approach to Quantum Phase Transitions
• Lecture 6 - Quantum-coherent transport in 1D systems; point contacts; scattering matrix
• Lecture 7 - Electrons in disordered potential: Landauer formalism and perturbation theory
• Lecture 8 - Localization phenomena; scaling approach to localization
• Lecture 9 - Graphene: band structure, Dirac-like low energy excitations
• Lecture 10 - Graphene: conductivity and the role of disorder
• Lecture 11 - Berry phases, Berry's curvature, examples.
• Lecture 12 - Integer Quantum Hall effect; edge states and the role of disorder
• Lecture 13 - Quantum Hall effect: bulk and transition. Percollation and flux insertion approaches
• Lecture 14 - Topological invariance and Hall conductivity

Beyond the Standard Model - Itay Yavin, Natalia Toro

• Lecture 1 - Lagrangian for complex scalar + Weyl fermion, Feynman rules
• Lecture 2 - 1-loop correction of fermion and scalar propagators, Hard cut-off regularization, Lo
• Lecture 3 - Dimensional regularization, Hierarchy problem
• Lecture 4 - Technical naturalness, Canceling the quadratic divergence using supersymmetry
• Lecture 5 - Supersymmetric gauge theory, Chiral supermultiplets, Vector supermultiplets
• Lecture 6 - Supersymmetry transformations, Production of charginos
• Lecture 7 - Dimensional analysis, Cross sections, Calculatin Feynman diagrams using Mathematica or MadGraph
• Lecture 8 - Effective field theories in the Standard Model, Chiral Lagrangian, Fermi theory
• Lecture 9 - Effective field theories as probes of new physics
• Lecture 10 - The role of exact and approximate symmetries in new physics seachers. Approximate symmetries of the SM
• Lecture 11 - Approximate symmetries of the SM continued. Parameter counting. CKM matrix.
• Lecture 12 - GIM mechanism, Kaon oscillations in the Standard Model, Kaon oscillations with supersymmetry, soft supersymmetry breaking
• Lecture 13 - Strong CP problem
• Lecture 14 - Axions and the strong CP problem.

Quantum Information - Andrew Childs

• Lecture 1 - Qubits, unitary operators, superdense coding.
• Lecture 2 - Circuit models, reversible computation, universal gate sets.
• Lecture 3 - Implementations (non-linear optics).
• Lecture 4 - Computational complexity.
• Lecture 5 - Computational complexity continued. Basic quantum algorithms: Deutsch-Jozsa.
• Lecture 6 - Phase estimation, quantum Fourier transform.
• Lecture 7 - RSA, Shor's algorithm.
• Lecture 8 - Grover's algorithm.
• Lecture 9 - Density matrices, quantum operations, POVMs.
• Lecture 10 - Distance measures, Helstrom measurement
• Lecture 11 - Entropy, entanglement concentration, compression
• Lecture 12 - Quantum data compression continued. Quantum error correction.
• Lecture 13 - Stabilizer codes.

Cosmology - Latham Boyle

• Lecture 1 - Review of Differential Geometry: Manifolds & Tensors, the Connection, the Metric
• Lecture 2 - Review of GR: Einstein equations, the Energy-momentum tensor
• Lecture 3 - GR vs. Yang-Mills theory; Maximally symmetric space-times
• Lecture 5 - The FRW mwtric, Friedman equation, Continuity equation
• Lecture 6 - Kinematics of FRW: geodesics, horizons; The horizon problem
• Lecture 7 - The flatness problem; Matter, rediation and dark energy; the history of the Universe
• Lecture 8 - Thermodynamics & Statistical Mechanics in the Universe; Decoupling and Freeze-out
• Lecture 9 - BBN & CMB
• Lecture 10 -Dark Matter: observational evidence & candidates
• Lecture 11 - Cold & Hot DM, non-thermal relics; Baryogenesis
• Lecture 12 - The 3 Big Bang problems; Inflation
• Lecture 13 - Inflation & Perturbations
• Lecture 14 - QFT in curved space: Bogoliubov transformations, Unruh temperature

Quantum Information - David Cory

• Lecture 1 - Neutron interferometry, pure state case.
• Lecture 2 - Uses of neutron interferometry, mixed state case.
• Lecture 3 - Incoherent processes in NI - magnetic field in one path.
• Lecture 4 - Incoherent processes in NI - wedge in one path.
• Lecture 5 - Spin in NI.
• Lecture 6 - NMR.
• Lecture 7 - NMR. Rotating wave approximation.
• Lecture 8 - NMR. Bloch equations. Characterizing a qubit. Hahn echo.
• Lecture 9 - NMR. Echo with diffusion.
• Lecture 10 - NMR, two-qubit operations.

Particle Theory - David Morrissey

• Lecture 1 - Evidence for Dark Matter
• Lecture 2 - Dark Matter distributions. Thermal DM creation
• Lecture 3 - Thermal creation of DM. The Boltzmann equation.
• Lecture 4 - DM freeze out. Justification of kinetic equilibrium. Solving the Boltzman equation. S-wave and p-wave. Yield.
• Lecture 5 - Computing yield from the Boltzmann equation. The WIMP miracle. Candidates for WIMPs: Supersymmetry
• Lecture 6 - WIMPs continued. SUSY and R parity. Universal extra dimensions (UED). Resonant enhancement. Coannihilation.
• Lecture 7 - Coannihilation continued. Non-thermal DM. Gravitino as a DM candidate. Limitation of gravitino as a thermal DM candidate. SuperWIMP DM.
• Lecture 8 - Non-thermal DM: Massive particles decay. Asymmetric DM. Direct detection of DM. Kinematics of direct detection.
• Lecture 9 - Direct detection of DM. Scalar-Scalar interaction.
• Lecture 10 - Direct detection continued. Vector-vector and axial vector-axial vector interactions. Experimental searched for DM.

Condensed Matter - Guifre Vidal, Xiao-Gang Wen

• Lecture 1 - Quantum systems; entanglement in bipartite systems; measures of entanglement
• Lecture 2 - Scaling of correlations and entanglement. Valence bond solids.
• Lecture 3 - Free fermions and computation of entropy for free fermions
• Lecture 4 - Ground states of quadratic Hamiltonians
• Lecture 5 - Entanglement and Universality
• Lecture 6 - Tensor network states; diagrammatic notation, propertiesm computational cost
• Lecture 7 - Matrix product states
• Lecture 8 - Transfer matrix and calculation of observables in MPS formalism
• Lecture 9 - Multi-scale entanglement renormalization ansatz (MERA)
• Lecture 10 - Projected entangled-pair states (PEPS)
• Lecture 11 - Quantum phases and symmetry breaking in many-body physics
• Lecture 12 - Fractional quantum Hall states and dancing picture of topological order
• Lecture 13 - String liquid: dancing rules and topological degeneracy of the ground state
• Lecture 14 - Definition of topological order; topological and local particle-like excitations
• Lecture 15 - Fractional statistics of topological quasiparticles

Cosmology - Matt Johnson

• Lecture 1 - Homogeneous universe, Penrose diagrams
• Lecture 2 - Angular diameter distance, perturbed universe, gauge invariant perturbation theory
• Lecture 3 - Perturbed perfect fluid, Boltzmann equations
• Lecture 4 - First-order Boltzmann equation, collision terms
• Lecture 5 - Large scale inhomogeneities during radiation domination, physical versus comoving scales
• Lecture 6 - Baryon acoustic oscillations, damping, Sachs-Wolfe effect
• Lecture 7 - Power spectrum, acoustic oscillations
• Lecture 8 - Cosmic variance, Sachs-Wolfe pateau, comparing theory to Planck results
• Lecture 9 - Homogeneous limit of inflation
• Lecture 10 - QFT in curved spacetime
• Lecture 11 - QFT in curved spacetime: particle production
• Lecture 12 - Correlation functions, Schroedinger picture for QFT, Bunch-Davies Vacuum
• Lecture 13 - Scalar fluctuations in an inflating background
• Lecture 14 - Primordial scalar power spectrum
• Lecture 15 - Comparing inflactionary models with Planck data, eternal inflation

String Theory - Pedro Vieira

• Lecture 1 - Introduction to CFT's: Motivation
• Lecture 2 - Definition of CFT's, Conformal transformations
• Lecture 3 - 2-point and 3-point correlation functions, CFT data
• Lecture 4 - State-operator correspondence, primaries & descendants, unitary bounds, AdS space
• Lecture 5 - Operator Product Expansion, Conformal blocks
• Lecture 6 - Recent Advances in CFTs: Bootstrap Equations
• Lecture 7 - Matrix Model and Large N Limit
• Lecture 8 - Open-Closed String Duality, Maldacena's Decoupling Argument
• Lecture 9 - Maldacena's Decoupling Argument Part2: AdS/CFT Correspondence
• Lecture 10 - Geometry of ADS
• Lecture 11 - N=4 SYM, Anomalous Dimensions
• Lecture 12 - Calculation of Anomalous Dimensions with Spin Chain Techniques
• Lecture 13 - Calculation of Anomalous Dimensions on the String Theory Side (Strong Coupling): the BMN and Folded String Solutions
• Lecture 14 - Spin Chains and Integrability; Bethe Equations
• Lecture 15 - Bootstrap Program: Integrable Model with O(4), Cusp Anomalous at All Couplings