PSI Lectures/2011

Front

Complex Analysis - Tibra Ali

• Lecture 1 - Review of the basics of complex numbers. Geometrical interpretation in terms of teh Argand-Wessel plane. DeMoivre's theorem and applications. Branch points and branch cuts.
• Lecture 2a Lecture 2b - Cauchy-Riemann equations. Holomorphic functions and harmonic functions. Contour integration.
• Lecture 3 - Cauchy's theorem and integral formula. Taylor's theorem. Singularities. Laurent's series. Residues.
• Lecture 4 - Applications of the integral formula to evaluate integrals. Trigonometric integrals, semi-circular contours, mousehole contours, keyhole contours.

Linear Algebra - Anna Kostouki

• Lecture 1 - Linear Vector Spaces, Linear Operators, Scalar Products, Dual Spaces, Adjoint Operators, Eigenvalues Eigenvectors, Hermitian Unitary Operators.
• Lecture 3 - Group Theory: Finite groups and the permutation group. SU(2) and SO(3).
• Lecture 4 - The Lorentz and Poincaré groups (a short review of Special Relativity).

Differential Equations - Sarah Croke

• Lecture 1 - First order differential equations; examples: Einstein theory of radiation, optical attenuations; methods of solution.
• Lecture 2 - Second order differential equations, homogeneous and inhomogeneous; reduction of order; variation of parameters; the Wronskian.
• Lecture 3 - Series solutions; Euler's equation; Extended power series method, form of solutions in different cases; Bessel's equation.
• Lecture 4 - Bessel Functions; Separation of variables; Spherical Harmonics; WKB approximation.

Evaluation of Integrals and Calculous of Variations -Denis Dalidovich

• Lecture 1 - Gaussian Integrals in one and many dimensions. Averages with the Gaussian weight.
• Lecture 2 - Wick's Theorem. Imaginary Gaussian Integral. Gaussian Integral with Grassman variables.
• Lecture 3- Functionals and functional derivatives. Euler-Lagrange equations; examples from classical mechanics.
• Lecture 4 - Noether's theorem. Functionals describing continuous systems; Lagrangian density. Extrema of functionals subject to contraints; Lagrange multipliers.

Special Functions and Distributions - Dan Wohns

• Lecture 1 - Dirac delta; Test functions; Distributions and their derivatives.
• Lecture 2 - Orthogonal polynomials; Recurrence relations; Weights.
• Lecture 3 - Generalized Rodrigues' formulae; Classification of orthogonal polynomials; Sturm-Liouville theory.

Lie Groups and Lie Algebra's - Freddy Cachazo

• Lecture 1 - Introduction to Lie Groups and Lie Algebras in Physics. Lie groups, representations, structure constants.
• Lecture 2 - The Poincaré group algebra. Representations on Hilbert space. Massless and massive irreps. The Little Group.
• Lecture 3 - Classifications of Lie Algebras. Helicity and Spin. Highest weight representations of SU(2).
• Lecture 4 - The Adjoint representation. Classification of (simple) Lie Algebras. Roots diagrams and Dynkin diagrams.
• Lecture 5 - The group associated with the standard model of particle physics. Weights. Highest weight representations. Fundamental and anti-fundamental representations of su(3). Tensor products of representations. Clebsch-Gordan Decomposition. Young's Tableaux.

Mathematica - Pedro Vieira

• Lecture 4 - Harmonic Oscillator and Perturbation Theory

Core

Quantum Theory - Adrian Kent

• Lecture 1 - Gaussian wave-packets, double-slit experiment, tension with special relativity.
• Lecture 2 - Unitary evolution, Path integrals.
• Lecture 3 - Discussion of path integral. Problems deriving classical physics from quantum theory.
• Lecture 4 - Feynman checkerboard model, Angular momentum.
• Lecture 5 - Spin, Bloch sphere, Quantum Zeno effect, Mixed states.
• Lecture 6 - Guest Lecturer: Lucien Hardy. Interferometry, Elitzur-Vaidman bomb tester.
• Lecture 7 - Guest Lecturer: Lucien Hardy. Quantum-optical interferometry, Ou-Hong-Mandel effect.
• Lecture 8 - Guest Lecturer: Rafael Sorkin. The quantum measure. Three-slit experiment. Classical action.
• Lecture 9 - Guest Lecturer: Rafael Sorkin. Mathematical details of the quantum measure. Unitarity.
• Lecture 10 - Density matrices - definition and properties. Mixed states on the Bloch sphere. Proper and improper mixtures.
• Lecture 11 - Entanglement. Partial trace. No-signaling.
• Lecture 12 - EPR argument. Bell-CHSH inequalities. Experimental tests.
• Lecture 13 - Hidden variables. Extensions of Bell-CHSH inequalities. No cloning.
• Lecture 15 - Measurements in QM. Kraus operators. Decoherence. Many-worlds.

Relativity - Neil Turok

• Lecture 1 - Maxwell's Theory and Special Relativity.
• Lecture 8 - Action for relativistic particle, Einstein's equations.
• Lecture 9 - The Stress Energy Tensor of a perfect fluid in GR, the Einstein - Hilbert Action, spherically symmetric solutions of Einstein's equations.
• Lecture 10 - Schwarzschild solution, crossing the horizon, Krustal extension.
• Lecture 11 - Schwarzschild solution, crossing the horizon, Krustal extension.
• Lecture 12 - Particles in Schwarzschild, Precession of the Perihelion.
• Lecture 13 - Rotating Black Hole (Kerr solution), Event horizons.
• Lecture 14 - Causal Diagrams, Cosmological Solutions: maximally symmetric spaces, Friedmann equations.
• Lecture 15 - Causal Diagrams, Cosmological Solutions: maximally symmetric spaces, Friedmann equations

Quantum Field Theory I - Konstantin Zarembo

• Lecture 3 - Klein-Gordon field, Conservation laws and symmetries.
• Lecture 4 - Noether's theorem, Quantization of Klein-Gordon field, Dirac equation.
• Lecture 6 - Solutions of the Dirac equation, Quantization of the Dirac field.
• Lecture 7 - Weyl fermions, Electromagnetic Field, Gauge transformations.
• Lecture 8 - Quantum Electrodynamics, Perturbation Theory.
• Lecture 9 - Response to Students' Questions, Dimensional Analysis.
• Lecture 12 - Feynman Propagator, Momentum Space Feynman Rules
• Lecture 14 - QED Feynman rules, the Coulomb potential, Yukawa theory.

Statistical Mechanics - Leo Kadanoff

• Lecture 1 - Introduction to statistical physics phenomena, Partition function.
• Lecture 2 - Partition functions: means and variances. Non-interacting particles in a box.
• Lecture 3 - Pressure of an ideal gas. One-Dimensional Ising model: exact solution.
• Lecture 4 - One-dimensional Ising model: correlation length and solution by renormalization.
• Lecture 5 - Two-dimensional Ising model: phase transitions.
• Lecture 6 - Hopping on a lattice and diffusion equation.
• Lecture 7 - Diffusion in momentum space. Brownian motion. Hamiltonian Dynamics.
• Lecture 8 - Statistical ensambles, Stochastic processes, Fokker-Planck equation.
• Lecture 10 - H-theorem. Kinetic equation for Fermi/Bose gases.
• Lecture 11 - Van-der-Vaals equation. The notion of a phase transition.
• Lecture 12 - Phase transitions, Mean field theory, Landau's theory.
• Lecture 13 - Limitations of the mean field theory, Fluctuations.

Quantum Field Theory II - François David

• Lecture 2 - Semi-classical Expansion, Free Scalar Field.
• Lecture 3 - Feynman propagator, Wick's Theorem, Interactions.
• Lecture 4 - Feynman Diagrams, Generating Functionals, Loop Expansion.
• Lecture 7 - Renormalization of the coupling constant in massless Phi^ Theory, Renormalization Group.
• Lecture 8 - Renormalization of the massless Phi^4, Operator Product Expansion.
• Lecture 10 - Renormalization Group Flow, Grassman Variables, Berezin Claculus.
• Lecture 11 - Berezin Calculus, Fermionic Path Integrals.
• Lecture 13 - Quantization of Non-abelian Guage Theories, Guage Fixing, Faddeev-Popov Method.
• Lecture 15 - Renormalization of Guage Theories, Dimensional Regularization, Asymptotic Freedom, Lattice Guage Theories.

Condensed Matter - Nandini Trivedi

• Lecture 1 - Basic ideas of Condensed Matter. Crystals, Bravais and reciprocal lattices, x-ray scattering, density-density correlations.
• Lecture 2 - Collective modes of a crystal, dynamical matrix; mode quantization and phonons; thermodynamics of phonons and specific heat.
• Lecture 3 - Symmetry breaking, long-range order and Goldstone modes; structure factor and Debye-Waller factor.
• Lecture 4 - Quantum Indistinguishability; Fermi gas and the notion of Fermi liquid; Bose gas and Bose-Einstein condensation.
• Lecture 5 - Electron-electron interactions and magnetism; Hund's rule; singlet-triplet splitting; spin Hamiltonian.
• Lecture 6 - Heisenberg Hamiltonian and symmetry breaking; Ferromagnetism: ground state and excitations (spin waves); Antiferromagnetic state.
• Lecture 7 - Antiferromagnets: spin singlets, RVB states, spin liquids in various dimensions; Schwinger boson approach; weakly interacting Bose gas.
• Lecture 8 - Interacting Bose gas: Bogoliubov transformation, energy spectrum, ground state energy, depletion of the condensate.
• Lecture 9 - Off-diagonal long-range order, phase fluctuations of condensate; Bose-Hubbard model, quantum phase transition.
• Lecture 10 - Properties of superfluids and the phase diagram of He-4; vortices and Berenzinskii-Kosterlitz-Thouless transition.
• Lecture 11 - Properties of superconductors; Cooper instability; Bardeen-Cooper-Schrieffer Hamiltonian.
• Lecture 12 - BCS theory: spectral function, density of states, gap equation, calculation of the critical temperature.
• Lecture 13 - Ginzburg-Landau theory: solutions for a bulk superconductor and superconductor with a boundary. London penetration depth and flux quantization.
• Lecture 14 - Vortices in superconductors; type-1 and type-2 superconductors: Abrikosov vortex lattice; Josephson effect.

Mathematical Physics - Carl Bender

• Lecture 1 - Perturbation series. Brief introduction to asymptotics.
• Lecture 2 - The Schroedinger equation. Riccati equation. Initial value problem. Perturbation series approach to solving the Schroedinger equation. The eigenvalue problem.
• Lecture 3 -Putting a perturbative parameter in the exponent. Thomas-Fermi equation. KdV equation. Eigenvalue problem - analytic structure of the energy function. The square root function. Branch cuts. Shanks transform.
• Lecture 4 - Acceleration of convergence. Shanks transform. Richardson extrapolation. Summing a divergent series. Euler summation. Borel summation. Generic summation machines.
• Lecture 5 - Summation of divergent series continued. Analytic continuation of zeta and gamma functions. The anharmonic oscillator.
• Lecture 6 - Continued fractions. Pade sequence. Stieltjes series.
• Lecture 7 - Pade technique for summing a series. Asymptotic series. Fuchs' theorem. Frobenius series.
• Lecture 8 - Local analysis. Asymtotic series solution to differential equations continued. WKB approximation.
• Lecture 9 - Asymptotic series solution to differential equations continued. Optimal asymptotic approximation. Airy functions. Stokes phenomenon.
• Lecture 10 - Asymptotic solutions to the inhomogeneous Airy equation. The rigourous theory of asymptotics. Stieltjes functions. The four properties of Stieltjes functions. Herglotz property.
• Lecture 11 - Proof of Herglotz property of Stieltjes functions. Stieltjes functions and the convergence of Pade sequences. The moment problem. Carleman condition. The anharmonic oscillator as an example of Carleman condition.
• Lecture 12 - Asymptotic distribution of the number of Feynman diagrams in phi^4 theory. Comparison with phi^6 and phi^8 theories. Sketch of the precise asymptotic expression for the coefficient of the perturbation theory.
• Lecture 13 - Accuracy of WKB. Solution to the Sturm-Liouville problem using WKB. Turning points. Trajectories in complex classical mechanics.
• Lecture 14 - Asymptotic solution to the Sturm-Liouville problem for two turning points. Asymptotic matching.
• Lecture 15 - Solution to the two turning-point problem. Examples: the harmonic oscillator. V(x) = x^4. A brief introduction to hyper asymptotics.

Conformal Field Theory -Jaume Gomis

• Lecture 1 - Introduction to CFTs (1): Conformal invariance of classical actions, RG flows and fixed points, classification of operators.
• Lecture 2 - Introduction to CFTs (2): Critical phenomena in statistical physics, phase transitions.
• Lecture 3 - Conformal Transformations Conformal Algebra.
• Lecture 4 - Conserved currents and the Stress Energy Tensor.
• Lecture 5 - Conformal Anomalies, Conformal Operators and Fields.
• Lecture 6 - Conformal Fields contiued: Primaries and Descendants.
• Lecture 8 - Correlators of Vectors and Tensors; D=2 CFTs: the complex plane, the de Witt algebra.
• Lecture 9 - Primary and quasi-primary Operators, Correlators and the Stress Tensor in D=2.
• Lecture 10 - Operator Product Expansion, Ward Identities, Virasoro Algebra.
• Lecture 11 - Hilbert Space in CFTs, Primaries and descendants.
• Lecture 12 - Operator/State Correspondence, Unitarity Bounds on CFTs.
• Lecture 13 - Minimal models in D=2; Null vector decoupling equation.
• Lecture 14 - Fusion rules; The Ising model in D=2.

Review

Standard Model (Review) - Philip Schuster, Natalia Toro

• Lecture 2 - Quark Model, Standard Model Langrangian.
• Lecture 4 - Standard Model Lagrangian after Electroweak Symmetry Breaking.
• Lecture 5 - Little Group, Single Particle States, Multi-Particle States.
• Lecture 6 - Lorentz Transformation of Multi-Particle States, Fields from the S-Matrix, Spin-Statistics.
• Lecture 7 - Particle Number Violation and Antiparticles, Effective Field Theories.
• Lecture 8 - Effective Field Theories, Sigma Model.
• Lecture 9 - Chiral Symmetry Breaking, Goldstone Bosons, Sigma Model for Pions.
• Lecture 12 - Jets, Altarelli-Parisi Splitting Functions.

Condensed Matter (Review) - Alioscia Hamma

• Lecture 1 - Outline of the course. Phase transitions, critical points, scaling, the role of dimensionality. The concepts of phase and symmetry.
• Lecture 2 - Review of the Ising model. Solidification transition. Transfer matrix formalism.
• Lecture 3 - Correlation functions. The correspondence between statistical and quantum mechanics. The notion of a quantum phase transition.
• Lecture 4 - Transverse Ising Model in one-dimension: ground state, quantum critical point, duality argument, exact solution using Jordan-Wigner transformation.
• Lecture 5 - Locality in quantum soin systems. Lieb-Robinson theorem.
• Lecture 6 - Lieb-Robinson bounds: Consequences of locality; effective light cone and the spread of information, bounds on correlation functions.
• Lecture 7 - Fidelity, quantum geometric tensor; Berry phases in an XY chain.
• Lecture 8 - Quantum geometric tensor near quantum phase transitions and for 1D Ising chain; the notion of entanglement.
• Lecture 9 - Entanglement in many body systems, von Neumann entropy and the role of dimensionality; Lattice Z_2 guage model and Elitzur's theorem.
• Lecture 10 - Phase transition in lattice Z_2 gauge model. Quantum lattice Z_2 guage theory, guage transforamtions.
• Lecture 11 - Gauge-invariant Hilbert space in Z_2 guage theory; the notion of topological quantum order.
• Lecture 13 - Entanglement in topologically ordered ground state. Quantum double model.
• Lecture 14 - Topological quantum phase transitions.
• Lecture 15 - Lattice U(1) guage theory and emergent photons.

Foundations of Quantum Mechanics (Review) - Rob Spekkens

• Lecture 1 - What's the problem? The realist strategy. The quantum measurement problem.
• Lecture 2 - The operational strategy. The most general types of preparations. Density operators.
• Lecture 3 - Operational quantum mechanics. The most general types of measurements. The most general types of transformations.
• Lecture 4 - POVMs. Unambiguous state discrimination. Operational formulation of quantum theory. The church of the larger (smaller) Hilbert space.
• Lecture 5 - A framework for convex operational theories. Operational classical theory. Operational quantum theory. Real vs complex field.
• Lecture 6 - Recasting the "orthodox" interpretation as a realist model. Realism via hidden variables. Psi-ontic vs psi-epistemic models. The Bell-Mermin model. The Kochen-Specker model.
• Lecture 7 - Evidence in favour of psi-epistemic hidden variable models. Restricted Liouville mechanics. Restricted statistical theory of bits.
• Lecture 8 - Bell's theorem. Experimental loopholes. No-signalling.
• Lecture 9 - Non-locality. Bell's definition of local causality. Applications of non-localtiy. Contextuality.
• Lecture 10 - Contextuality in more depth. The traditional definiton of contextuality in quantum theory. Bell-Kochen-Specker theorem. Proofs of noncontextuality. An operational notion of contextuality.
• Lecture 11 - Generalized notions of noncontextuality. Preparation noncontextuality. Operational test of preparation noncontextuality. Connection with nonlocality. Noncontextuality and negativity as notions of classicality.
• Lecture 12 - The deBroglie-Bohm interpretation. The deBroglie-Bohm interpretation for a single particle. Empty waves and occupied waves. The deBroglie-Bohm interpretation for many particles. Effective collapse of the guiding wave.
• Lecture 13 - The deBroglie-Bohm interpretation continued. The "standard distribution" as quantum equilibrium. Contextuality. Criticisms and responses.
• Lecture 14 - Dynamical collapse theories. The Ghirardi-Rimini-Weber model. Constraints on parameters. Criticisms.
• Lecture 15 - The Everett interpretation - "Many Worlds." Preferred basis problem. The problem with probabilities. Comparison to deBroglie-Bohm.

Quantum Gravity (Review) - Renate Loll

• Lecture 1 - Introduction to the subject of quantum gravity.
• Lecture 3 - Quantization of gravitational waves.
• Lecture 4 - Detectability of gravitational waves. Review of path integral in quantum mechanics.
• Lecture 5 - Perturbative path integral for gravity. Graviton propagator.
• Lecture 6 - Review of Hamiltonian mechanics. Dirac's conanonical quantization.
• Lecture 8 - Canonical Formulation of general relativity, ADM decomposotion. Dirac-Bergmann algorithm.
• Lecture 9 - Dirac algebra. Quantizing constrained systems.
• Lecture 10 - Dirac quantization for gravity. Wheeler-DeWitt equations.
• Lecture 12 - Non-perturbative gravitational path integral.
• Lecture 13 - Dynamical triangulations and quantum Regge calculus.
• Lecture 14 - Path Integral in terms of dynamical triangulations. Monte-Carlo simulations for path integral.

Gravitational Physics (Review) - Ruth Gregory

• Lecture 2 - Differential Forms, Exterior and Lie Derivatives.
• Lecture 3 - Connections and Curvature, Cartan's Equations of Structure.
• Lecture 4 - Examples: Gravitational Wave Spacetime, Warped Compactification.
• Lecture 5 - (A)dS Black Holes, Eucliean Method and Hawking Temperature.
• Lecture 7 - C-Metric, Multi Black Hole Solutions.
• Lecture 8 - Einstein Hilbert Action, Brans-Dicke Theory.
• Lecture 9 - Black Holes in Higher Dimensions, P-Branes.
• Lecture 12 - Gibbons-Hawking Term, Black Hole's Entropy.
• Lecture 14 - Gravitational Perturbation Theory, Counting Physical Degrees of Freedom.
• Lecture 15 - Beyond Einstein: Large Extra Dimensions, Randall-Sundrum Model.

Cosmology (Review) -Latham Boyle

• Lecture 2 - Review of General Relativity continued, General Relativity and Yang-Mills Theory.
• Lecture 3 - Einstein's equation and maximally symmetric solutions.
• Lecture 4 - Maximally symmetric space-times; FRW.
• Lecture 5 - Kinematics of FRW, conformal time, horizons.
• Lecture 6 - The Horizon Problem, Dynamics of FRW.
• Lecture 7 - The Flatness Problem. Thermodynamics, Statistical Mechanics, Particle Physics.
• Lecture 8 - Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) part 1.
• Lecture 9 - Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) part 2.
• Lecture 12 - Dark Matter and Dark Energy continued.

Quantum Information (Review) - Daniel Gottesman

• Lecture 1 - Classical gates. Reversible classical gates. Quantum gates.
• Lecture 2 - Universal gate sets. CP-maps. Purification.
• Lecture 3 - Implementations. Ion trap implementation.
• Lecture 4 - Comparison of implementations. Dynamical decoupling.
• Lecture 5 - Computational complexity. Complexity classes.
• Lecture 6 - Strong Church-Turing thesis. Complexity classes BQP and NP. Deutsch-Josza algorithm
• Lecture 8 - Shor's algorithm. Quantum Fourier transform.
• Lecture 11 - Compression. Mixed state entanglement.

String Theory (Review) - Freddy Cachazo

• Lecture 1 - Why String Theory? Historical Introduction
• Lecture 2 - Massless Fields in Curved Spacetime, Point Particle and Polyakov Actions
• Lecture 3 - Relativistic Strings: Equations of Motion, Constraints, Boundary Conditions.=
• Lecture 4 - Closed Strings: Mode Expansion and Quantization
• Lecture 5 -Quantizing Open Strings: String Spectrum, Critical Dimension
• Lecture 6 -String Theory as a Theory of Quantum Gravity
• Lecture 7 -String Theory as a Theory of Quantum Gravity
• Lecture 9 - by Lilia Anguelova - IIA String Theory from Dimensional Reduction of 11D SUGRA
• Lecture 11 - Superstrings: Spacetime Fermions, Critical Dimensions
• Lecture 13 - D-branes, T-duality, U(N) Gauge Group from Superstrings

Beyond the Standard Model (Review) - Veronica Sanz

• Lecture 1 - Intro to BSM. Evidence BSM: a)Dark Matter. Direct and indirect detection.
• Lecture 2 - b) Baryogensis. Sakharov conditions. c) Neutrino masses.
• Lecture 3 - Theoretical rationale for BSM. Technical naturalness. Gauge hierarchy problem.
• Lecture 4 -Explicit symmetry breaking and spontaneously broken symmetry. Other hierarchies in the Standard Model.
• Lecture 5 - Direct and Indirect constraints on BSM. The Peskin-Takeuchi S, T, U parameters. Flavour bounds. Forward-backward asymmetry.
• Lecture 6 -Supersymmetry. Coleman-Mandula no-go theorem. The Haag-Lopuszanski-Sohnius theorem. Chiral supermultiplet and the Wess-Zumino model
• Lecture 7 - Supersymmetric interactions. MSSM. Quadratic divergence in higgs mass. Cancellation of quadratic divergences from supersymmetric vertices.
• Lecture 8 - Soft SUSY breaking terms. The mu-problem. SUSY particle spectrum.
• Lecture 9 - Mass spectrum of MSSM. Dark matter candidate and gauge unification.
• Lecture 10 - SUSY breaking. Spontaneous SUSY breaking. Sum rule. SUSY breaking mediated by gravity, gauge sector and gauginos.
• Lecture 11 - Extra dimensions as a way of stabilizing the electroweak scale.
• Lecture 12 - Large extra dimensions continued. KK mechanism. ADD mechanism.
• Lecture 13 - Warped extra dimensios. The Randall-Sundrum scenario.
• Lecture 14 - Higgs searches at the LHC. SUSY searches at the LHC.

Exploration

Explorations in Quantum Information - David Cory

• Lecture 2 - Imperfections. Superoperators, CP maps.
• Lecture 3 - Bloch equations. Noise: composite pulse sequence; magnetic fields in neutron interferometry.
• Lecture 4 -Imperfections. Wedge in one path. Imperfect blades.
• Lecture 5 - Imperfections. Velocity impared to / from blade.
• Lecture 7 - NV centres in diamond. Physical system. Initialization and measurement.
• Lecture 9 - The rotating-wave approximation. Entanglement between NV centres.
• Lecture 10 - Hamiltonians and control of electron-nucker spin system.
• Lecture 12 - Superconducting rings. Josephson junction.
• Lecture 13 - Finite difference method. Eigenstructure of tilted potential for JJ circuit.
• Lecture 14 - Adding a parabolic potential to the JJ circuit. Mapping a Qubit. Hamiltonians and control of system.
• Lecture 15 - DiVincenzo criteria for superconducting qubit. 2-qubit circuit and control

Explorations in Cosmology - Matthew Johnson,Louis Leblond

• Lecture 1 - Review of the standard model of cosmology
• Lecture 4 -Unruh effect and particle production. de Sitter space.
• Lecture 5 - Scalar field fluctuations in de Sitter space. Inflationary models.
• Lecture 6 - Inflation: the homogeneous limit.
• Lecture 7 - Example:Chaotic inflation. Density perturbations produced during slow-roll inflation.
• Lecture 8 - Spectral index. Observational constraints on chaotic inflation. Gauges for scalar perturbations. Sachs-Wolfe effect.
• Lecture 9 - Connecting the primordial power spectra to CMB observables. Stochastic eternal inflation.
• Lecture 10 - Stochastic eternal inflation and the Fokker-Planck equation. Introduction to vacuum decay in QFT.
• Lecture 13 - Vacuum decay with gravity. False vacuum eternal inflation.
• Lecture 14 - False vacuum eternal inflation. Quantum cosmology and wave function of the universe.
• Lecture 15 - Challenges for inflation. Alternatives to inflation.

Explorations in String Theory - Pedro Vieira

• Lecture 1 - Introduction to the duality between string theory and large N gauge dualities
• Lecture 3 - The decoupling argument and the AdS/CFT conjecture
• Lecture 4 - More arguments pointing towards AdS/CFT
• Lecture 6 - The quark-antiquark potential, Wilson loops in QED and in non-abelian gauge theories
• Lecture 8 - Supersymmetric Wilson loops, rainbow diagrams; Recent developments: Localization, Integrability, Null Polygon Wilson Loops
• Lecture 9 - Conformal Field Theory: 2, 3 4-pt functions, the Operator Product Expansion, the Conformal Bootstrap
• Lecture 10 - AdS geometry; Pointlike string solution in AdS5xS5
• Lecture 11 - Circular rigid sting solution; Computation of anomalous dimensions in N=4 SYM
• Lecture 13 - Spin Chains: single and N-magnon excitations, Bethe ansatz
• Lecture 14 - Bethe ansatz, the circular string and the single cut solutions
• Lecture 15 -Higher loop corrections, thermodynamic Bethe ansatz

Explorations in Quantum Gravity - Carlo Rovelli

• Lecture 3 - Hamilton's function, Physics without time
• Lecture 8 - Ponzanno-Regge transition amplitude
• Lecture 10 - by Eugenio Bianchi - Spectrum of the volume operator
• Lecture 11 - by Eugenio Bianchi - Coherent states, Unitary representations of SL(2,C)
• Lecture 14 - Physical applications and future directions

Explorations in Particle Theory - David Morrissey

• Lecture 1 - Evidence for dark matter (DM). DM properties. Outline of course.
• Lecture 3 - DM production. Thermodynamic equilibrium. The Boltzmann equation.
• Lecture 4 - Freeze out. Solving the Boltzman equation. The WIMP miracle.
• Lecture 8 - Direct detection continued. Spin independent and spin
• Lecture 9 - Spin independent experimental searches: XENON100, CDMS, DAMA, CoGeNT, CRESST
• Lecture 12 - Indirect detection: photon signal; DM in stars
• Lecture 14 - Axions and the Strong CP problem. Axion cosmology.

Explorations in Numerical Relativity - Luis Lehner, Frans Pretorius

• Lecture 2 - Solutions of the wave equation using Crack-Nicholson algorithm; error evaluation and the problem of stability
• Lecture 3 - Arnowitt-Deser-Misner decomposition
• Lecture 4 - Gauss-Codazzi equations; 3+1 Approach to the Einstein Equations
• Lecture 5 - Hyperbolic equations; linearly degenerate vs truly nonlinear equations. Burgers equation; Riemann problem
• Lecture 6 - Roe Solver for Burgers equation. Genereal relativity and hydridynamics; primitive and conserved variables
• Lecture 7 - Magneto-hydrodynamics in general relativity
• Lecture 8 - Magneto-hydrodynamics in general relativity (numerical implementation)
• Lecture 10 - Gravitational waves overview (nature in GR plus sources)
• Lecture 11 - Einstein's equation with generalized harmonic gauge conditions
• Lecture 14 -Adaptive mesh refinement/parallel computation

Explorations in Condensed Matter - Dmitry Abanin

• Lecture 1 - What is mesoscopics? Examples of mesoscopic systems
• Lecture 2 - Localization of electrons by disorder; week and strong localization; the concept of dephasing
• Lecture 3 - Scattering matrix approach to quantum transport; Landauer mechanism and localization
• Lecture 4 - Physical realization of !D transort; Band structure of graphene; Berry phases
• Lecture 5 - Integer Quantum Hall Effect (IQHE)
• Lecture 6 - Semiclassical percolation picture of Quantum Hall transition; Laughlin approach to transverse conductivity
• Lecture 7 - Hall conductivity and Berry phases; Hall conductivity as a topological invariant
• Lecture 8 - Part 1 Part 2 -Quantum Hall effect in graphene. Interacting electrons in magnetic field
• Lecture 9 - Fractional Quantum Hall effect and wave functions