PSI Lectures/2011

2010 <<<     >>> 2012

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 2a  Lecture 2b- Abstract Algebras, Structure Constants, Homomorphisms, Clifford   Grassmann Algebras.


 * 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.


 * Lecture 4- Gamma; Zeta; Hypergeometric functions

Integral Transforms and Green's Functions - David Kubiznak

 * Lecture 1- Fourier Series


 * Lecture 2- Laplace  Fourier transform


 * Lecture 3 - Green's functions


 * Lecture 4- Applications

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 1- Mathematica Basics


 * Lecture 2 - Heisenberg Spin Chain


 * Lecture 3- Gamma Matrices


 * Lecture 4- Harmonic Oscillator and Perturbation Theory


 * Lecture 5- Q A Session

RESEARCHER PRESENTANTIONS:

 * Presentation 1 - Paul Fendley
 * Presentation 2 - Joseph Minahan
 * Presentation 3 - Matthias Staudacher
 * Presentation 4 - Yakir Aharonov
 * Presentation 5 - Vladimir Kazakov
 * Presentation 6 - Itay Yavin
 * Presentation 7 - Guifre Vidal
 * Presentation 8 -Lucien Hardy
 * Presentation 9 - Laurent Freidel
 * Presentation 10 - Robert Spekkens
 * Presentation 11 - Lee Smolin
 * Presentation 12 - Cliff Burgess
 * Presentation 13 -Avery Broderick
 * Presentation 14 - Pavel Kovtun
 * Presentation 15 - Subir Sachdev

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 14 - Approximate cloning. Quanutm money.


 * Lecture 15 - Measurements in QM.  Kraus operators.   Decoherence.   Many-worlds.

Relativity - Neil Turok

 * Lecture 1- Maxwell's Theory and Special Relativity.


 * Lecture 2- Lorentz Transformations.


 * Lecture 3 - Manifolds.


 * Lecture 4 - Tensors and Manifolds.


 * Lecture 5- The Connection.


 * Lecture 6- Geodesics, The Reimann Tensor.


 * Lecture 7- Tensors in GR.


 * 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 1a  Lecture 1b - Second Quantization, Phonons.


 * Lecture 2- Phonons, Divergences.


 * Lecture 3- Klein-Gordon field, Conservation laws and symmetries.


 * Lecture 4 - Noether's theorem, Quantization of Klein-Gordon field, Dirac equation.


 * Lecture 5a  Lecture 5b - Lorentz invariance and symmetries of Dirac Lagrangian.


 * 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 10 - Interaction Picture.


 * Lecture 11- Wick's Theorem, Feynman Diagrams.


 * Lecture 12- Feynman Propagator, Momentum Space Feynman Rules


 * Lecture 13- Amplitudes, Cross Sections, Decay Rates.


 * 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 9 - Boltzmann 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.


 * Lecture 14 - Scaling and renormalization group.

Quantum Field Theory II - François David

 * Lecture 1- Path Integral, Euclidean Time.


 * 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 5- Effective Action at One Loop.


 * Lecture 6 - Renormalization of Phi^4 Theory.


 * 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 9 - Wilsonian Renormalization.


 * Lecture 10- Renormalization Group Flow, Grassman Variables, Berezin Claculus.


 * Lecture 11- Berezin Calculus, Fermionic Path Integrals.


 * Lecture 12 - Non-abelian Gauge Theories.


 * Lecture 13 - Quantization of Non-abelian Guage Theories, Guage Fixing, Faddeev-Popov Method.


 * Lecture 14 - Faddeev-Popov Lagrangian, Ghosts.


 * 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.


 * Lecture 15- Josephson junction in a magnetic field.

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 7- Correlation Functions in CFTs.


 * 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.

Standard Model (Review) - Philip Schuster, Natalia Toro

 * Lecture 1- Particle Bestiary.


 * Lecture 2 - Quark Model, Standard Model Langrangian.


 * Lecture 3 - Standard Model Lagrangian.


 * 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 10- Pions as Pseudo-Nambu-Goldstone Bosons.


 * Lecture 11 - Light meson masses, Pion Decays.


 * Lecture 12 - Jets, Altarelli-Parisi Splitting Functions.


 * Lecture 13 - Higgs Mechanism.


 * Lecture 14- Massive Vector Bosons and Unitarity.


 * Lecture 15 - Higgs Searches.

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 12 - Toric code. String-net condensation.


 * 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 2- Weak gravitational waves.


 * 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 7- Constrained Hamiltonian systems.


 * 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 11 - The notion of loop quantum gravity.


 * 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.


 * Lecture 15 - Casual dynamical triangulations.

Gravitational Physics (Review) - Ruth Gregory

 * Lecture 1- Manifolds and Tensors.


 * 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 6- Cosmic Strings and Domain Walls.


 * 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 10 - Kaluza-Klein Theory, KK Black Holes.


 * Lecture 11 - Gausse-Codazzi Formalism.


 * Lecture 12 - Gibbons-Hawking Term, Black Hole's Entropy.


 * Lecture 13 - Israel's junction Conditions.


 * 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 1 - Review of General Relativity


 * 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 10 - The Standard Model of Cosmology.


 * Lecture 11- Dark Matter and Dark Energy.


 * Lecture 12 - Dark Matter and Dark Energy continued.


 * Lecture 13 - Baryogenesis.


 * Lecture 14 - Ifnlation


 * Lecture 15- Ifnlation 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 7- Factoring. RSA. Shor's algorithm.


 * Lecture 8- Shor's algorithm. Quantum Fourier transform.


 * Lecture 9 - Grover's algorithm.


 * name=Daniel_Gottesman       Lecture 10 - Distance measures. Entropy.


 * Lecture 11 - Compression. Mixed state entanglement.


 * Lecture 12- Quantum error-correcting codes.


 * Lecture 13 -Stabilizer codes. Fault-tolerance


 * Lecture 14- Quantum key distribution

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 8 - by Lilia Anguelova - 11D SUGRA


 * Lecture 9- by Lilia Anguelova - IIA String Theory from Dimensional Reduction of 11D SUGRA


 * name=Freddy_Cachazo Lecture 10- RNS Formalism


 * Lecture 11 - Superstrings: Spacetime Fermions, Critical Dimensions


 * Lecture 12- Type IIA and IIB Superstring Theories


 * Lecture 13 - D-branes, T-duality, U(N) Gauge Group from Superstrings


 * Lecture 14-M-Theory and 5 String Theories

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.

Explorations in Quantum Information - David Cory

 * Lecture 1- Neutron interferometry. Ideal case.


 * 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 6 -Spin degree of freedom in NI


 * Lecture 7- NV centres in diamond. Physical system. Initialization and measurement.


 * Lecture 8 - Spin exchange interaction


 * Lecture 9- The rotating-wave approximation. Entanglement between NV centres.


 * Lecture 10 - Hamiltonians and control of electron-nucker spin system.


 * Lecture 11-


 * 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 2 - QFT om curved space


 * Lecture 3 - Unruh effect


 * 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 11 - Vacuum decay in CM.


 * Lecture 12- 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 2- Large N theories are simpler


 * Lecture 3- The decoupling argument and the AdS/CFT conjecture


 * Lecture 4 - More arguments pointing towards AdS/CFT


 * Lecture 5 - N=4 SYM; Wilson loops


 * Lecture 6 - The quark-antiquark potential, Wilson loops in QED and in non-abelian gauge theories


 * Lecture 7- Minimal surfaces in AdS


 * 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 12 - N=4 SYM and Heisenberg Spin Chains


 * 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 1- Quanta of space.


 * Lecture 2 - What is quantum gravity


 * Lecture 3 - Hamilton's function, Physics without time


 * Lecture 4 - Quantum physics without time


 * Lecture 5 - Classical GR in tetrad formalism


 * Lecture 6- Euclidean 3D gravity


 * Lecture 7 - Math of SU(2)


 * Lecture 8 - Ponzanno-Regge transition amplitude


 * Lecture 9 - Towards real quantum world


 * Lecture 10- by Eugenio Bianchi - Spectrum of the volume operator


 * Lecture 11 - by Eugenio Bianchi - Coherent states, Unitary representations of SL(2,C)


 * Lecture 12 - Quantum dynamics in 4D


 * Lecture 13 - Properties of the full theory


 * 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 2 - Dark matter and structure.


 * Lecture 3 - DM production. Thermodynamic equilibrium. The Boltzmann equation.


 * Lecture 4 - Freeze out. Solving the Boltzman equation. The WIMP miracle.


 * Lecture 5 - LSP as WIMP.


 * Lecture 6 - Models of Non-thermal DM.


 * Lecture 7 - Direct detection of DM.


 * Lecture 8 - Direct detection continued. Spin independent and spin


 * Lecture 9 - Spin independent experimental searches: XENON100, CDMS, DAMA, CoGeNT, CRESST


 * Lecture 10 - Indirect detection of DM


 * Lecture 11 - Indirect detection continued.


 * Lecture 12 - Indirect detection: photon signal; DM in stars


 * Lecture 13 - DM signals at colliders. Axions


 * Lecture 14 - Axions and the Strong CP problem. Axion cosmology.

Explorations in Numerical Relativity - Luis Lehner, Frans Pretorius

 * Lecture 1- Finite difference technique.


 * 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 9- Evolution in Maxwell equations


 * Lecture 10 - Gravitational waves overview (nature in GR plus sources)


 * Lecture 11 - Einstein's equation with generalized harmonic gauge conditions


 * Lecture 12- Gravitational waves


 * Lecture 13 - BSSN/Generalized harmonic evolution


 * 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 1Part 2 -Quantum Hall effect in graphene. Interacting electrons in magnetic field


 * Lecture 9- Fractional Quantum Hall effect and wave functions