2011/2012 PSI Lectures

Watch recorded courses from 2011/2012 PSI Lecture Series

Watch Freddy Cachazo -  PSI 2012, String Theory Review

VIEW TABS FOR DIFFERENT LECTURES IN 2011/2012YEAR

Mathematics Review:

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

 

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

 

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

Core Courses:

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.
  •     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
  • 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

 

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 1 Part 2 -Quantum Hall effect in graphene. Interacting electrons in magnetic field
  •     Lecture 9 - Fractional Quantum Hall effect and wave functions