## Graduate Courses

**ELE 561**

**/PHY 565**

**/MSE 556**

**Fundamentals of Nanophotonics**Introduction to theoretical techniques for understanding and modeling nanophotonic systems, emphasizing important algebraic properties of Maxwell's equations. Topics covered include Hermitian eigensystems, photonic crystals, Bloch's theorem, symmetry, band gaps, omnidirectional reflection, localization and mode confinement of guided and leaky modes. Techniques covered include Green's functions, density of states, numerical eigensolvers, finite-difference and boundary-element methods, coupled-mode theory, scattering formalism, and perturbation theory. The course explores application of these techniques to current research problems.Alejandro W. Rodriguez

**MAT 595**

**/PHY 508**

**Topics in Mathematical Physics: Random Operators and Critical Phenomena**Spring 2015: In the first half the term, the course will focus on the theory or random operators, and in particular on the spectra and dynamics of operators with random potential and in the second half, the discussion will focus on the critical behavior in some of the basic models of mathematical statistical mechanics, scaling limits of their critical states, and the random fractal structures which emerge in the resulting continuum theories. Presentations/lectures by A. Aizenman, S. Warzel and H. Duminil-Copin.Michael Aizenman

**PHY 506**

**/MSE 576**

**Advanced Quantum Mechanics**This is a one-semester course in advanced quantum mechanics. The emphasis is on systems with more than one degree of freedom: dynamics, mixed states, entanglement, measurement, coherent states, decoherence, resonance, exchange, Hartree-Fock, Dirac equation, other topics.David A. Huse

**PHY 510**

**Advanced Quantum Field Theory**Relations between Quantum Field Theory and Statistical Mechanics, Renormalization Group, Non-Abelian Gauge Theories, Asymptotic Freedom, Quantum Chromodynamics, Chiral Lagrangians, General Constraints on RG Flows.Igor R. Klebanov

**PHY 521**

**Introduction to Mathematical Physics**An introduction to mathematically rigorous methods in physics. Topics to be covered include classical and quantum statistical mechanic, quantum many-body problem, group theory, Schroedinger operators, and quantum information theory.Elliott H. Lieb

**PHY 529**

**High-Energy Physics**An overview of modern elementary particle physics and the Standard Model. Specific topics include: weak decays, W and Z physics, deep inelastic scattering, CP violation, neutrino oscillations, Higgs searches, with an emphasis on areas of current interest.Mariangela Lisanti

**PHY 536**

**/MSE 577**

**Advanced Condensed Matter Physics II**Course introduces and present ongoing theoretical investigations of new research topics in condensed matter physics: topological insulators and Chern numbers, topological superconductors, the fractional quantum Hall effect and non-abelian statistics, as well as new high-temperature superconductors. The techniques needed to deal with such systems, such as Chern numbers, topological band theory, Berry phases, conformal field theory, Chern-Simons theory, t-J models, Gutzwiller wavefunctions, Hubbard models, are explained.Frederick D. Haldane

**PHY 546**

**Higher Spin Theories and AdS/CFT (Half-Term)**This course is an introduction to higher spin gravity theories and the recent advances in understanding their role in the context of the AdS/CFT correspondence. Topics include: free equations for massless higher spin fields in flat and (A)dS space; introduction to Vasiliev interacting higher spin theory in (A)dS; review and checks of the AdS/CFT dualities between higher spin gravity in AdS space and vector model conformal field theories.Simone Giombi

**PHY 561**

**Biophysics**The course presents a broader view of biological physics. While the course starts with an overview of the fundamentals of biological physics, using Frauenfelder's text book as a guide, the course will move on to higher levels of biological systems, using evolution and ecology as our primary organizing principles. The course will have a section on the Physics of Cancer at the end.Robert H. Austin

**PHY 563**

**Physics of the Universe: Origin & Evolution**The course is the first of a two-semester survey (along with PHY 564) of fundamental concepts which underly contemporary cosmology. The first semester focuses on the nearly homogeneous evolution of the universe including the standard big bang picture, inflationary cosmology, dark matter, and the possibility of present-day accelerated expansion. The second semester focuses on the late stages in the evolution of the universe, when gravity results in the growth of large-scale structure, perturbations in the cosmic microwave background, gravitational lensing and other non-linear phenomena.Paul J. Steinhardt