Computational modeling of scientific problems and implementation of the numerical methods. Dynamical systems based on ordinary differential equations, nonlinear dynamics and chaos, potentials and fields, random systems, statistical mechanics, phase transitions, molecular dynamics, computational quantum mechanics, interdisciplinary topics such as protein folding, self-organized criticality, genetic algorithms.

Quantization of free fields. Propagators. Interacting fields and the S-matrix. Loop expansion of the S-matrix and Feynman diagrams. Path integral techniques. QED. Radiative corrections. Renormalization. Effective field theories.

Optical micro-cavities. Fabry-Perot cavity. Quality factor. Finesse. Free-spectral bands. Whispering gallery modes. Coupling. Photonic molecules, glasses, crystals and meta-materials. Optical micro-cavities. Fabry-Perot cavity. Quality factor. Finesse. Free-spectral bands. Whispering gallery modes. Coupling. Photonic molecules, glasses, crystals and meta-materials.

Quantum theory of light. Coherent light. Non-classical states of light. Quantum interferometry. Quantum measurements. Interaction of light with matter. Cavity quantum electrodynamics. Quantum entanglement and quantum teleportation. Non-linear optics. Photonic band gaps. Quantum information theory and the fundamental principles of quantum computation.

Survey of the techniques for the generation of picosecond and femtosecond pulses from lasers; active and passive mode locking, saturable absorbers, master equation, theory of Kerr lens mode locking; propagation of ultrashort pulses in nonlinear and dispersive media; Measurement and characterization of ultrashort pulses; applications of femtosecond lasers in spectroscopy, medicine, and industry.

Lorentz transformations and Minkowski space-time. Tensors and spinors. Variational formulation of relativistic wave equations. Noether theorem: Symmetries and conservation laws.

Introduction to non-Abelian gauge field theories. QCD. Spontaneous symmetry breakdown and mass generation. Standard model of electroweak interactions. Non-perturbative effects. Supersymmetry.

Review of electromagnetism; geometrical optics, analysis of optical systems; wave properties of light, Gaussian beams, beam optics; interaction of light with matter, spontaneous and stimulated emission, optical amplification, theory and applications of lasers, optical interactions in semiconductors, light emitting diodes and diode lasers; detectors, noise in detection systems; light propagation in anisotropic crystals, Pockels and Kerr effect, light modulators; nonlinear optics, second harmonic generation, phase matching, nonlinear optical materials.

Principles of optical microscopes. Microscopy methods. Photo-physics of dye molecules. Exciting fluorescence and its observation. Dipole radiation near planar interfaces. Photon-counting analysis. Flourescence correlation spectroscopy. Flourescence resonance energy transfer (FRET). Optical spectroscopy at low temperatures. Semiconducting nano-crystals. Metallic nano-particles.

Random walk problems and probability concepts. Theory of polymers. Statistical mechanical concepts with emphasois on self-avoiding walks and biological polymer models: ensembles, free energy, entropy, scaling. Lattices as interacting models of random systems and phase transitions. Dynamical phenomena: Master equation (Examples: random walk and lattice growth), Langevin equation and its generalizations. Chaos and order.