Which property of a material is more familiar to us than its color? And yet, the strange laws of quantum mechanics, which rule atoms, electrons and photons, are key to the understanding of this most beautiful feature! The invention and engineering of novel materials has shaped human civilization, from the Bronze age to the Silicon age. This lecture is an invitation to explore materials down to the scale of their intimate constituents – atoms and electrons. We'll address questions such as: do we master quantum mechanics well enough today to explain how materials behave from the only knowledge of the atoms which build them? Have we reached the stage where the principles of quantum mechanics allow for the design of a novel material with specific functionalities?

Sommerfeld Lecture Series, From copper-oxide superconductors to rare-earth compounds, materials with strong electronic correlations have focused enormous attention over the last two decades. Solid-state chemistry, new elaboration techniques and improved experimental probes are constantly providing us with examples of novel materials with surprising electronic properties, the latest example being the recent discovery of iron-based high-temperature superconductors.

In this colloquium, I will emphasize that the classic paradigm of solid-state physics, in which electrons form a gas of wave-like quasiparticles, must be seriously revised for strongly correlated materials. Instead, a description accounting for both atomic-like excitations in real-space and quasiparticle excitations in momentum space is requested. I will review how Dynamical Mean-Field Theory -an approach that has led to significant advances in our understanding of strongly correlated materials- fulfills this goal.

New frontiers are also opening up, which bring together condensed-matter physics and quantum optics. `Artificial materials' made of ultra-cold atoms trapped by laser beams can be engineered with a remarkable level of controllability, and allow for the study of strong- correlation physics in previously unexplored regimes.

Sommerfeld Lecture Series, According to the Landau description of Fermi liquids, low- energy excitations in metals are constructed out of quasiparticles – long-lived excitations which have the same quantum numbers as those of an electron in vacuum. In metals with strong correlations however, quasiparticles become fragile: they are destroyed above a characteristic energy or temperature scale, the quasiparticle coherence scale. This energy scale can be remarkably low, even in materials which are not close to a Mott metal-insulator transition, for example as a result of the Hund's rule coupling. I will provide evidence that this is relevant for many materials, especially oxides of the 4d transition metals. In other materials, such as cuprates, quasiparticles are destroyed selectively in specific regions of momentum-space. The understanding of charge and thermal transport in such ``bad metals'' is a key issue, with both fundamental and practical implications.

Eleventh ASC Lecture Series, Recent developments in cosmology suggest that the big bang was not a unique event in the cosmic history. Other big bangs constantly erupt in remote parts of the uni- verse, producing new worlds with great variety of physical properties. Some of these worlds are similar to ours, while others are strikingly different and even obey different laws of physics. I will discuss the origin of this new worldview, its possible observational tests, and some of its bizarre implications.

Eleventh ASC Lecture Series, Cosmic strings are linear defects that could be formed at a phase transition in the early universe. Strings are predicted in a wide class of particle physics models. In particular, fundamental strings of superstring theory can have astronomical dimensions and play the role of cosmic strings. I will discuss recent progress in understanding the evolution of cosmic strings and possible ways of detecting them.

Twelfth Arnold Sommerfeld Lecture Series, In many modern materials, electrons quantum‐entangle with each other across long distances, and produce new phases of matter, such as high temperature super‐conductors. We face the challenge of describing the entanglement of 10^{23} electrons, which is being met by many ideas, including some drawn from string theory.

Twelfth Arnold Sommerfeld Lecture Series, String theory was originally constructed as a unification of the quantum field theory of elementary particles with Einstein's theory of gravitation. Unexpectedly, it has led to the discovery of new "dualities" which have given us a new perspective on quantum field theories not coupled to gravity. Some of the latter theories are relevant to the strongly-interacting quantum many body problems of condensed matter physics. I will survey some of the challenging open problems associated with condensed matter experiments, and discuss the insights gained from string theory.

Twelfth Arnold Sommerfeld Lecture Series, The last three decades have witnessed the discovery of many new superconductors, with properties dramatically different from the conventional low temperature superconductors described by the Bardeen-Cooper- Schrieffer theory. These new superconductors can have much higher critical temperature, and all display antiferromagnetism in their phase diagrams. I will introduce the theory of quantum phase transitions, and use it to interpret recent experiments on these materials.

Thirteenth ASC Lecture Series, During more than 100 years of its history Quantum Mechanics passed all of the experimental

checks and transformed itself from a counterintuitive concept to the undisputable foundation of the modern physics. Along with this it did not lose its ability to surprise and still allows for new astonishing discoveries such as Bose-Einstein condensation of ultracold gases. Manifestations of the quantum mechanics on the macroscopic scales are especially impressive. In recent years the interest in condensed matter physics evolved from studying bulk properties of naturally occurring materials to constructing complex materials and systems not found in nature, and controlling rather than observing quantum mechanics. Within this tendency the concept of quantum condensation remains the central one.

Controllable quantum behavior can be achieved in systems of weakly coupled locally coherent elements. An array of Josephson junctions between superconducting islands is a representative but not the exclusive example. Other examples of such systems are ultracold gases in optical lattices, excitons and photons in semiconductor cavities, etc. Global phase coherence exists in these systems can be destroyed by reducing the coupling. In Josephson arrays this destruction is manifested by the phase transition from superconducting to insulating state.

This talk is about the relation between the classical and the quantum worlds. Some of the quantum effects, e.g. interference, can be realized in classical systems, others like Einstein- Podolsky-Rosen paradox are “truly quantum”. It turns out that the quantum condensation has a classical analog: synchronization (mode-locking) in nonlinear dynamics. Discovered by Huygens almost 350 years ago the synchronization is the most fundamental nonlinear phenomenon. However the synchronization happens when the system is driven by outside forces, while one can think about BEC in thermodynamic equilibrium. On the other hand quantum systems can be also driven. One of the familiar examples is coherent state of photons

generated by a laser: this generation happens only in the presence of a pumping and does not exist in the equilibrium. The interest to the quantum systems out of equilibrium is rapidly growing due to the desire to control and manipulate quantum states. I will discuss the similarities between macroscopic quantum and classical behaviors. It looks like new interesting physics emerges on the crossroads of the quantum mechanics, condensed matter physics, and nonlinear dynamics.

Sommerfeld Lecture Series, Which property of a material is more familiar to us than its color? And yet, the strange laws of quantum mechanics, which rule atoms, electrons and photons, are key to the understanding of this most beautiful feature! The invention and engineering of novel materials has shaped human civilization, from the Bronze age to the Silicon age. This lecture is an invitation to explore materials down to the scale of their intimate constituents – atoms and electrons. We'll address questions such as: do we master quantum mechanics well enough today to explain how materials behave from the only knowledge of the atoms which build them? Have we reached the stage where the principles of quantum mechanics allow for the design of a novel material with specific functionalities?