Euclidean gravity on a sphere (euclidean de-Sitter) gives rise to some phase factors. We discuss how these phase factors change when we include an observer. We also discuss situations involving products of spheres.

We start by describing the geometrical notions central to Einstein's theory of gravity. We then discuss current ideas for how spacetime geometry could emerge in a quantum theory of gravity. We will see that quantum entanglement plays a crucial role.

Materials science has always balanced on the twin pillars of observation and abstraction—from the alchemists’ crude recipes to today’s AI-driven materials design. In this talk, we begin by revisiting the pre-quantum era, when early chemists grappled with the nature of elements and compounds, and examine how Mendeleev’s periodic table first imposed order on the chemical world. We then show that what underpins this table is the surprising power of integers and discrete mathematics—why you can’t “slip in” between whole numbers—and trace how that insight underlies quantum mechanics, blurring the boundary between chemistry and physics. Building on these foundations, we survey modern families of functional materials—superconductors, antiferromagnets, charge-density waves, high-temperature superconductors, and semiconductors—and ask what makes them uniquely useful, from microchips to maglev trains. Just as Mendeleev used patterns to predict new elements, we discuss the quantum strategies for classifying the much larger set of materials, formed by these elements, today—introducing topology and topological invariants, showing how band-structure integers classify phases of matter. We highlight online databases that catalog these discoveries. Finally, we look ahead to how machine learning and artificial intelligence, guided by our new periodic table of materials, are revolutionizing the search for novel compounds, ushering in a new era of predictive materials discovery.

I will show how a new set of twisted materials based on the M point rather than the K point can realize a series of exotic phases of matter, including quantum spin liquids and charge glasses. These materials, which have been exfoliated and twisted experimentally, will be at the forefront of new moire discoveries.

We will review the beginning of experimental and theoretical studies of moire systems and their evolution up to present. This type of systems represent a new way of “growing” materials, and has tremendous potential both for fundamental physics as well as for applications. Two dimensional periodic crystals, whose separation between atoms is of order angstroms, can be twisted controllably with respect to each other such that they form new “periodicities”, called moire periodicities. In the new “unit cell” we find thousands of atoms of the original crystal. These atoms behave in ways that are incredibly counterintuitive. We show how the controlled twisting of graphene and MoTe2 layers has led to a slew of states of matter not possible in bulk conventional materials. We will show how the collective behavior of thousands of p orbitals in a moire unit cell of graphene can create single Heavy fermion at moire scale, and how the interaction between such fermions can lead to a perfect quantum simulator of an Anderson model. We will then present a catalogue of possible twistable materials and show how a huge variety of strongly interacting models can be realized in twisted homo and hetero twisted bilayers and multilayers of these materials.

In this talk, I will discuss the applications of cavity electrodynamics for controlling many-body electron systems. The focus will be on achieving strong coupling between cavities and collective excitations of interacting electrons at Terahertz and IR frequencies. As a specific example I will consider a cavity platform based on a two dimensional electronic material encapsulated by a planar cavity consisting of ultrathin polar van der Waals crystals. I will also discuss how metallic mirrors sandwiching a paraelectric material can modify the transition into the ferroelectric state. Finally, I will review a general question of theoretically describing ultrastrong coupling waveguide QED. I will present a novel approach to this problem based on a non-perturbative unitary transformation that entangles photons and matter excitations. In this new frame of reference, the factorization between light and matter becomes exact for infinite interaction strength and an accurate effective model can be derived for all interaction strengths.

It is commonly recognized that scientific discoveries result in new technologies. In this talk we will discuss the reverse: behind every conceptual breakthrough lies some technological advance. To illustrate this point, we will review how modern progress in optical technologies is revolutionizing our understanding of quantum matter. We will discuss experiments that showed that we can optically control materials, and even suggest light-induced superconductivity. We’ll delve into a new type of magnetism, discovered in layered materials using sensitive light reflection experiments rather than measurements of magnetization. We’ll cover how we can use optical lattices with tunable geometries to create several paradigmatic models of electron systems and shed light onto their puzzling properties. We will finally discuss why understanding technology is important for theoretical physicists.

This talk will present an overview of recent progress towards a solution of one of the grand-challenges of modern science: understanding the properties of interacting electrons in molecules and solids. After an introduction to the physics I will argue our theoretical understanding of a basic model system, the two dimensional Hubbard model, has reached the level that we can say with confidence that its superconducting properties capture key aspect of the high-Tc superconductivity in copper-oxide materials. I will then summarize the current status of our extension of the methods to fully physically realistic systems, emphasizing the areas of theoretical uncertainty and the prospects for resolution.

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.

Mathematics has proven to be "unreasonably effective" in understanding nature. The fundamental laws of physics can be captured in beautiful formulae. Remarkably, ideas from quantum theory turn out to carry tremendous mathematical power as well, even though we have little daily experience dealing with elementary particles. The bizarre world of quantum physics not only represents a more fundamental description of nature than what preceded it, it also provides a rich context for modern mathematics. In recent years ideas from quantum field theory, elementary particles physics and string theory have completely transformed mathematics, leading to solutions of deep problems, suggesting new invariants in geometry and topology. Could the logical structure of quantum theory, once fully understood and absorbed, inspire a new realm of mathematics that might be called “quantum mathematics” and will this new language enable us to formulate the fundamental laws of physics?

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.

Two of the most amazing ideas in physics are the holographic principle and quantum error correction. The holographic principle asserts that all the information contained in a region of space is encoded on the boundary of the region, albeit in a highly scrambled form. Quantum error correction is the foundation of our hope that large-scale quantum computer can be operated to solve hard problems. I will argue that these two ideas are closely related, and will describe quantum codes which realize the holographic principle. These codes provide simplified models of quantum spacetime, opening new directions in the study of quantum gravity, though many questions remain.

Where do we come from? Science is making progress on this age-old question of humankind. The Universe was once much smaller than the size of an atom. Small things mattered in the small Universe, where quantum physics dominated the scene. To understand the way the Universe is today, we have to solve remaining major puzzles. The Higgs boson that was discovered recently is holding our body together from evaporating in a nanosecond. But we still do not know what exactly it is. The mysterious dark matter is holding the galaxy together, and we would not have been born without it. But nobody has seen it directly. And what is the very beginning of the Universe?

In recent decades, physicists and astronomers have discovered two beautiful Standard Models, one for the quantum world of extremely short distances, and one for the universe as a whole. Both models have had spectacular success, but there are also strong arguments for new physics beyond these models. In this lecture, we will review these models, their successes and their shortfalls. We will describe how experiments in the near future could point to new physics suggesting a profound conceptual revolution, which could change our view of the world.

Superconductivity is a state of matter where electrons can flow without resistance and where magnetic fields are expelled. It was discovered serendipitously more than a hundred years ago. Today, superconductors are essential components of medical imaging devices as well as high energy particles accelerators. Understanding this phenomena was one of the greatest intellectual challenges of the twentieth century. A dramatic advance was provided by the BCS (Bardeen Cooper Schrieffer) theory 45 years after. It posits that superconductivity is the result of macroscopic condensation of electron pairs, which are held together by the vibrations of the lattice. The condensate is a macroscopic quantum objects and its rigidity accounts for its striking macroscopic properties. The BCS theory was so successful that by the early 70’s superconductivity was considered a completely understood subject with the maximum achievable critical temperature having been reached experimentally around 30K. In the late 80’s this field of research took a dramatically turn with the discovery of new ceramic compounds which superconduct at temperatures as high as 160 K. These materials, cannot be described by straightforward extensions of the BCS theory. Scientists are still working on finding new explanations for these materials and we will describe the challenge they pose. The quest for room temperature superconductivity thus continues. A breakthrough in this field would have unimaginable consequences, changing the way we transmit electricity from its generation to its consumption to the way we design computers.

A combination of ideas originating from Condensed Matter physics, Supersymmetric Field Theory, and AdS/CFT has led to a detailed web of conjectured dualities. These relate the long distance behavior of different short distance theories. These dualities clarify a large number of confusing and controversial issues in Condensed Matter physics and in the study of 2+1 dimensional quantum field theory.

A piece of paper or candy wrapper crackles when it is crumpled. A magnet crackles when you change its magnetization slowly. The earth crackles as the continents slowly drift apart, forming earthquakes. Crackling noise happens when a material, when put under a slowly increasing strain, slips through a series of short, sharp events with an enormous range of sizes. There are many thousands of tiny earthquakes each year, but only a few huge ones. The sizes and shapes of earthquakes show regular patterns that they share with magnets and many other systems. This suggests that there must be a shared scientific explanation. We shall hear about crackling noise and that it is a symptom of a surprising truth: the system behaves the same on small, medium, and large scales.

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.

The amazing and mysterious laws of the quantum world will be outlined: superposition, entanglement and no cloning. Their impact on science and technology will be discussed, including quantum teleportation, secure quantum communication, quantum money, powerful quantum algorithms and quantum machine learning.

We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient computation. We study the correlation between quantum chaos diagnostics, the circuit expressibility and the optimization of the control parameters.