Sommerfeld Lecture Series (ASC)

Populations and communities rarely evolve in static environments; their fitness landscapes fluctuate across space and time, forming what may be called a noisy seascape. This talk examines how such variability modifies classical models of population dynamics and community stability. Beginning from the logistic equation, I will show how spatiotemporal fluctuations in fitness lead naturally to power-law population statistics and, under certain conditions, to the empirical (fractional) Richards growth law. Extending these ideas to interacting species reveals that the combined effects of dispersal and environmental noise can stabilize large, diverse communities despite strong competitive interactions. The resulting framework connects extinction, growth, and coexistence within a unified view of life on a noisy seascape.

Active systems are driven out of equilibrium by exchanging energy and momentum with their environment. This endows them with anomalous mechanical properties which leads to rich phenomena when active fluids are in contact with boundaries, inclusions, or disordered potentials. Indeed, studies of the mechanical pressure of active fluids and of the dynamics of passive tracers have shown that active systems impact their environment in non-trivial ways, for example, by propelling and rotating anisotropic inclusions. Conversely, the long-ranged density and current modulations induced by localized obstacles show how the environment can have a far-reaching impact on active fluids. This is best exemplified by the propensity of bulk and boundary disorder to destroy bulk phase separation in active matter, showing active systems to be much more sensitive to their surroundings than passive ones.

Quantum physics teaches us that even the emptiest vacuum is teeming with fluctuations of electromagnetic fields. When these fluctuations are confined between objects, they produce measurable forces: the Casimir effect describes an attraction between uncharged conductors arising solely from the confinement of the quantum void. In this talk, I will explore how this subtle quantum phenomenon connects to ideas of attraction, repulsion, and mechanical work. After introducing the origin and measurement of the Casimir force, I will discuss whether it can be made repulsive, and why true levitation remains elusive in equilibrium. Extending these ideas beyond equilibrium reveals new possibilities: radiation pressure from heat, nonreciprocal materials that generate motion and work without contact, and rotating bodies that spontaneously emit light. Together, these examples show how the restless quantum vacuum continues to surprise us.

Active systems are driven out of equilibrium by exchanging energy and momentum with their environment. This endows them with anomalous mechanical properties which leads to rich phenomena when active fluids are in contact with boundaries, inclusions, or disordered potentials. Indeed, studies of the mechanical pressure of active fluids and of the dynamics of passive tracers have shown that active systems impact their environment in non-trivial ways, for example, by propelling and rotating anisotropic inclusions. Conversely, the long-ranged density and current modulations induced by localized obstacles show how the environment can have a far-reaching impact on active fluids. This is best exemplified by the propensity of bulk and boundary disorder to destroy bulk phase separation in active matter, showing active systems to be much more sensitive to their surroundings than passive ones.

Populations and communities rarely evolve in static environments; their fitness landscapes fluctuate across space and time, forming what may be called a noisy seascape. This talk examines how such variability modifies classical models of population dynamics and community stability. Beginning from the logistic equation, I will show how spatiotemporal fluctuations in fitness lead naturally to power-law population statistics and, under certain conditions, to the empirical (fractional) Richards growth law. Extending these ideas to interacting species reveals that the combined effects of dispersal and environmental noise can stabilize large, diverse communities despite strong competitive interactions. The resulting framework connects extinction, growth, and coexistence within a unified view of life on a noisy seascape.

Quantum physics teaches us that even the emptiest vacuum is teeming with fluctuations of electromagnetic fields. When these fluctuations are confined between objects, they produce measurable forces: the Casimir effect describes an attraction between uncharged conductors arising solely from the confinement of the quantum void. In this talk, I will explore how this subtle quantum phenomenon connects to ideas of attraction, repulsion, and mechanical work. After introducing the origin and measurement of the Casimir force, I will discuss whether it can be made repulsive, and why true levitation remains elusive in equilibrium. Extending these ideas beyond equilibrium reveals new possibilities: radiation pressure from heat, nonreciprocal materials that generate motion and work without contact, and rotating bodies that spontaneously emit light. Together, these examples show how the restless quantum vacuum continues to surprise us.

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.

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.

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.

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.

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.

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.

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.

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.

Recent experiments suggest the phenomenon of light induced superconductivity above Tc in two different materials: fullerene superconductor K3C60 and high Tc cuprate YBCO. I will discuss the distinct phenomena taking place in these systems. In K3C60, the unusual character of electron-phonon interactions results in enhanced BCS pairing through optical driving and the slow relaxation of superconducting correlations after they have been created. In YBCO the light induced state is short lived and its properties can be explained from the perspective of a Floquet material. I will present a general theoretical framework for understanding Floquet materials, in which the pump-induced oscillations of a collective mode lead to the parametric generation of excitation pairs. This can result in features such as photo- induced edges in reflectivity, enhancement of reflectivity, and even light amplification.

Recent experiments suggest the phenomenon of light induced superconductivity above Tc in two different materials: fullerene superconductor K3C60 and high Tc cuprate YBCO. I will discuss the distinct phenomena taking place in these systems. In K3C60, the unusual character of electron-phonon interactions results in enhanced BCS pairing through optical driving and the slow relaxation of superconducting correlations after they have been created. In YBCO the light induced state is short lived and its properties can be explained from the perspective of a Floquet material. I will present a general theoretical framework for understanding Floquet materials, in which the pump-induced oscillations of a collective mode lead to the parametric generation of excitation pairs. This can result in features such as photo- induced edges in reflectivity, enhancement of reflectivity, and even light amplification.

The density of states of a unitary quantum field theory is known to have a universal behavior at high energy. In two dimensions, this behavior is described by the Cardy formula. When the theory has symmetry, it is interesting to find out how the Hilbert space is decomposed into irreducible representation of the symmetry. In this talk, I will derive universal formulas for the decomposition of states at high energy with respect to both internal global symmetry and spacetime symmetry. The formulae are applicable to any unitary quantum field theory in any spacetime dimensions. As a byproduct, we resolve one of the outstanding questions on the stability of non-abelian black holes. We will also derive the high energy asymptotic behavior of correlation functions. (Based on work with Nathan Benjamin, Daniel Harlow, Monica Kang, Jaeha Lee, Sridip Pal, David Simmons-Duffin, Zhengdi Sun, and Zipei Zhang.)

Although predictions of quantum gravity are typically at extremely high energy, several non-trivial constraints on its low energy effective theory have been found over the last decade or so. I will start by explaining why the unification of general relativity and quantum mechanics has been difficult. After introducing the holographic principle as our guide to the unification, I will discuss its use in finding constraints on symmetry in quantum gravity. I will also discuss other conjectural constraints on low energy effective theories, collectively called swampland conditions, and their consequences.

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.

Fluid turbulence is a major unsolved problem of physics exhibiting an emergent complex structure from simple rules. We will briefly review the problem and discuss three avenues towards its solution: field theory, holography and machine learning.

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.

The density of states of a unitary quantum field theory is known to have a universal behavior at high energy. In two dimensions, this behavior is described by the Cardy formula. When the theory has symmetry, it is interesting to find out how the Hilbert space is decomposed into irreducible representation of the symmetry. In this talk, I will derive universal formulas for the decomposition of states at high energy with respect to both internal global symmetry and spacetime symmetry. The formulae are applicable to any unitary quantum field theory in any spacetime dimensions. As a byproduct, we resolve one of the outstanding questions on the stability of non-abelian black holes. We will also derive the high energy asymptotic behavior of correlation functions. (Based on work with Nathan Benjamin, Daniel Harlow, Monica Kang, Jaeha Lee, Sridip Pal, David Simmons-Duffin, Zhengdi Sun, and Zipei Zhang.)

Although predictions of quantum gravity are typically at extremely high energy, several non-trivial constraints on its low energy effective theory have been found over the last decade or so. I will start by explaining why the unification of general relativity and quantum mechanics has been difficult. After introducing the holographic principle as our guide to the unification, I will discuss its use in finding constraints on symmetry in quantum gravity. I will also discuss other conjectural constraints on low energy effective theories, collectively called swampland conditions, and their consequences.

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.

Fluid turbulence is a major unsolved problem of physics exhibiting an emergent complex structure from simple rules. We will briefly review the problem and discuss three avenues towards its solution: field theory, holography and machine learning.

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.

Gravitational wave signals from coalescing binary black holes are detected, and analyzed, by using large banks of template waveforms. The construction of these templates makes an essential use of the analytical knowledge of the motion and radiation of gravitationally interacting binary systems. A new angle of attack on gravitational dynamics consists of considering (classical or quantum) scattering states. Modern amplitude techniques have recently given interesting novel results. These results are reaching a level where subtle conceptual issues arise (quantum-classical transition, radiative effects versus conservative dynamics, massless limit,...).

The observation of gravitational wave signals by the two interferometers of the Laser Interferometer Gravitational-Wave Observatory (LIGO), and by the Virgo interferometer, has brought the first direct evidence for the existence of black holes, and has also been the first observation of gravitational waves in the wave-zone. After reviewing the historical path that led to our understanding of gravitational waves and black holes, the colloquium will present the theoretical developments on the motion and gravitational radiation of binary black holes that have been crucial in interpreting the LIGO-Virgo events as being emitted by the coalescence of two black holes.

In November 2015, Albert Einstein finalized a new theory of gravitation, General Relativity (GR), which describes gravitation as a deformation of the structure of space-time. It took many years of conceptual deepening and observational discoveries to fully grasp several of the most novel predictions of GR (gravitational waves, black holes, cosmological expansion). GR is the current standard model for the gravitational interaction, and plays a crucial role in the description of many physical systems: solar system, neutron stars, binary pulsars, galaxies, black holes, cosmology. For many years, GR was considered as being completely separate from the (quantum) description of the other interactions. However, several theoretical frameworks (string theory, supergravity) point towards a key role of GR in the search for a unified description of physics. GR has passed with flying colors all current experimental tests, but some puzzles remain unanswered.

Gravitational wave signals from coalescing binary black holes are detected, and analyzed, by using large banks of template waveforms. The construction of these templates makes an essential use of the analytical knowledge of the motion and radiation of gravitationally interacting binary systems. A new angle of attack on gravitational dynamics consists of considering (classical or quantum) scattering states. Modern amplitude techniques have recently given interesting novel results. These results are reaching a level where subtle conceptual issues arise (quantum-classical transition, radiative effects versus conservative dynamics, massless limit,...).

The observation of gravitational wave signals by the two interferometers of the Laser Interferometer Gravitational-Wave Observatory (LIGO), and by the Virgo interferometer, has brought the first direct evidence for the existence of black holes, and has also been the first observation of gravitational waves in the wave-zone. After reviewing the historical path that led to our understanding of gravitational waves and black holes, the colloquium will present the theoretical developments on the motion and gravitational radiation of binary black holes that have been crucial in interpreting the LIGO-Virgo events as being emitted by the coalescence of two black holes.

In November 2015, Albert Einstein finalized a new theory of gravitation, General Relativity (GR), which describes gravitation as a deformation of the structure of space-time. It took many years of conceptual deepening and observational discoveries to fully grasp several of the most novel predictions of GR (gravitational waves, black holes, cosmological expansion). GR is the current standard model for the gravitational interaction, and plays a crucial role in the description of many physical systems: solar system, neutron stars, binary pulsars, galaxies, black holes, cosmology. For many years, GR was considered as being completely separate from the (quantum) description of the other interactions. However, several theoretical frameworks (string theory, supergravity) point towards a key role of GR in the search for a unified description of physics. GR has passed with flying colors all current experimental tests, but some puzzles remain unanswered.

Thermodynamics provides a robust conceptual framework and set of laws that govern the exchange of energy and matter. Although these laws were originally articulated for macroscopic objects, nanoscale systems also exhibit “thermodynamic-like” behavior – for instance, biomolecular motors convert chemical fuel into mechanical work. To what extent can the laws of thermodynamics be scaled down to apply to individual microscopic systems, and what new features emerge at the nanoscale? I will describe some of the recent progress and challenges associated with addressing these questions.

Thermodynamics provides a robust conceptual framework and set of laws that govern the exchange of energy and matter. Although these laws were originally articulated for macroscopic objects, nanoscale systems also exhibit “thermodynamic-like” behavior – for instance, biomolecular motors convert chemical fuel into mechanical work. To what extent can the laws of thermodynamics be scaled down to apply to individual microscopic systems, and what new features emerge at the nanoscale? I will describe some of the recent progress and challenges associated with addressing these questions.

Our understanding of simple solids, is firmly grounded on the Fermi liquid concept and powerful computational techniques built around the density functional theory. These ideas form the basis of our “standard model” of solid state physics and have provided us with an accurate description of many materials of great technological significance. Correlated electron systems are materials for which the the standard model of solid state physics fails dramatically. The best known example being the copper oxide high temperature superconductors. Correlated electron materials continue to be discovered accidentally and surprise us with their exceptional physical properties and their potential for new applications. The most recent example is provided by the iron arsenide based high temperature superconductors. From a theoretical perspective describing strongly correlated electron systems pose one of the most difficult non-perturbative challenges in physics. In this colloquium I will give an elementary introduction to the field of strongly correlated electron materials and Dynamical Mean Field Theory (DMFT) a non perturbative method which provides a zeroth order picture of the strong correlation phenomena in close analogy with the Weiss mean field theory in statistical mechanics. Applications materials containing f and d electrons will be presented to show how the anomalous properties of correlated materials emerge from their atomic constituents. I will conclude with an outlook of the challenges ahead and the perspectives for a rational material design.

Strongly correlated metals exhibit anomalous transport properties which have puzzled condensed matter physicists for many years. They are characterized by large resistivities which exceed the Mott Ioffe Reggel limit and large thermoelectric responses, which cannot be explained in terms of standard Fermi liquid quasiparticles. Dynamical Mean Field Theory (DMFT) calculations [1,2] carried out on a doped one band Hubbard model suggest that this behavior originate in the strong temperature dependence of thee parameters of the underlying resilient (non-Landau) quasiparticles. We will test these ideas by analyzing low energy optical spectroscopy measurements in several prototypical compounds starting with the archetypal correlated material Sesquioxide V2O3. We will also show first principles, material specific, LDA+DMFT calculations which are in very good agreement with the experiments [3].

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.

The Principle of Least Action is both profound and practical. Since its first formulation by Maupertuis and Euler nearly three centuries ago, the Principle has been, and continues to be, a formidable battlehorse for penetrating unchartered territory in theoretical physics. The Principle, its connection with, and implications for, our ideas of symmetry, space, time, quantum mechanics, thermodynamics and gravitation, are glanced at.

The theory of phase transitions splits between abrupt transitions (nucleation and growth, critical droplets) and continuous transitions (scaling and universality). I’ll discuss wonderful biophysics examples for each: Michelle Wang’s twisting single molecules of DNA, and with Sarah Veatch’s discovery of universal Ising critical fluctuations in living cell membranes. (1) Plectonemes are the helically wound loops formed in garden hoses and electrical cords when they are overtwisted. Wang's group studies their equilibrium formation in overtwisted DNA, where they observe reversible transitions over the free energy barrier. This system, with well-known continuum elasticity and a controlled disorder, forms an unusual opportunity to test our ideas about the nucleation of phase transitions, and to generalize them to include randomness. (2) Sarah Veatch in Baird's group has recently made an amazing discovery – cell membranes, when stripped from the cytoskeleton, sit just above an Ising critical point. Cooled by 5%, they phase separate into two components: differing mixtures of lipids and proteins. We've tried to answer three questions: Why don't intact cells undergo this phase separation? Why would a cell want to sit near a critical point? What does statistical mechanics tell us about lipid rafts and the formation of protein aggregates?

“With four parameters I can fit an elephant; with five I can make it wag its tail.” Systems biology models of the cell have an enormous number of reactions between proteins, RNA, and DNA whose rates (parameters) are hard to measure. Models of climate change, ecosystems, and macroeconomics also have parameters that are hard or impossible to measure directly. If we fit these unknown parameters, fiddling with them until they agree with past experiments, how much can we trust their predictions? Multiparameter fits are sloppy; the parameters can vary over enormous ranges and still agree with past experiments. Nonetheless, they can often make useful predictions about future experiments, even allowing for these huge parameter uncertainties: a few stiff combinations of parameters govern the behavior. Third, these sloppy models all appear strikingly similar to one another – for example, the stiffnesses in every case we’ve studied are spread roughly uniformly over a range of over a million. We will use ideas and methods from differential geometry to explain what sloppiness is and why it happens so often. Finally, we shall show that models in physics are also sloppy – that sloppiness makes science possible.

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.

Does the world embody beautiful ideas? Pythagoras and Plato intuited that it should, Newton and Maxwell showed, in impressive examples, how it could. Modern physics demonstrates, in depth and detail, that it does. I will narrate, through notable examples, how the concept of beauty in physical law has evolved – and how it continues to guide our quest for ultimate understanding.

This talk is devoted to quantum propagation of dipole excitations in two dimensions in the presence of disorder. This problem differs from the conventional Anderson localization due to existence of long range hops. We found that the critical wave functions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T-invariant the states are critical for all values of the parameters. Otherwise, there can be a “normal metal - perfect metal" transition between this “ordinary" diffusion and the Levy-flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified non-linear supermatrix

Localization of the eigenfunctions of quantum particles in a random potential was discovered by P.W. Anderson more than 50 years ago in connection with spin relaxation and charge transport in disordered solids. Later experimentally was realized localization of other quantum particles and classical waves: light, microwaves, sound, cold atoms. At the same time it became clear that the domain of applicability of the concept of localization is much broader. In particular, it can be extended to various problems in condensed matter physics that involve not only disorder, but also interaction between quantum particles. We will consider manifestation of the Anderson localization in model systems: interacting Bose and Fermi gases and disordered spin models. This will allow us to discuss such phenomena as superconductor-metal-insulator (superfluid- normal fluid-glass) transitions. In particular, we will introduce a new class of finite-temperature phase transitions that can exist even in one-dimensional systems and manifest themselves in transport rather than equilibrium properties. We will also be able to get some insight on some problems in quantum computational complexity.

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.