Deadline to Register
Thursday February 9, 2023
All participants must register.
Sidney Nagel, University of Chicago
Giulio Biroli, École Normale Supérieure
Andrea Cavagna, Universita di Roma Spaienza
Patrick Charbonneau, Duke University
Laura Foini, CNRS IPhT Université Paris-Saclay
Andrea Liu, University of Pennsylvania
Xiaoming Mao, University of Michigan
Cris Moore, Santa Fe Institute
David Reichman, Columbia University
Past Annual Meetings:
The Simons Collaboration on Cracking the Glass Problem will meet for its final annual meeting with the goal to review the progress made pursuing the original, stated goals of the collaboration, which were to develop a complete and quantitative description of the glass transition, connecting the explicit and quantitative mean-field and zero-temperature theories that have been developed. The collaboration’s aim was to create a predictive theory of glasses, including dynamics, as well as the tools to develop such a framework, which has had important ramifications for a broad range of fields and has provided a new vision for this branch of statistical and mathematical physics.
The annual meeting will also explore new connections between the many fields of research that are involved with glassy and amorphous problems. These areas are intimately connected and talks during the meeting will address a few of these activities.
THURSDAY, MARCH 10
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Andrea Liu | Glass Concepts for Materials Design 10:30 AM BREAK 11:00 AM Cristopher Moore | Algorithms from Tensor Networks 12:00 PM LUNCH 1:00 PM Xiaoming Mao | Topological Mechanics in Disordered Networks 2:00 PM BREAK 2:30 PM Andrea Cavagna | Natural Swarms in 3.99 Dimensions 3:30 PM BREAK 4:00 PM Laura Foini | The Eigenstate Thermalization Hypothesis and Thermal Correlation Functions in Many-Body Quantum Systems 5:00 PM DAY ONE CONCLUDES
FRIDAY, MARCH 11
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Giulio Biroli | Glass Transition and Glassy Dynamics: A Real Space Perspective 10:30 AM BREAK 11:00 AM Patrick Charbonneau | Starting from d->oo to Crack the Glass Problem 12:00 PM LUNCH 1:00 PM David Reichman | Progress and Possibilities: Where We Stand on Cracking the Glass Problem 2:00 PM MEETING CONCLUDES
École Normale Supérieure
Glass Transition and Glassy Dynamics: A Real Space Perspective
One of the main aims of our collaboration has been to identify and characterize the emergent structural and dynamical properties associated with the glass transition, and provide a theoretical framework to predict and explain them. In this talk, Giulio Biroli will present recent achievements along this line of research and discuss the challenges that remain ahead. Biroli will follow a real-space perspective in which the goal is to understand how local excitations and local rearrangements combine together and lead to relaxation and flow in super-cooled liquids. Biroli will discuss the main physical mechanisms identified, the directions being followed to construct a quantitative theory and the connection with the high-dimensional approach.
Sapienza Università di Roma
Natural Swarms in 3.99 Dimensions
Collective behavior is found in a startling variety of biological systems, from clusters of bacteria and colonies of cells, up to insect swarms, bird flocks and vertebrate groups. A unifying ingredient is the presence of strong correlations: experiments in bird flocks, fish schools, mammal herds, insect swarms, bacterial clusters and proteins have found that the correlation length is significantly larger than the microscopic scales. In the case of natural swarms of insects, another key hallmark of statistical physics has been verified, namely dynamic scaling: spatial and temporal relaxation are entangled into one simple law, so that the relaxation time scales as a power of the correlation length, thus defining the dynamical critical exponent, z. Within statistical physics, strong correlations and scaling laws are the two steppingstones leading to the renormalization group (RG): when we coarse-grain short-scale fluctuations, the parameters of different models flow towards one common fixed point ruling their large-scale behavior. RG fixed points therefore organize into few universality classes the macroscopic behavior of strongly correlated systems, thus providing parameter-free predictions of the collective behavior. Biology is vastly more complex than physics, but the widespread presence of strong correlations and the validity of scaling laws can hardly be considered a coincidence, and they rather call for an exploration of the correlation-scaling-RG path also in collective biological systems. However, to date there is yet no successful test of an RG prediction against experimental data on living systems. In this talk Andrea Cavagna will apply the renormalization group to the dynamics of natural swarms of insects. Swarms of midges in the field are strongly correlated systems, obeying dynamic scaling with an experimental exponent z=1.37 +/- 0.11, significantly smaller than the naive value z = 2 of equilibrium overdamped dynamics. Cavagna will show that this anomalous exponent can indeed be reproduced by an RG calculation to one-loop, provided that off-equilibrium activity and inertial dynamics are both considered; the theory gives z=1.35, a value closer to the experimental exponent than any previous theoretical determination and perfectly in line with the numerical value, z=1.35 +/- 0.04. This successful result is a significant step towards testing the core idea of the RG even at the biological level, namely that integrating out the short-scale details of a strongly correlated system impacts on its large-scale behavior by introducing anomalies in the dimensions of the physical quantities. In the light of this, it is fair to hope that the renormalization group, with its most fruitful consequence — universality — may have an incisive impact also in biology.
Starting from d → ∞ to Crack the Glass Problem
One of the three pillars of the Simons Collaboration on Cracking the Glass Problem is the exact solution of simple glass models in the limit of infinite spatial dimension, d. Throughout the collaboration, this core solution has been refined and significantly enriched. It has also been variously extended to finite-dimensional contexts and its theoretical predictions have been carefully compared with numerical results obtained in various d. While some features of the d → ∞ solution and its finite-dimensional extension were found to be remarkably robust, others have required a careful consideration of fluctuations and activated processes, and yet others remain works in progress. In this talk, Patrick Charbonneau will review the successes and challenges of this epistemic approach, notably covering jamming criticality, Gardner physics, out-of-equilibrium quenches and instanton calculations.
Centre National de la Recherche Scientifique, Institut de Physique Théorique
The Eigenstate Thermalization Hypothesis and Thermal Correlation Functions in Many-Body Quantum Systems
The development of the eigenstate thermalization hypothesis (ETH) was conducted with the aim of explaining the mechanism by which chaotic systems reach thermal equilibrium from a generic state. ETH implies a form for the matrix elements of the local operators between the eigenstates of the Hamiltonian, and since then, numerous studies have led to the characterization of these objects in increasingly fine detail, providing a solid framework for understanding the (thermo)dynamics of quantum many-body systems. ETH can be derived by analogy with the theory of random matrices and, in fact, in this ansatz these matrix elements are modeled as pseudo-random variables. In their work, Laura Foini and collaborators have provided a generalization of the ETH ansatz in order to take into account the correlations between the elements of the matrix which are essential to describe the high-order correlation functions.
Laura Foini will explain how, by analogy with random matrix theory, one can assume a certain hierarchy between these correlations and will discuss how this generalized ansatz underlies a relationship between ETH and free probability, a branch of mathematics that studies non-commutative random variables. This relationship allowed us to unveil a particular structure of the time-dependent correlation functions in thermal equilibrium.
University of Pennsylvania
Glass Concepts for Materials Design
In many-body systems, we normally specify the interactions and study the resulting properties — this is known as the forwards problem. The materials design problem is an inverse problem in which we first specify the desired properties and then determine the interactions required to achieve them. Similar inverse problems are solved routinely in machine learning with neural networks. For example, to classify images, one first specifies a learning cost function that penalizes incorrect identifications, and then minimizes the cost function with respect to “learning degrees of freedom” that specify the neural networks, such as node weights. A set of node weights that reaches the global minimum of the cost function corresponds to a neural network that correctly classifies a set of images, but the cost function can have a complex landscape with many local minima. Learning in neural networks can therefore face the same challenges as the glass problem, in which a physical cost function with a potentially complex landscape, such as the free energy or energy, must be minimized with respect to physical degrees of freedom, such as the particle positions. Our collaboration has pioneered a new strategy for inverse design of materials in which one specifies a learning cost function that embodies the desired properties, which is minimized with respect to learning degrees of freedom that specify interactions. Because the materials are physical systems, however, one must simultaneously minimize a physical cost function, such as the energy, with respect to physical degrees of freedom. Thus, the inverse design problem requires two different cost functions — a learning and a physical cost function — to be minimized with respect to two sets of degrees of freedom — the learning and physical degrees of freedom — which are coupled to each other. Andrea Liu will discuss how ideas from the glass problem have not only led to progress in inverse design but has also led to new approaches to machine learning that use local rules instead of global gradient descent to learn in a distributed way that is not achievable in artificial neural networks.
University of Michigan
Topological Mechanics in Disordered Networks
Topological mechanics is a new field where concepts of topologically protected states of matter are realized in mechanical systems, leading to robust soft modes and self-stress states protected by topology. So far, most studies of topological mechanics focus on periodic lattices which permit convenient mathematical characterization of topological indices. Can topological states arise in disordered mechanical systems? In this talk, Xiaoming Mao will review current research where new experiments and theories are proposed to realize and characterize disordered topological mechanical systems and discuss their far-reaching implications on robust properties in natural and engineered materials.
Santa Fe Institute
Algorithms from Tensor Networks
Suppose we have a noisy observation of a rank-one tensor. That is, there is a hidden vector, v, and we observe v’s p-th outer product with itself, giving a tensor of arity p, with Gaussian noise in every entry. Given the resulting tensor T, our goal is to reconstruct v, as well as to reject the null hypothesis that the tensor consists only of noise. In physics terms, this is a planted p-spin model, where p is the arity of the tensor. Computationally, it is a tensor version of PCA. But we lack a theory of linear algebra for tensors, so we can’t simply look at the dominant eigenvector and hope it is correlated with v. What should we do instead? What is the “spectrum” of a tensor anyway?
Many algorithms approach problems like this by “flattening” the tensor into a matrix, and then using the resulting matrix in a spectral algorithm. But a more natural approach is to form a tensor network with copies of the observed tensor, and contract it to obtain a scalar or vector. This scalar might help us solve the hypothesis testing problem, and the vector might help us reconstruct v. Cristopher Moore will review the use of this type of algorithm in the previous papers of others and make some observations about them in general, including whether they can succeed all the way down to the conjectured computational phase transition.
Progress and Possibilities: Where We Stand on Cracking the Glass Problem
Nearly seven years ago our collaboration put forward a roadmap for addressing the theoretical description of the glass transition, a multi-pronged approach taking advantage of progress in the description of the jamming transition and the rigorous formulation of a high dimensional theory of glasses was put forward. Largely through the lens of computer simulation techniques which have leveraged crucial advances made under the auspices of the collaboration, David Reichman will highlight key progress that has been made and outstanding open problems which have yet to be solved.
Participation & Funding
Participation in the meeting falls into the following four categories. An individual’s participation category is communicated via their letter of invitation.
Group A – PIs and Speakers
The foundation will arrange and pay for all air and train travel to the conference as well as hotel accommodations and reimbursement of local expenses.
Group B – Out-of-town Participants
The foundation will arrange and pay for all air and train travel to the conference as well as hotel accommodations and reimbursement of local expenses.
Group C – Local Participants
Individuals in Group C will not receive financial support, but are encouraged to enjoy all conference-hosted meals.
Group D – Remote Participants
Individuals in Group D will participate in the meeting remotely. Please register at the link above and a remote participation link will be sent to you approximately two weeks prior to the meeting.
Air and Train
The foundation will arrange and pay for all air and train travel to the conference for those in Groups A and B. Please provide your travel specifications by clicking the registration link above. If you are unsure of your group, please refer to your invitation sent via email.
For participants in Groups A & B driving to Manhattan, The James NoMad Hotel offers valet parking. Please note there are no in-and-out privileges when using the hotel’s garage, therefore it is encouraged that participants walk or take public transportation to the Simons Foundation.
Participants in Groups A & B who require accommodations are hosted by the foundation for a maximum of three nights at The James NoMad Hotel. Any additional nights are at the attendee’s own expense. To arrange accommodations, please register at the link above.
The James NoMad Hotel
22 E 29th St
New York, NY 10016
(between 28th and 29th Streets)
For driving directions to The James NoMad, please click here.
ALL in-person meeting attendees must be vaccinated against the COVID-19 and wear a mask when not eating or drinking.
Individuals in Groups A & B will be reimbursed for meals not hosted by the Simons Foundation as well as local expenses, including ground transportation. Additional information in this regard will be emailed on the final day of the meeting.