Talks

New quantum simulation platforms provide an unprecedented microscopic perspective on the structure of strongly correlated quantum matter. This allows to revisit decade-old problems from a fresh perspective, such as the two-dimensional Fermi-Hubbard model, believed to describe the physics underlying high-temperature superconductivity. In order to fully use the experimental as well as numerical capabilities available today, we need to go beyond conventional observables, such as one- and two-point correlation functions. In this talk, I will give an overview of recent results on the Hubbard model obtained through novel analysis tools: using machine learning techniques to analyze quantum gas microscopy data allows us to take into account all available information and compare different theories on a microscopic level. In particular, we consider Anderson's RVB paradigm to the geometric string theory, which takes the interplay of spin and charge degrees of freedom microscopically into account. The analysis of data from quantum simulation experiments of the doped Fermi-Hubbard model shows a qualitative change in behavior around 20% doping, up to where the geometric string theory captures the experimental data better. This microscopic understanding of the low doping limit has led us to the discovery of a binding mechanism in so-called mixed-dimensional systems, which has enabled the observation of pairing of charge carriers in cold atom experiments.
Intriguingly, mixed-dimensional systems exhibit similar features as the original two-dimensional model, e.g. a stripe phase at low temperatures. At intermediate to high temperatures, we use Hamiltonian reconstruction tools to quantify the frustration in the spin sector induced by the hole motion and find that the spin background is best described by a highly frustrated J1-J2 model.

Zoom link:  https://pitp.zoom.us/j/99449352935?pwd=cXdYYTJ2c1hVZ014SWRwZi9LRjQ3dz09

We begin by reviewing the role of coadjoint orbits in the representation theory of nilpotents groups and then, to connect with the recent applications in physics of coadjoint orbits "around the corner" of the mathematical framework developed by Kirillov, we review the classification of coadjoint orbits of the Virasoro group. This will allow us to connect with more recent developments, including e.g. the study of coadjoint orbits of BMS algebras.

Mapping the intensity of the 21 cm emission line from neutral hydrogen (HI) is a promising technique for characterizing the 3D matter distribution over large volumes of the Universe and out to high redshifts.  The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a radio interferometer specifically designed for this purpose.  CHIME recently reported the detection of 21 cm emission from large-scale structure between redshifts 0.8 and 1.4.  This was achieved by stacking maps of the radio sky, constructed from 102 nights of CHIME data, on the angular and spectral locations of galaxies and quasars from the eBOSS clustering catalogs.  In this talk, I will introduce the experiment and provide an overview of the detection.  I will describe key aspects of both the data processing pipeline and the simulation pipeline used to model the stacked signal.  I will discuss the implications of the detection.  Finally, I will evaluate the prospects for using CHIME -- and it's successor, the Canadian Hydrogen Observatory and Radio-transient Detector (CHORD) -- to measure the power spectrum of 21 cm emission, identify the signature of baryon acoustic oscillations, and constrain dark energy.

Zoom link:  https://pitp.zoom.us/j/94362295704?pwd=NnQxa1pteWJVTzVBTVFYUmlsWnlVUT09

This lecture aims at introducing the notion of asymptotic symmetries in gravity and the derivation of the related surface charges by means of covariant phase space techniques. First, after a short historical introduction, I will rigorously define what is meant by “asymptotic symmetry” within the so-called gauge-fixing approach. The problem of fixing consistent boundary conditions and the formulation of the variational principle will be briefly discussed. In the second part of the lecture, I will introduce the covariant phase space formalism, as conceived by Wald and coworkers thirty years ago, which adapts the Hamiltonian formulation of classical mechanics to Lagrangian covariant field theories. With the help of this fantastic tool, I will elaborate on the construction of canonical surface charges associated with asymptotic symmetries and address the crucial questions of their conservation and integrability on the phase space. In the third and last part, I will conclude with an analysis of the algebraic properties of the surface charges, describing in which sense they represent the asymptotic symmetry algebra in full generality, without assuming conservation or integrability. For pedagogical purposes, the theoretical concepts will be illustrated throughout in the crucial and well-known case of radiative asymptotically flat spacetimes in four dimensions, as described by Einstein’s theory of General Relativity, and where many spectacular and unexpected features appear even in the simplest case of historical asymptotically Minkowskian boundary conditions. In particular, I will show that the surface charge algebra contains the physical information on the flux of energy and angular momentum at null infinity in the presence of gravitational radiation.

Abstract   Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the stochastic block model. In the present work, we consider the case of networks with missing links that is important in application and show that the variational approximation to the maximum likelihood estimator converges at the minimax rate. This provides the first minimax optimal and tractable estimator for the problem of parameter estimation for the stochastic block model. We complement our results with numerical studies of simulated and real networks, which confirm the advantages of this estimator over current methods.

Abstract Graph neural networks (GNNs) are successful at learning representations from most types of network data but suffer from limitations in large graphs, which do not have the Euclidean structure that time and image signals have in the limit. Yet, large graphs can often be identified as being similar to each other in the sense that they share structural properties. Indeed, graphs can be grouped in families converging to a common graph limit -- the graphon. A graphon is a bounded symmetric kernel which can be interpreted as both a random graph model and a limit object of a convergent sequence of graphs. Graphs sampled from a graphon almost surely share structural properties in the limit, which implies that graphons describe families of similar graphs. We can thus expect that processing data supported on graphs associated with the same graphon should yield similar results. In this talk, I formalize this intuition by showing that the error made when transferring a GNN across two graphs in a graphon family is small when the graphs are sufficiently large. This enables large-scale graph machine learning by transference: training GNNs on moderate-scale graphs and executing them on large-scale graphs.

Abstract The theory of graph limits is an important tool in understanding properties of large networks. We begin the talk with a survey of this theory, concentrating in particular on the sparse setting. We then investigate a power-law random graph model and cast it in the sparse graph limit theory framework. The distinctively different structures of the limit graph are explored in detail in the sub-critical and super-critical regimes. In the sub-critical regime, the graph is empty with high probability, and in the rare event that it is non-empty, it consists of a single edge. Contrarily, in the super-critical regime, a non-trivial random graph exists in the limit, and it serves as an uncovered boundary case between different types of graph convergence.

Abstract The goal of this talk is to describe probabilistic approaches to three major problems for dynamic networks, both of which are intricately connected to long range dependence in the evolution of such models: 1.Nonparametric change point detection: Consider models of growing networks which evolve via new vertices attaching to the pre-existing network according to one attachment function $f$ till the system grows to size $τ(n) < n$, when new vertices switch their behavior to a different function g till the system reaches size n. The goal is to estimate the change point given the observation of the networks over time with no knowledge of the functions driving the dynamics. We will describe non-parametric estimators for such problems. 2. Detecting the initial seed which resulted in the current state of the network: Imagine observing a static time slice of the network after some large time $n$ started with an initial seed. Suppose all one gets to see is the current topology of the network (without any label or age information). Developing probably efficient algorithms for estimating the initial seed has inspired intense activity over the last few years in the probability community. We will describe recent developments in addressing such questions including robustness results such as the fixation of so called hub vertices as time evolves. 3. Co-evolving networks: models of networks where dynamics on the network (directed random walks towards the root) modifies the structure of the network which then impacts behavior of subsequent dynamics. We will describe non-trivial phase transitions of condensation around the root and its connection to quasi-stationary distributions of 1-d random walks.