Colloquium

As of late March 2020, Covid-19 has already secured its status among the most expansive pandemics of the last century. Covid-19 is caused by a coronavirus--SARS-CoV-2--that causes a severe respiratory disease in a fraction of those infected, and is typified by several important features: ability to infect cells of various kinds, contagiousness prior to the onset of symptoms, and a widely varying experience with disease across patient demographics.

In this seminar, I discuss the many lessons that the scientific community has learned from Covid-19, including insight from molecular evolution, cell biology, and epidemiology. I discuss the role of mathematical and computational modeling efforts in understanding the trajectory of the epidemic, and highlight modern findings and potential research questions at the interface of virology and materials science. I will also introduce areas of inquiry that might be of interest to the physics community.

Historically, new particles and forces in the Standard Model have most often revealed themselves at high-energy particle colliders. Certain phenomena beyond the Standard Model, however, are best studied by using carefully designed low-energy precision measurements, or via their imprints on astrophysical and cosmological observables. In this talk, I will provide a concise overview of some of the new experiments and searches devised to look for new physics beyond the Standard Model. In particular, I will discuss recent developments in the new experimental and theoretical program of cosmological collider physics and how we can use the cosmological collider as a tool to study the structure of the Higgs potential at very high energies.

As our understanding of the universe and its fundamental building blocks extends to shorter and shorter distances, experiments capable of probing these scales are becoming increasingly difficult to construct. Fundamental particle physics faces a potential crisis: an absence of data at the shortest possible scales. Yet remarkably, even in the absence of experimental data, the requirement of theoretical consistency puts stringent constraints on viable models of fundamental particles and their interactions. In this talk I’ll discuss a variety of criteria that constrain theories of particles in flat spacetime and de Sitter. Such criteria have the possibility to address questions such as: What low energy theories admit consistent UV completions? Which massive particles are allowed in an interacting theory? Is string theory the unique weakly coupled UV completion of General Relativity?

In our four-dimensional world supersymmetry is the only extension of the classical Poincaré invariance which laid the foundation of modern physics in the beginning of the 20th century. Supersymmetry, a new geometric symmetry extending Poincaré, was discovered in 1970 –– it was overlooked for decades because of its quantum nature. In the next 10 years or so supersymmetry 

assumed the role of a universal framework in which new models for natural phenomena and regularities (e.g. the concept of naturalness) have been developed. It gave rise to a powerful stream of theoretical phenomenology.

The fact that LHC at CERN produced no evidence for low-energy supersymmetry (and naturalness as well) was a powerful blow. However, despite its absence in experiments the less known second mission of supersymmetry is highly successful, with remarkable advances occurring on a regular basis. Supersymmetry proved its power and uniqueness for those who address hard questions in strongly coupled field theories, including Yang-Mills. Some supersymmetry-based exact results obtained in four dimensions are the main topics of my talk. In the past one could hardly dream that such results are possible.

Theories beyond the Standard Model of particle physics often predict new, light, feebly interacting particles whose discovery requires novel search strategies. A light particle, the QCD axion, elegantly solves the outstanding strong-CP problem of the Standard Model; cousins of the QCD axion can also appear, and are natural dark matter candidates.  First, I will discuss my experimental proposal based on thin films, in which dark matter can efficiently convert to detectable single photons. A prototype experiment is underway, and current techniques promise to reach significant new dark matter parameter space.

Second, I will show how rotating black holes turn into axionic and gravitational wave beacons, creating nature's laboratories for ultralight bosons. When an axion's Compton wavelength is comparable to a black hole size, energy and angular momentum from the black hole source exponentially-growing bound states of particles, forming `gravitational atoms'.  These `gravitational atoms' emit monochromatic gravitational wave signals, enabling current searches at gravitational wave observatories to discover ultralight axions. If the axions interact with one another, instead of gravitational waves, black holes populate the universe with axion waves.

Stacking two graphene layers twisted by the ‘magic angle’ 1.1º generates flat energy bands, which in turn catalyzes various strongly correlated phenomena depending on filling and sample details. While this system is most famous for the superconducting and insulating states observed at fractional fillings, I argue that charge neutrality presents an interesting interplay of disorder and interactions.

In scanning tunnelling microscopy (STM), the most striking signature of interactions occurs close to charge neutrality, where the splitting between the flat bands increases dramatically. In analogy with quantum Hall ferromagnetism, I show that this effect may be qualitatively understood as the result of an exchange energy gain. A low-energy manifold of gapped, symmetry-breaking states is identified, one of which possesses quantum valley Hall order. Transport measurements yield ostensibly conflicting information at charge neutrality: while some samples reveal semimetallicity (as expected when correlations are weak), yet others exhibit robust insulation. I reconcile these observations and those of STM by arguing that strong interactions supplemented by weak, smooth disorder stabilize a network of locally gapped quantum valley Hall domains with spatially varying Chern numbers determined by the disorder landscape—--even when an entirely different order is favored in the clean limit. I conclude with a discussion of experimental tests of this proposal via local probes and transport.

The average entanglement entropy of subsystems of random pure states is (nearly) maximal. In this talk, we discuss the average entanglement entropy of subsystems of highly excited eigenstates of integrable and nonintegrable many-body lattice Hamiltonians. For translationally invariant quadratic models (or spin models mappable to them) we prove that, when the subsystem size is not a vanishing fraction of the entire system, the average eigenstate entanglement entropy exhibits a leading volume-law term that is different from that of random pure states. We argue that such a leading term is likely universal for translationally invariant (noninteracting and interacting) integrable models. For random pure states with a fixed particle number (random canonical states) away from half filling and normally distributed real coefficients, we prove that the deviation from the maximal value grows with the square root of the system's volume when the size of the subsystem is one half of that of the system. We then show that the average entanglement entropy of highly excited eigenstates of a particle number conserving quantum chaotic model is the same as that of random canonical states.

A scientific understanding of modern deep learning is still in its early stages. As a first step towards understanding the learning dynamics of neural networks, one can simplify the problem by studying limits that might have theoretical tractability and practical relevance. I’ll begin with a brief survey of our earlier body of work that has investigated the infinite width limit of deep networks, a topic of active study recently. With these results in hand, it nonetheless appears there is still a gap towards theoretically describing neural networks at finite width. I’ll argue that the choice of learning rate is one crucial factor in dynamics away from the infinite width limit and naturally classifies deep networks into two classes separated by a sharp transition. This is elucidated in a class of solvable simple models we present, which give quantitative predictions for the two classes. Quite remarkably, we test these predictions empirically in practical settings and find excellent agreement. 

Yasaman Bahri is a research scientist on the Google Brain team. Her current research program is to build a scientific understanding of deep learning using a combination of theoretical analysis and empirical investigation. Prior to Google, she was at the University of California, Berkeley, where she received her Ph.D. in physics in 2017, specializing in theoretical quantum condensed matter.

Beginning with the landmark gravitational wave detections by LIGO/Virgo, we have been gaining an unprecedented view of the dynamics of strongly curved spacetime originally predicted by Einstein. Enabling and motivated by these observations, there has been rapid development in the theoretical and computational tools we use to understand and interpret the nature of gravity and matter in this regime. This is essential to fulfilling the promise of gravitational wave astronomy to not only be a new window on the astrophysics of black hole and neutron star mergers, but also to be a unique probe of fundamental physics. I will illustrate this, highlighting the example of how black holes can be used to search for new particles. The same theoretical tools also allow us to push Einstein's theory to the extreme in search of the limits of its predictability, for example testing cosmic censorship, the idea that the breakdown in Einstein's equations associated with unhalted collapse is always hidden behind a black hole horizon. I will describe some recent work resolving a long-standing putative counterexample to this conjecture.

While the concept of topology is often introduced by contrasting oranges with bagels, the idea of topologically distinct quantum phases of matter is far more abstract. In this talk, we will focus on a more tangible form of topology that also arises in quantum condensed matter system: when the sites in a lattice are dragged around in a symmetric manner, what attributes of the lattice would remain unchanged? Such deformation can be viewed as the lattice analog of the familiar (mental) exercise of transforming a bagel into a coffee mug. We will first introduce the mathematical framework for identifying the topological classes of lattices, and then discuss how these invariants can constrain and inform the more abstract notion of topological phases of matter that emerge.

High resolution hydrodynamic simulations of galaxy formation are powerful tools, which can provide important information on the properties of the dark matter halo. Combined with the information obtained from the second data release of the Gaia satellite, simulations can significantly improve our understanding of the dark matter distribution in the Solar neighborhood. Determining the local dark matter velocity distribution is crucial for the correct analysis and interpretation of data from dark matter direct detection experiments. I will discuss the local dark matter distribution of Milky Way-like galaxies extracted from state-of-the-art hydrodynamic simulations, and present an analysis of direct detection data using this distribution. I will also discuss the properties of the dark matter component of the radially anisotropic stellar population recently discovered in the Gaia data, using the Auriga simulations. In particular, I will present the local dark matter density and velocity distributions of the simulated Milky Way-like galaxies with and without the anisotropic substructure, and discuss their implications for dark matter direct detection.

Last fall, a team at Google announced the first-ever demonstration of "quantum computational supremacy"---that is, a clear quantum speedup over a classical computer for some task---using a 53-qubit programmable superconducting chip called Sycamore.  In addition to engineering, Google's accomplishment built on a decade of research in quantum computing theory.  This talk will discuss questions like: what exactly was the contrived computational problem that Google solved?  How does one verify the outputs using a classical computer?  And how confident are we that the problem really is classically hard---especially in light of subsequent counterclaims by IBM?  I'll end with a proposed application for Google's experiment---namely, the generation of certified random bits, for use (for example) in proof-of-stake cryptocurrencies---that I've been developing and that Google is now working to demonstrate.