ICTS

I will describe the world-wide research efforts led by Microsoft Corporation to build a fault-tolerant topological quantum computer using non-Abelian Majorana zero modes in solid state systems. These Majorana particles are their own anti-particles as envisioned by Ettore Majorana a long time ago in the context of particle physics, and are predicted to exist as exotic bound states in the energy gap of topological superconductors. Recent experiments have observed telltale signatures of the physical existence of these Majorana particles in semiconductor-superconductor hybrid nanowires.

Topology and the electromagnetic responses of quantum materials This talk starts by reviewing the remarkable theoretical and experimental progress in topological materials over the past decade. Three-dimensional topological insulators realize a particular electromagnetic coupling known as “axion electrodynamics”, and understanding this leads to an improved understanding of magnetoelectricity in all materials. We then turn to how topological Weyl and Dirac semimetals can show unique electromagnetic responses; we argue that in linear response the main observable effect solves an old problem via the orbital moment of Bloch electrons, and how in nonlinear optics there should be a new quantized effect, at least approximately.

Quantum field theory (QFT) combines two of the revolutions of 20th century physics, quantum mechanics and special relativity. It is used in the description of the Standard Model of particle physics, which is tested with incredible accuracy. It is also the natural framework to describe the quantum behavior of systems with a very large number of degrees of freedom, like the electrons in a solid. In addition, QFT also plays a fundamental role in our only candidate theory of quantum gravity, String Theory. QFT has also led to deep and surprising results in mathematics. Even though QFT is so central to our understanding of physics, there are good reasons to believe that we still lack crucial insights about its underlying structure.

Active matter, in which sustained energy transduction breaks detailed balance at the scale of the constituent particles, is a key ingredient in the physicist's answer to the question ""What Is Life?"" It is also an area of intense interest in nonequilibrium physics, yielding insights into mechanics and statistics in living matter and its imitations from subcellular to oceanic scales. My talk will present selected results from recent theoretical and experimental work with colleagues and students on order, fluctuations, topological defects and entropy production in active systems.

One of the basic goals of the theory of computing is to model behaviour of ""intelligent"" systems (computers or humans). Behaviour includes ability to acquire information (or knowledge), analyzing it (or reasoning) and communicating it. The theories of Turing (universal computation) and Shannon (reliable communication) offer the foundations for this study covering much of the terrain. And the remarkable progress in the technologies of computing and communication is a testament to the success of these theories. Unfortunately this success has also exposed problems in the intersection of the two fields that neither captures adequately. In our work on ""communcation amid uncertainty"" we explore some such problems, where the ability of two communicating entities to compute allows them to acquire large *mostly* common context. The commonality of the context should enable communication to be even more efficient. On the other hand the ""uncertainty"" about the context (the fact the context is only mostly common) leads to novel mathematical questions and challenging fundamental aspects of the classical theory, such as the operational definition of entropy. In this talk we will brielfy describe some of the questions and (partial) answers in this setting communication with uncertainty.

Bias is an increasingly observed phenomenon in the world of machine learning (ML): From gender bias in image search, racial bias in court bail pleas, to biases in worldviews depicted in personalized news feeds. At the core, what is powering these ML application are algorithms for fundamental computational tasks such as classification, data summarization, ranking, and online learning. Such algorithms have traditionally been designed with the goal of maximizing some notion of “utility” and identifying or controlling bias in their output has not been a consideration. I will focus on the problem of data summarization and present a mathematical framework that allows for ''fair algorithms'' while maintaining their utility. Developing algorithms in this setting has led to new mathematical techniques involving polynomials and entropy, leading to advances at the core of theoretical computer science."

Over the past two years, LIGO and Virgo have opened a new window into the cosmos through the direct detections of gravitational waves from binary black hole and binary neutron star mergers. In this presentation, I will highlight the recent LIGO-Virgo discoveries, discuss what they reveal about the high energy universe, and give a preview of what may come in the future for this new and exciting field.

The talk will discuss classical Heisenberg spin chains whose time evolution is given by Hamiltonian spin-precessional dynamics. I will first discuss the hydrodynamics of the slow fields, corresponding to conserved quantities, which provide a macroscopic description of the system. At low temperatures, we show the emergence of an additional slow field which leads to anomalous scaling of dynamical correlation functions. I will then discuss the growth and propagation of localized perturbations in this system which happens ballistically at all temperatures.

Understanding rare events in graphs and networks The mathematical theory of large deviations attempts to understand the probabilities and consequences of rare events. In spite of the growing importance of graphs and networks in the modern world, we did not have the tools to understand large deviations in graphical structures until quite recently. I will talk about the development of this new area in probability theory and its surprising implications.

During the last few decades, it has become increasingly clear that the Universe is full of black holes. There are literally millions in each galaxy. Most black holes are identified and studied through the energetic radiation emitted by hot gas orbiting the holes. However, until now, astronomers have never been able to obtain a close-up image of any black hole. This is about to change. The Event Horizon Telescope (EHT), an Earth-spanning radio interferometer, is poised to obtain the first event-horizon-scale images of Sagittarius A*, the supermassive black hole at the center of our Galaxy. EHT images are predicted to show certain geometrical distortions, which will provide new tests of the relativistic space-time near a black hole. The EHT will also provide an unprecedented close-up movie of the orbiting, radiating gas near the black hole. This will open up new opportunities for the study of high energy phenomena in hot magnetized astrophysical plasmas.

While technological revolutions in neuroscience now enable us to record from ever increasing numbers of neurons, for the forseeable future we will still only record an infinitesimal fraction of the total number of neurons in mammalian circuits controlling complex behaviors. Nevertheless, despite operating within this extreme under-sampling limit, a wide array of statistical procedures for dimensionality reduction of multineuronal recordings uncover remarkably insightful, low dimensional neural state space dynamics whose geometry reveals how behavior and cognition emerge from neural circuits. What theoretical principles explain this remarkable success? In essence, how is it that we can understand anything about the brain while recording an infinitesimal fraction of its degrees of freedom? We develop an experimentally testable theoretical framework to answer this question. By making a novel conceptual connection between neural measurement and the theory of random projections, we derive scaling laws relating how many neurons we must record to accurately recover state space dynamics, given the complexity of the behavioral or cognitive task, and the smoothness of neural dynamics. Moreover we verify these scaling laws in the motor cortical dynamics of monkeys performing a reaching task. Overall, these results yield conceptual insights into how the complexity of neural dynamics is upper-bounded by the complexity of cognition and behavior itself.

Molecular archaeology: using genomes to reconstruct two billion years of cellular life It has been exactly 50 years since Lynn Margulis (at the time, Lynn Sagan) proposed her famous endosymbiont hypothesis. It is now well established that mitochondria were once free-living bacteria with their own division machinery which took up residence within another cell, thus creating the first true eukaryote. The physical fossil record suggests that eukaryotes emerged from prokaryotic ancestors over two billion years ago. Molecular archaeology can help uncover how this occurred. Using a new phylogenetic method with deep time resolution, we have retraced the earliest steps by which the host cell tamed the bacterial endosymbiont.