Scientific Series

Representations of the fundamental groups of surfaces appear so often in geometry that it's tempting to see them primarily as geometric structures. In recent years, however, researchers have uncovered beautiful new features of these representations by thinking of them instead as dynamical systems. As an invitation to the dynamical point of view, I'll describe how geometric tools from the study of billiards can be used to build invariants of surface group representations.

Cold dark matter provides a remarkably good description of cosmology and astrophysics. However, observations connected with small scales might be in tension with this framework. In particular, structure formation simulations suggest that the density profiles of dwarf spheroidal galaxies should exhibit cusps, in contrast to observations. I will show that Fermi repulsion can explain the observed cored density profiles in dwarf galaxies for sub-keV fermionic dark matter.  While in conventional dark matter scenarios, such sub-keV thermal dark matter would be excluded by free streaming bounds, I will argue that these constraints are ameliorated in models with dark matter at lower temperature than conventional thermal scenarios. Finally, I will outline a class in which the dark matter typically has a lower temperature than the thermal expectation, dubbed Flooded Dark Matter, and discuss aspects of model building.

Astrophysical black hole candidates, although long thought to have a horizon, could be horizonless ultra-compact objects. This intriguing possibility is motivated by the black hole information paradox and a plausible fundamental connection with quantum gravity. In this talk I will consider the asymptotically free quadratic gravity as the UV completion of general relativity. Using a classical theory that captures its main features, we find that sufficiently dense matter produces a novel horizonless solution, the 2-2-hole. It closely matches the exterior Schwarzschild solution down to about a Planck proper length of the would-be horizon. I will describe interesting features of the 2-2-hole and various physical implications. As a generic static solution, the 2-2-hole may be the nearly black endpoint of gravitational collapse.

Black holes of 1 million to 20 billion solar masses have been found at the centers of galaxies.

New observational data and improved orbit models in the past several years have substantially expanded the sample of black holes with dynamically measured masses.  I will describe recent progress in discovering a new population of ultra-massive black holes and its impact on our understanding of the symbiotic relationships between black holes and galaxies.  I will discuss the implications for the ongoing pulsar timing array experiments searching for nano-Hertz gravitational waves from merging supermassive black hole binaries.

The modeling of pulsar radio and gamma-ray emission suggests that in order to interpret the observations one needs to understand the field geometry and the plasma state in the emission region. In recent years, significant progress has been achieved in understanding the magnetospheric structure in the limit of abundant plasma supply. However, the very presence of dense plasma everywhere in the magnetosphere is not obvious. Even the region where the observed emission is produced is subject to debate. To address this from first principles, we constructed global kinetic simulations of pulsar magnetospheres using relativistic Particle-in-Cell codes, which capture the physics of plasma production and particle acceleration. In this talk I will describe how plasma is produced in magnetospheres of pulsars. I will present modeling of high-energy lightcurves, calculated self-consistently from particle motion in the pulsar magnetosphere. I will also show evidence that observed radio emission is powered by non-stationary discharge at the polar cap.

Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we develop a threshold theorem for quantum supremacy with noisy quantum circuits in the pre-threshold region, where quantum error correction does not work directly. By using the postselection argument, we show that the output sampled from the noisy quantum circuits cannot be simulated efficiently by classical computers based on a stable complexity theoretical conjecture, i.e., non-collapse of the polynomial hierarchy. By applying this to fault-tolerant quantum computation with the surface codes, we obtain the threshold value 2.84% for quantum supremacy, which is much higher than the standard threshold 0.75% for universal fault-tolerant quantum computation with the same circuit-level noise model. Moreover, contrast to the standard noise threshold, the origin of quantum supremacy in noisy quantum circuits is quite clear; the threshold is determined purely by the threshold of magic state distillation, which is essential to gain a quantum advantage.

Conformal Field Theory (CFT) describes the long-distance
dynamics of numerous quantum and statistical many-body systems. The
long-distance limit of a many-body system is often so complicated that
it is hard to do precise calculations. However, powerful new
techniques for understanding CFTs have emerged in the last few years,
based on the idea of the Conformal Bootstrap. I will explain how the
Bootstrap lets us calculate critical exponents in the 3d Ising Model
to world-record precision, how it explains striking relations between
magnets and boiling water, and how it can be applied to questions
across theoretical physics.

The moduli space of vacua of 3d N=4 gauge theories splits essentially into two ``branches”: the Higgs branch parametrised by the vevs of hypermultiplet scalars and the Coulomb branch parametrised by the vevs of dressed monopole operators. They can be described as complex algebraic varieties. I will present a new approach to the analysis of the Higgs and Coulomb branches based on the type IIB brane realisation of the gauge theory. Focusing on abelian theories, I will show how the addition of new ingredients in the brane setup can be linked to the path integral insertions of Higgs or Coulomb operators. I will explain how this construction can be used to derive the ring relations and study mirror symmetry.

Positive representations are infinite-dimensional bimodules for the quantum group and its modular dual where both act by positive essentially self-adjoint operators. Fifteen years ago Ponsot and Teschner showed that positive representations are closed under taking tensor products in the case g = sl(2), however similar conjecture remains open for all other types. I will outline its proof for g = sl(n) based on a joint work in progress with Gus Schrader. I will also argue that this conjecture is the key step towards the proof of the modular functor conjecture for quantized higher Teichmuller theories.