Talks

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.

Topological states of matter are of of fundamental interest in contemporate condensed matter physics. Today, the fractional Quantum Hall effect remains the only known experimental system expected to exhibit intrinsic topological order. The question remains whether also different systems might stabilize this kind of ordering. Chiral spin liquids are an analogue of Fractional Quantum Hall Effect wave functions for spin systems. These wavefunctions have been envisioned in 1987 but only very recently several simple frustrated quantum spin models have been proposed realizing this physics. In this talk we will introduce chiral spin liquids, discuss their relation to the Fractional Quantum Hall effect and present our recent numerical studies that provide conclusive evidence for the emergence of this exotic state of matter in extended frustrated Heisenberg models. In the course of these projects novel algorithms and techniques for large scale Exact Diagonalization were developed and applied. We briefly discuss these techniques and show that they allow for sparse diagonalizations of Heisenberg systems up to 48-50 spin-1/2 particles.