Talks

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.

I will explain how cosmological dynamics emerge from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

The first detections of gravitational waves by LIGO-Virgo initiated the era of Gravitation-Wave Astronomy. Gravitational-waves serve as a new and independent probe of the Universe. In addition, the combination of gravitational-waves with information from other messengers, such as electromagnetic emission from the same source, will lead to a more complete and accurate understanding of cosmology and astrophysics. In this talk, I will discuss some interesting learnings from the Advanced LIGO-Virgo first observing run and several scientific goals we expect to reach in the next few years.