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Let G be a split semi-simple algebraic group over Q. We introduce a natural cluster structure on moduli spaces of G-local systems over surfaces with marked points. As a consequence, the moduli spaces of G-local systems admit natural Poisson structures, and can be further quantized. We will study the principal series representations of such quantum spaces. It will recover many classical topics, such as the q-deformed Toda systems, quantum groups, as well as the modular functor conjecture for such representations, which should lead to new quantum invariants of threefolds. This talk will mainly be based on joint work with A.B. Goncharov.

We derive Schwarzian correlation functions using the BF formulation of Jackiw-Teitelboim gravity, where bilocal operators are interpreted as boundary-anchored Wilson lines in the bulk. Crossing Wilson lines are associated with OTO-correlators and give rise to 6j-symbols. We discuss the semi-classical bulk black hole physics contained within the correlation functions.

Extensions including bulk defects related to the other coadjoint orbits are discussed.

How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, preads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements' possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields - quantum information, condensed matter, and high-energy physics - can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots. 

NYH, Bartolotta, and Pollack, accepted by Comms. Phys. (in press) arXiv:1806.04147.

Computing vacuum expectation values is paramount in studying Quantum Field Theories (QFTs) since they provide relevant information for comparing the underlying theory with experimental results. However, unless the ground state of the system is explicitly known, such computations are very difficult and Monte Carlo simulations generally run months to years on state-of-the-art high performance computers. Additionally, there are various physically interesting situations, in which most numerical methods currently in use are not applicable at all (e.g., the early universe or setting requiring Lorentzian backgrounds). Thus, new algorithms are required to address such problems in QFT. In recent joint work with K. Jansen (NIC, DESY Zeuthen), I have shown that zeta-functions of Fourier integral operators can be applied to regularize vacuum expectation values with Euclidean and Lorentzian backgrounds and that these zeta-regularized vacuum expectation values are in fact physically meaningful. In order to prove physicality, we introduced a discretization scheme which is accessible on a quantum computer. Using this discretization scheme, we can efficiently approximate ground states on a quantum device and henceforth compute vacuum expectation values. Furthermore, the Fourier integral operator $\zeta$-function approach is applicable to Lattice formulations in Lorentzian background.