Abstract:
In some models of quantum-gravity-inspired quantum spacetimes, relativistic symmetries are modified (deformed or broken) at the Planck scale, so that spacetime itself might behave like a dispersive medium for particle propagation (in-vacuo dispersion). The long (cosmological) distance traveled by ultra-relativistic particles emitted by transient astrophysical sources could provide a huge source of amplification for the tiny (Planckian) effects, offering a precious opportunity for experimental tests. I present a brief introduction to these phenomenological studies, with particular attention to scenarios based on k-Minkowski/k-Poincaré noncommutative spacetime, and discuss some recent results concerning tests of in-vacuo dispersion in the observation of gamma-ray-bursts photons and (IceCube) astrophysical neutrinos

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Though a full description of black hole radiation may require quantum gravity, many analyses of BH evaporation still involve, either implicitly or explicitly, key assumptions about some classical BH spacetime, often expressed in the form of (Penrose) spacetime diagrams. In this talk we discuss how such diagrams can be exactly generated for specific models - providing detailed depictions of both local and global structure - and ask what can be learned by doing so. We compare naive models to those approximating a semiclassical back reaction, as well as comparing singular and curvature-regulated models. We then consider implications for various unitarity questions including long term and Page time unitarity, and identify some open questions for further discussion.

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I will present a proposal for a rigorous construction of the scattering matrix in perturbative relativistic quantum electrodynamics. The construction uses adiabatic switching of the interaction and is inspired by ideas from the modified scattering theory in quantum mechanics. The constructed scattering matrix is defined in the standard Fock space and is translationally invariant as well as gauge invariant. However, the physical interpretation of states in the Fock space and the representation of the group of spacetime translations acting in this space are nonstandard

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We propose a systematic way of exploring phenomena of scalar field theories in (1+1)-dimensions. We call this procedure a `mechanization' -- the field is replaced by fixed number of joints (N) connected by straight edges. As a result, we obtain a sequence of algebraically tractable, general-purpose collective coordinate mechanical models. We observe step-by-step emergence of dynamical objects and associated phenomena as N increases. Mech-kinks and mech-oscillons -- mechanical analogs of kinks and oscillons (bions) -- appear in the simplest models, while more intricate dynamical patterns, such as bouncing phenomenon and bion pair-production, emerge gradually as decay states of high-N mech-oscillons.

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Pauli stabilizer models are many body quantum systems whose ground states are described by eigenequations for a set of mutually commuting clock and shift operators. They have been considered first as toy models of topological quantum computation. They serve also as particularly tractable examples of topological order. Mathematical theory of stabilizer models, based on commutative algebra, was developed mostly by J. Haah. I will review this approach and discuss my recent progress with B. Yang: construction of modules of topological charges and braiding for any spatial and qudit dimension.

Abstract:
Pauli stabilizer models are many body quantum systems whose ground states are described by eigenequations for a set of mutually commuting clock and shift operators. They have been considered first as toy models of topological quantum computation. They serve also as particularly tractable examples of topological order. Mathematical theory of stabilizer models, based on commutative algebra, was developed mostly by J. Haah. I will review this approach and discuss my recent progress with B. Yang: construction of modules of topological charges and braiding for any spatial and qudit dimension.

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An approach to FQHE based on the theory of symmetric polynomials in the second quantization is very fruitful. In particular, we can prove the Laughlin's fractionalization relation for quasiholes and derive from it the analogous one for quasiparticles. Out of it, we find the quasielectron wavefunction which significantly differs from the existing proposals, but in contrast to them is not an Anzatz but is derived within this framework. Its form reveals an exact fusion mechanism for particle fractionalization. We support our findings with Monte Carlo simulations. This second-quantized approach also provides an elegant justification for Reed's argument for condensation. Finally, we formulate the hypothesis, complementary to Wen's one, and prove it for certain FQH fluids. This talk is based on joint work with Z. Nussinov, G. Ortiz, and A. Seidel.

Abstract:
Semiclassical Gravity and Quantum Field Theory in Curved Spacetimes describe the propagation of a quantum matter field over classical curved spacetimes. Solutions of the so-called semiclassical Einstein equations, which govern the interplay between matter and geometry in the semiclassical regime, incorporate the backreaction of the quantum field on the background geometry. In this talk, I present some applications of the semiclassical Einstein equations in the framework of Cosmology and Black Hole Physics. In the former case, the proof of existence and uniqueness of local cosmological solutions is reviewed for a free massive scalar field arbitrary coupled with the curvature. In the latter case, the evaporation of spherically symmetric dynamical black holes sourced by the quantum trace anomaly is shown for a free massless, conformally coupled scalar field. Finally, the linear stability of semiclassical theories of gravity with higher-order derivative terms is discussed in a toy model, which mimics the evolution induced by semiclassical Einstein equations in physically relevant backgrounds, such as cosmological spacetimes.