Related papers: Colored discrete spaces: higher dimensional combin…
The combinatorial characterization of generic rigidity for bar-joint frameworks in dimensions $d \ge 3$ has been a long-standing open problem in discrete geometry. While the two-dimensional case was resolved in 1927 by Pollaczek-Geiringer…
The central topic of this thesis is two dimensional Quantum Gravity and its properties. The term Quantum Gravity itself is ambiguous as there are many proposals for its correct formulation and none of them have been verified experimentally.…
In this thesis, we focus on higher-curvature extensions of Einstein gravity as toy models to probe universal properties of conformal field theory (CFT) using the gauge/gravity duality. In this context, we are particularly interested in…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is…
We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a…
I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are…
Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions…
We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, which naturally leads to a notion of vanishing mean curvature…
We show that the quantization ambiguities of loop quantum cosmology, when considered in wider generality, can be used to produce discretionary dynamical behavior. There is an infinite dimensional space of ambiguities which parallels the…
In this talk we review the work in [1,2,3] where we have studied the applicability of the color-kinematics duality to the scattering of two distinguishable scalar matter particles with one gluon emission in QCD, or one graviton emission in…
Solvable theories of 2D dilaton gravity can be obtained from a Liouville theory by suitable field redefinitions. In this paper we propose a new framework to generate 2D dilaton gravity models which can also be exactly solved in the…
Vacuum quasi-topological gravity with infinitely many terms in the action satisfies Markov's limiting curvature hypothesis: the spherically symmetric solutions are regular and all curvature invariants are bounded by solution-independent…
We construct and study general static, spherically symmetric, magnetically charged solutions in Einstein-Maxwell-dilaton gravity in four dimensions. That is, taking Einstein gravity coupled to a ${\rm U}(1)$ gauge field and a massless…
We study quantum gravity in $2+\epsilon$ dimensions in such a way to preserve the volume preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the…
We show that, in four-dimensional spacetimes with an arbitrary Einstein metric, with and without a cosmological constant, perturbative dynamical degrees of freedom in generic quadratic-curvature gravity can be decoupled into massless and…
We present a simple holographic QCD model that provides a unified description of vector mesons and nucleons in a confining background based on Einstein-dilaton gravity. For the confining background we consider analytical solutions of the…
We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of discrete geometries: it computes the…
We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is…
We consider discretized gravity in six dimensions, where the two extra dimensions have been compactified on a hyperbolic disk of constant curvature. We analyze different realizations of lattice gravity on the disk at the level of an…