https://neckpinch.com/authors/davide-de-biasio/New arXiv papers by Davide De Biasio, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2307.08320arxiv:2307.08320Mon, 17 Jul 2023 00:00:00 GMTDavide De Biasio — After an introductory chapter on the quantum supersymmetric string, in which particular attention will be devoted to the techniques via which phenomenologically viable models can be obtained from the ultraviolet microscopic degrees of freedom, and a brief review of the swampland program, the technical tools required to deal with geometric flows will be outlined. The evolution of a broad family of scalar and metric bubble solutions under Perelman's combined flow will be then discussed, together with their asymptotic behaviour. Thereafter, the geometric flow equations associated to a generalised version of Perelman's entropy function will be derived and employed in defining the action-induced flow associated to a given theory for a scalar field and a dynamical metric. The problem of preserving Einstein field equations along the corresponding moduli space trajectories will be cured by allowing a supplementary energy-momentum tensor term to appear along the flow. In a particular example, such contribution will be shown to precisely reproduce the infinite tower of states with exponentially dropping masses postulated by the distance conjecture.Perelman entropyPhysics https://arxiv.org/abs/2211.04231arxiv:2211.04231Tue, 08 Nov 2022 00:00:00 GMTDavide De Biasio — In this work, the problem of constructing geometric flow equations that preserve Einstein field equations for the spacetime metric is addressed. After having briefly discussed the main features of Ricci flow, the on-shell flow equations for a system comprised of a dynamical metric and a set of matter fields are constructed. Then, two examples in which the matter content is just a single, self-interacting scalar field are analysed in detail, imposing the geometric flow equations to be the action-induced ones. In conclusion, an explicit connection to the Swampland Distance Conjecture is proposed.Ricci flowPhysics https://arxiv.org/abs/2210.14705arxiv:2210.14705Wed, 26 Oct 2022 00:00:00 GMTDavide De Biasio, Julian Freigang, Dieter Lust, Toby Wiseman — Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we consider the analog for the Einstein-Maxwell action, which gives Ricci flow with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell field. We argue that this flow is well-posed for static spacetimes with pure electric or magnetic potentialsand show it preserves both non-extremal and extremal black hole horizons. In the latter case we find the flow of the near horizon geometry decouples from that of the exterior. The Schwarzschild black hole is an unstable fixed point of Ricci flow for static spacetimes. Here we consider flows of the Reissner-Nordström (RN) fixed point. The magnetic RN solution becomes a stable fixed point of the flow for sufficient charge. However we find that the electric RN black hole is always unstable. Numerically solving the flow starting with a spherically symmetric perturbation of a non-extremal RN solution, we find similar behaviour in the electric case to the Ricci flows of perturbed Schwarzschild, namely the horizon shrinks to a singularity in finite time or expands forever. In the magnetic case, a perturbed unstable RN solution has a similar expanding behaviour, but a perturbation that decreases the horizon size flows to a stable black hole solution rather than a singularity. For extremal RN we solve the near horizon flow for spherical symmetry exactly, and see in the electric case two unstable directions which flow to singularities in finite flow time. However, even turning these off, and fixing the near horizon geometry to be that of RN, we numerically show that the flows appear to become singular in the vicinity of its horizon.Ricci flowSingularitiesStability & uniquenessRotational symmetry & warped productsPhysicsNumerics & visualization https://arxiv.org/abs/2209.10297arxiv:2209.10297Wed, 21 Sep 2022 00:00:00 GMTDavid Martín Velázquez, Davide De Biasio, Dieter Lust — In the following work, an attempt to conciliate the Ricci flow conjecture and the Cobordism conjecture, stated as refinements of the Swampland distance conjecture and of the No global symmetries conjecture respectively, is presented. This is done by starting from a suitable manifold with trivial cobordism class, applying surgery techniques to Ricci flow singularities and trivialising the cobordism class of one of the resulting connected components via the introduction of appropriate defects. The specific example of Ω^(SO)₄ is studied in detail. A connection between the process of blowing up a point of a manifold and that of taking the connected sum of such with ℂP}ⁿ is explored. Hence, the problem of studying the Ricci flow of a K3 whose cobordism class is trivialised by the addition of 16 copies of ℂP}² is tackled by applying both the techniques developed in the previous sections and the classification of singularities in terms of ADE groups.Ricci flowSingularitiesSurgery