While island biogeography focuses on species richness equilibrium driven by immigration and extinction, and metapopulation theory examines single-species dynamics across fragmented habitats, their interplay remains poorly understood. In particular, the species-area relationship remains a subject of ongoing debate, yet there are limited theoretical foundations to explain it. To address this, we developed a multiscale stochastic metapopulation model to investigate diversity patterns on islands, bridging the gap between island biogeography and metapopulation theory. Our model integrates regional colonization from a mainland with local colonization-extinction processes within islands at the single-species level, then extends this to multiple, independent species. By analyzing the stationary properties of this model, we generate novel predictions of Species Area Relationship (SAR) based on local extinction rates, within-island colonization rates, and mainland immigration rates. We demonstrate how the interplay of these parameters influences the relationship, predicting patterns that can resemble either the power-law of Arrhenius or the semi-logarithmic relationship of Gleason, depending on the relative importance of mainland immigration versus within-island dynamics, and on the nature of the species abundance distribution in the mainland. This unified framework offers new insights into the mechanisms driving species richness and distribution across spatial scales, providing a more holistic understanding of biodiversity patterns in fragmented landscapes.

We discuss recent improvements of the cold and dense QCD pressure owing to an all-order resummation of the soft modes, or to the so-called renormalization group optimized perturbation theory (RGOPT). Both approaches show a significant improvement of the residual renormalization scale dependence with respect to the state-of-the-art results for the perturbative pressure.

Stacking 2D materials into van der Waals heterostructures implies the emergence of interlayer interactions, modifying electronic scattering in a given layer. We develop an efficient ab initio approach to compute the electrodynamic response of 2D heterostructures, including long range Coulomb interactions between electrons, polar phonons, and plasmons. We extract electron scattering from this model and solve a system of coupled Boltzmann transport equations for electrons and electrodynamic modes. This accounts for non-trivial momentum exchanges such as the so-called phonon drag. We study the effects of remote electron-plasmon-phonon couplings on the electronic transport properties of 2D materials. We also show that a dynamical treatment of electronic screening has a significant impact on the mobility of doped semiconductors with a Fermi level around the band edge. Indeed, polar phonons dynamically coupled with electron-hole excitations scatter momentum differently than the standard polar phonons, whether bare or statically screened.

Superconductivity in few-layer semiconducting transition-metal dichalcogenides (TMDs) can be induced by field-effect doping through ionic-liquid gating. While several experimental observations have been collected over the years, a fully consistent theoretical picture is still missing. Here we develop a realistic framework that combines the predictive power of first-principles simulations with the versatility and insight of Bardeen-Cooper-Schrieffer gap equations to rationalize such experiments. The multivalley nature of semiconducting TMDs is taken into account, together with the doping- and momentum-dependent electron-phonon and Coulomb interactions. Consistently with experiments, we find that superconductivity occurs when the electron density is large enough that the Q valleys get occupied, as a result of a large enhancement of electron-phonon interactions. Despite being phonon driven, the superconducting state is predicted to be sensitive to Coulomb interactions, which can lead to the appearance of a relative sign difference between valleys and thus to a s + − character. We discuss qualitatively how such scenario may account for many of the observed physical phenomena for which no microscopic explanation has been found so far, including in particular the presence of a large subgap density of states, and the sample-dependent dome-shaped dependence of T c on accumulated electron density. Our results provide a comprehensive analysis of gate-induced superconductivity in semiconducting TMDs, and introduce an approach that will likely be valuable for other multivalley electronic systems, in which superconductivity occurs at relatively low electron density.

2D materials have shown fascinating fundamental physics and exciting technological prospects. Many applications rely on the ability to conduct electrons efficiently. At room temperature, this is mostly limited by the scattering of electrons by phonons. A clear understanding of transport mechanisms, along with predictive ab initio simulations, are then key to design performant and energy-efficient devices.The prototypical 2D transport setup is an electrostatically-doped semiconducting layer encapsulated by a dielectric material. We will discuss 3 major challenges to model electron-phonon scattering in this system: dimensionality, electrostatic doping and interlayer couplings. The first 2 concern the proper simulation of electron-phonon interactions in single 2D layers. The third one accounts for the additional scattering mechanisms between layers in van der Waals heterostructures. Combining solutions to all 3 challenges paves the way towards a full description of electron-phonon scattering and electronic transport in 2D heterostructures.Reduced dimensionality has strong, universal impact on all materials, notably via changes in the long wavelength behaviour of the Fröhlich interaction. Electrostatic doping refers the ubiquitous use of field effects to induce charges in 2D materials and tune their Fermi level. The added carriers screen electron-phonon scattering. We will see how to include this effect in doped semiconductors. Usually, it tends to decrease scattering, but we will also discuss a counter-intuitive enhancement mechanism in multi-valley materials like transition-metal dichalcogenides. Interlayer couplings refers the remote interactions between electrons and phonons in different layers. They are very too costly to simulate directly in first-principles codes due to the size of the associated supercells. We will discuss a newly developed model to compute long-range Coulomb interactions between electrons and polar excitations including phonons and plasmons in van der Waals heterostructures, at a reasonable relatively negligible computational cost.

BPS indices encoding the entropy of supersymmetric black holes in compactifications of Type II string theory on Calabi-Yau threefolds, known in mathematics as generalized Donaldson-Thomas invariants, possess remarkable (mock) modular properties. I'll explain the physical origin of mock modularity and show, for a set of one-parameter threefolds, how it can be used, together with wall-crossing and direct integration of topological string, to compute the BPS indices and other topological invariants. As a result, one obtains explicit (mock) modular functions encoding infinite sets of D4-D2-D0 BPS indices as well as new boundary conditions for the holomorphic anomaly equation of the topological string partition function allowing to overcome the limitations of the direct integration method. In the end, I'll present preliminary results on the asymptotic growth of DT invariants hinting for the existence of some phase transitions.