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Formamidinium-lead-iodide (FAPbI$_3$) has established itself as the state of the art for high solar-energy conversion efficiency in perovskite-based solar cells. At room temperature, FAPbI$_3$ has a peculiar crystal structure with tetragonal symmetry where the PbI$_6$ framework is distorted from the perfect cubic structure, while the FA molecules are randomly rotated. This is well known experimentally, but the theory is still deficient in describing FAPbI$_3$ with appropriate models in which the system size is adequately taken into account. Using ab initio molecular dynamics at 300 K and first-principle calculations, we prove that, in order to obtain a proper description of the system, three factors must be satisfied simultaneously: the band gap, the minimization of structural distortion, and the zeroing out of the dipole moment. We show that the net dipole moment zeroes out as the system size increases due to PbI6 octahedra distortions rather than FA rotations. We also show that the band gap oscillations in temperature are correlated to octahedra tilting. The optimum between simulations and experimental properties indicates that FAPbI$_3$ is properly described by a system size approaching the nano-scale., Comment: 10 pages, Supplementary Information

We predict that in InAs/GaSb nanowires with an inverted band alignment a transverse electric field induces a collapse of the hybridization gap, and a semimetal phase occurs. We use a self-consistent k.p approach and an adapted Bernevig-Hughes-Zhang model to show that massless Dirac points result from exact cancellation between the kinetic electron-hole coupling and the field-controlled spin-orbit coupling. End states - mid-gap states localized at the extremes of a finite nanowire - are supported up to a critical field, but suddenly fade away as the system is driven through the semimetal phase, eventually evolving to trivial surface states, which expose a spin-orbit induced topological transition to the normal phase., Comment: 18 pages, includes Supplementary Information

Introduction. Here we reported the virological, entomological and epidemiological characteristics of the large autochthonous outbreak of dengue (DENV) occurred in a small village of the Lombardy region (Northern Italy) during summer 2023. Methods. After the diagnosis of the first autochthonous case on 18 August 2023, public health measures, including epidemiological investigation and vector control measures, were carried out. A serological screening for DENV antibodies detection was offered to the population. In the case of positive DENV IgM, a second sample was collected to detect DENV RNA and verify seroconversion. Entomological and epidemiological investigations were also performed. A modeling analysis was conducted to estimate the dengue generation time, transmission potential, distance of transmission, and assess diagnostic delays. Results. Overall, 416 subjects participated to the screening program and 20 were identified as DENV-1 cases (15 confirmed and 5 probable). In addition, DENV-1 infection was diagnosed in 24 symptomatic subjects referred to the local Emergency Room Department for suggestive symptoms and 1 case was identified through blood donation screening. The average generation time was estimated to be 18.3 days (95% CI: 13.1-23.5 days). R0 was estimated at 1.31 (95% CI: 0.76-1.98); 90% of transmission occurred within 500m. Entomological investigations performed in 46 pools of mosquitoes revealed the presence of only one positive pool for DENV-1. Discussion. This report highlights the importance of synergic surveillance, including virological, entomological and public health measures to control the spread of arboviral infections.

Full-shell hybrid nanowires (NWs), structures comprising a superconductor shell that encapsulates a semiconductor (SM) core, have attracted considerable attention in the search for Majorana zero modes (MZMs). However, the predicted Rashba spin-orbit coupling (SOC) in the SM is too small to achieve substantial topological minigaps. In addition, the SM wavefunction spreads all across the section of the nanowire, leading typically to a finite background of trivial subgap states with which MZMs may coexist. To overcome both problems, we explore the advantages of utilizing core-shell hole-band NWs as the SM part of a full-shell hybrid, with an insulating core and an active SM shell. In particular, we consider InP/GaSb core-shell NWs, which allow to exploit the unique characteristics of the III-V compound SM valence bands. We demonstrate that they exhibit a robust hole SOC that emerges from the combination of the intrinsic spin-orbit interaction of the SM active shell and the confinement effects of the nanostructure, thus depending mainly on SM and geometrical parameters. In other words, the SOC is intrinsic and does not rely on neither electric fields, which are non-tunable in a full-shell hybrid geometry, nor on the strain at the interface, contrary to what happens in Ge/Si heterostructures. As a result, core-shell SM hole-band NWs are found to be a promising candidate to explore Majorana physics in full-hell hybrid devices, addressing several challenges in the field., Comment: 30 pages, 4 figures; Resubmission to SciPost with minor changes

Full-shell nanowires have been proposed as an alternative nanowire design in the search of topological superconductivity and Majorana zero modes (MZMs). They are hybrid nanostructures consisting of a semiconductor core fully covered by a thin superconductor shell and subject to a magnetic flux. In this work we critically examine this proposal, finding a very rich spectral phenomenology that combines the Little-Parks modulation of the parent-gap superconductor with flux, the presence of flux-dispersing Caroli-de Gennes-Matricon (CdGM) analog subgap states, and the emergence of MZMs across finite flux intervals that depend on the transverse wavefunction profile of the charge density in the core section. Through microscopic simulations and analytical derivations, we study different regimes for the semiconductor core, ranging from the hollow-core approximation, to the tubular-core nanowire appropriate for a semiconductor tube with an insulating core, to the solid-core nanowire. We compute the phase diagrams for the different models in cylindrical nanowires and find that MZMs typically coexist with CdGM analogs at zero energy, rendering them gapless. However, we also find topologically protected parameter regions, or islands, with gapped MZMs. In this sense, the most promising candidate to obtain topologically protected MZMs in a full-shell geometry is the nanowire with a tubular-shaped core. Moving beyond pristine nanowires, we study the effect of mode mixing perturbations. Strikingly, mode mixing can act like a topological $p$-wave pairing between particle-hole Bogoliubov partners, and is therefore able to create new topologically protected MZMs in regions of the phase diagram that were originally trivial. As a result, the phase diagram is utterly transformed and exhibits protected MZMs in around half of the parameter space., Comment: 28 pages, 13 figures. Final version

We introduce a notion of \emph{infinitesimal derived foliation}. We prove it is related to the classical notion of infinitesimal cohomology, and satisfies some formal integrability properties. We also provide some hints on how infinitesimal derived foliations compare to our previous notion of derived foliations., Comment: 19 pages

We study integrability results for derived foliations in the holomorphic context. We prove a global integrability theorem by flat groupoids, as well as global algebraic integrability in the presence of a compact leaf with finite holonomy groups. These results are generalization to the derived (and thus singular) setting of well know results and constructions: integration of holomorphic foliations by smooth groupoid and global stability in the holomorphic situation., Comment: 33 Pages. Future chapter of a book project

In this paper we define and study a generalization of the Belinson-Drinfeld Grassmannian to the case where the curve is replaced by a smooth projective surface $X$, and the trivialization data are given on loci suitably associated to a nonlinear flag of closed subschemes. In order to do this, we first establish some general formal gluing results for moduli of almost perfect complexes, perfect complexes and torsors. We then construct a simplicial object $Fl_X$ of flags of closed subschemes of a smooth projective surface $X$, naturally associated to the operation of taking union of flags. We prove that this simplicial object has the 2-Segal property. For an affine complex algebraic group $G$, we finally define a derived, flag analog $Gr_X$ of the Beilinson-Drinfeld Grassmannian of $G$-bundles on the surface $X$, and show that most of the properties of the Beilinson-Drinfeld Grassmannian for curves can be extended to our flag generalization. In particular, we prove a factorization formula, the existence of a canonical flat connection, and define a chiral product on suitable sheaves on $Fl_X$ and on $Gr_X$. We also sketch the construction of actions of flags analogs of the loop group and of the positive loop group on $Gr_X$. To fixed ``large'' flags on $X$, we associate ``exotic'' derived structures on the classical stack of $G$-bundles on $X$. Analogs of the flag Grassmannian for other Perf-local stacks (replacing the stack of $G$-bundles) are briefly considered, and flag factorization is proved for them, too., Comment: Completely re-written and extended to the context derived algebraic geometry. Several new results and constructions added (e.g. flag chiral structures, exotic derived structures on the classical stack of G-bundles). 71 pages

This paper is part of an ongoing series of works on the study of foliations on algebraic varieties via derived algebraic geometry. We focus here on the specific case of globally defined vector fields and the global behaviour of their algebraic integral curves. For a smooth and proper variety $X$ with a global vector field $\nu$, we consider the induced vector field $\nu_{g,n}$ on the derived stack of stable maps, of genus $g$ with $n$ marked points, to $X$. When $(g,n)$ is either $(0,2)$ or $(1,0)$, the derived stack of zeros of $\nu_{g,n}$ defines a proper \emph{moduli of algebraic trajectories} of $\nu$. When $(g,n)=(0,2)$ algebraic trajectories behave very much like rational algebraic paths from one zero of $\nu$ to another, and in particular they can be composed. This composition is represented by the usual gluing maps in Gromov-Witten theory, and we use it give three categorical constructions, of different categorical levels, related, in a certain sense, by decategorification. In order to do this, in particular, we have to deal with virtual fundamental classes of non-quasi-smooth derived stacks. When $(g,n)=(1,0)$, zeros of $\nu_{1,0}$ might be thought as algebraic analogues of periodic orbits of vector fields on smooth real manifolds. In particular, we propose a Zeta function counting the zeros of $\nu_{1,0}$, that we like to think of as an algebraic version of Ruelle's dynamical Zeta function. We conclude the paper with a brief indication on how to extend these results to the case of general one dimensional foliation $F$, by considering the derived stack of $F$-equivariant stable maps., Comment: 35 pages

We investigate the electronic band structure of modulation-doped GaAs/AlGaAs core-shell nanowires for both n- and p-doping. We developed an 8-band Burt-Foreman k.p Hamiltonian approach to describe coupled conduction and valence bands in heterostructured nanowires of arbitrary composition, growth directions, and doping. Coulomb interactions with the electron/hole gas are taken into account within a mean-field self-consistent approach. We map the ensuing multi-band envelope function and Poisson equations to optimized, non-uniform real-space grids by the finite element method. Self-consistent charge density, single-particle subbands, density of states and absorption spectra are obtained at different doping regimes. For n-doped samples, the large restructuring of the electron gas for increasing doping results in the formation of quasi-1D electron channels at the core-shell interface. Strong heavy-hole/light-hole coupling of hole states leads to non parabolic dispersions with mass inversion, similarly to planar structures, which persist at large dopings, giving rise to direct LH and indirect HH gaps. In p-doped samples the hole gas forms an almost isotropic, ring-like cloud for a large range of doping. Here, as a result of the increasing localization, HH and LH states uncouple, and mass inversion takes place at a threshold density. A similar evolution is obtained at fixed doping as a function of temperature. We show that signatures of the evolution of the band structure can be singled out in the anisotropy of linearly polarized optical absorption., Comment: 20 pages, 13 figures, double column; updated captions, corrected typos

Clocked Cubical Type Theory is a new type theory combining the power of guarded recursion with univalence and higher inductive types (HITs). This type theory can be used as a metalanguage for synthetic guarded domain theory in which one can solve guarded recursive type equations, also with negative variable occurrences, and use these to construct models for reasoning about programming languages. Combining this with HITs allows for the use of type constructors familiar from set-theory based approaches to semantics, such as quotients and finite powersets in these models. In this paper we show how to reason about the combination of finite non-determinism and recursion in this type theory. Unlike traditional domain theory which takes an ordering of programs as primitive, synthetic guarded domain theory takes the notion of computation step as primitive in the form of a modal operator. We use this extra intensional information to define two guarded recursive (finite) powerdomain constructions differing in the way non-determinism interacts with the computation steps. As an example application of these we show how to prove applicative similarity a congruence in the cases of may- and must-convergence for the untyped lambda calculus with finite non-determinism. Such results are usually proved using operational reasoning and Howe's method. Here we use an adaptation of a denotational method developed by Pitts in the context of domain theory., Comment: In Proceedings MFPS 2021, arXiv:2112.13746

Guarded recursion is a powerful modal approach to recursion that can be seen as an abstract form of step-indexing. It is currently used extensively in separation logic to model programming languages with advanced features by solving domain equations also with negative occurrences. In its multi-clocked version, guarded recursion can also be used to program with and reason about coinductive types, encoding the productivity condition required for recursive definitions in types. This paper presents the first type theory combining multi-clocked guarded recursion with the features of Cubical Type Theory, as well as a denotational semantics. Using the combination of Higher Inductive Types (HITs) and guarded recursion allows for simple programming and reasoning about coinductive types that are traditionally hard to represent in type theory, such as the type of finitely branching labelled transition systems. For example, our results imply that bisimilarity for these imply path equality, and so proofs can be transported along bisimilarity proofs. Among our technical contributions is a new principle of induction under clocks. This allows universal quantification over clocks to commute with HITs up to equivalence of types, and is crucial for the encoding of coinductive types. Such commutativity requirements have been formulated for inductive types as axioms in previous type theories with multi-clocked guarded recursion, but our present formulation as an induction principle allows for the formulation of general computation rules., Comment: 29 pages

This is the second of series of papers on the study of foliations in the setting of derived algebraic geometry based on the central notion of derived foliation. We introduce sheaf-like coefficients for derived foliations, called quasi-coherent crystals, and construct a certain sheaf of dg-algebras of differential operators along a given derived foliation, with the property that quasi-coherent crystals can be interpreted as modules over this sheaf of differential operators. We use this interpretation in order to introduce the notion of good filtrations on quasi-coherent crystals, and define the notion of characteristic cycle. Finally, we prove a Grothendieck-Riemann-Roch (GRR) formula expressing that formation of characteristic cycles is compatible with push-forwards along proper and quasi-smooth morphisms. Several examples and applications are deduced from this, e.g. a GRR formula for D-modules on possibly singular schemes, and a foliated index formula for weakly Fredholm operators., Comment: First draft, 40 pages

It is well known that univalence is incompatible with uniqueness of identity proofs (UIP), the axiom that all types are h-sets. This is due to finite h-sets having non-trivial automorphisms as soon as they are not h-propositions. A natural question is then whether univalence restricted to h-propositions is compatible with UIP. We answer this affirmatively by constructing a model where types are elements of a closed universe defined as a higher inductive type in homotopy type theory. This universe has a path constructor for simultaneous "partial" univalent completion, i.e., restricted to h-propositions. More generally, we show that univalence restricted to $(n-1)$-types is consistent with the assumption that all types are $n$-truncated. Moreover we parametrize our construction by a suitably well-behaved container, to abstract from a concrete choice of type formers for the universe., Comment: 21 pages, long version of paper accepted at LICS 2020

This is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and rigid derived foliations on smooth complex algebraic varieties and on their associated formal and analytic versions. Their truncations are classical singular foliations. We prove that a quasi-smooth rigid derived foliation on a smooth complex variety $X$ is formally integrable at any point, and, if we suppose that its singular locus has codimension $\geq 2$, then the truncation of its analytification is a locally integrable singular foliation on the associated complex manifold $X^h$. We then introduce the derived category of perfect crystals on a quasi-smooth rigid derived foliation on $X$, and prove a Riemann-Hilbert correspondence for them when $X$ is proper. We discuss several examples and applications., Comment: Added a few results. Submitted version

We present an $\ell$-adic trace formula for saturated and admissible dg-categories over a base monoidal dg-category. Moreover, we prove K\"unneth formulas for dg-category of singularities, and for inertia-invariant vanishing cycles. As an application, we prove a version of Bloch's Conductor Conjecture (stated by Spencer Bloch in 1985), under the additional hypothesis that the monodromy action of the inertia group is unipotent., Comment: 47 pages, final submitted version

We prove a Hochschild-Kostant-Rosenberg decomposition theorem for smooth proper schemes $X$ in characteristic $p$ when $\dim X\leq p$. The best known previous result of this kind, due to Yekutieli, required $\dim X

This text is based on a talk by the first named author at the first congress of the SMF (Tours, 2016). We present Bloch's conductor formula, which is a conjectural formula describing the change of topology in a family of algebraic varieties when the parameter specialises to a critical value. The main objective of this paper is to describe a general approach to the resolution of Bloch's conjecture based on techniques from both non-commutative geometry and derived geometry., Comment: French, 23 pages, Expos\'e au premier congr\`es de la SMF (Tours, 2016)

In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational equivalence. We also add a few elementary and easy observations on these representation problems that we were not able to locate in the literature., Comment: Notes for students, 7 pages

This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning with coinductive types. We wish to implement GDTT with decidable type checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\"of type theory in which the identity type is replaced by abstract paths between terms. CTT provides a computational interpretation of functional extensionality, enjoys canonicity for the natural numbers type, and is conjectured to support decidable type-checking. Our new type theory, guarded cubical type theory (GCTT), provides a computational interpretation of extensionality for guarded recursive types. This further expands the foundations of CTT as a basis for formalisation in mathematics and computer science. We present examples to demonstrate the expressivity of our type theory, all of which have been checked using a prototype type-checker implementation. We show that CTT can be given semantics in presheaves on the product of the cube category and a small category with an initial object. We then show that the category of presheaves on the product of the cube category and omega provides semantics for GCTT., Comment: Final version; Special Issue on Homotopy Type Theory and Univalent Foundations, Journal of Automated Reasoning, 2017

In this paper we prove formal glueing along an arbitrary closed substack $Z$ of an arbitrary Artin stack $X$ (locally of finite type over a field $k$), for the stacks of (almost) perfect complexes , and of $G$-bundles on $X$ (for $G$ a smooth affine algebraic $k$-group scheme). By iterating this result, we get a decomposition of these stacks along an arbitrary nonlinear flag of closed substacks in $X$. By taking points over the base field, we deduce from this both a formal glueing, and a flag-related decomposition formula for the corresponding symmetric monoidal derived $\infty$-categories of (almost) perfect modules. When $X$ is a quasi-compact and quasi-separated scheme, we also prove a localization theorem for almost perfect complexes on $X$, which parallels Thomason's localization results for perfect complexes. This is one of the main ingredients we need to provide a global characterization of the category of almost perfect complexes on the punctured formal neighbourhood. We then extend all of the previous results - i.e. the formal glueing and flag-decomposition formulas - to the case when $X$ is a derived Artin stack (locally almost of finite type over a field $k$), for the derived versions of the stacks of (almost) perfect modules, and of $G$-bundles on $X$. We close the paper by highlighting some expected progress in the subject matter of this paper, related to a Geometric Langlands program for higher dimensional varieties. In an Appendix (for $X$ a variety), we give a precise comparison between our formal glueing results and the rigid-analytic approach of Ben-Bassat and Temkin., Comment: Enlarged version, sharpened old results and added new ones

In this paper we establish a precise comparison between vanishing cycles and the singularity category of Landau-Ginzburg models over a complete discrete valuation ring. By using noncommutative motives, we first construct a motivic $\ell$-adic realization functor for dg-categories. Our main result, then asserts that, given a Landau-Ginzburg model over a complete discrete valuation ring with potential induced by a uniformizer, the $\ell$-adic realization of its singularity category is given by the inertia-invariant part of vanishing cohomology. We also prove a functorial and $\infty$-categorical version of Orlov's comparison theorem between the derived category of singularities and the derived category of matrix factorizations for a Landau-Ginzburg model over a noetherian regular local ring., Comment: Appeared in Journal de l'\'Ecole Polytechnique 5 (2018), p. 651-747

This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning with coinductive types. We wish to implement GDTT with decidable type-checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\"of type theory in which the identity type is replaced by abstract paths between terms. CTT provides a computational interpretation of functional extensionality, is conjectured to have decidable type checking, and has an implemented type-checker. Our new type theory, called guarded cubical type theory, provides a computational interpretation of extensionality for guarded recursive types. This further expands the foundations of CTT as a basis for formalisation in mathematics and computer science. We present examples to demonstrate the expressivity of our type theory, all of which have been checked using a prototype type-checker implementation, and present semantics in a presheaf category., Comment: 17 pages, to be published in proceedings of CSL 2016

Building on recent results by A. Blanc, M. Robalo and the authors, we present an $\ell$-adic trace formula for smooth and proper dg-categories over a base $\mathbb{E}_{\infty}$-algebra $B$. We also give a variant when $B$ is only an $\mathbb{E}_2$-algebra. As an application of this trace formula, we propose a strategy of proof of Bloch's conductor conjecture. This is a research announcement and detailed proofs will appear elsewhere., Comment: Research announcement; 15 pages

We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such spaces., Comment: Notes written for the proceedings of the AMS summer institute, University of Utah, Salt Lake City 2015. 38 pages

The technologies of heating, photovoltaics, water photocatalysis and artificial photosynthesis depend on the absorption of light and novel approaches such as coherent absorption from a standing wave promise total dissipation of energy. Extending the control of absorption down to very low light levels and eventually to the single photon regime is of great interest yet remains largely unexplored. Here we demonstrate the coherent absorption of single photons in a deeply sub-wavelength 50% absorber. We show that while absorption of photons from a travelling wave is probabilistic, standing wave absorption can be observed deterministically, with nearly unitary probability of coupling a photon into a mode of the material, e.g. a localised plasmon when this is a metamaterial excited at the plasmon resonance. These results bring a better understanding of the coherent absorption process, which is of central importance for light harvesting, detection, sensing and photonic data processing applications., Comment: 13 pages, 5 figures, Published in Nature Communications: 10.1038/ncomms8031

In homotopy type theory, the truncation operator ||-||n (for a number n > -2) is often useful if one does not care about the higher structure of a type and wants to avoid coherence problems. However, its elimination principle only allows to eliminate into n-types, which makes it hard to construct functions ||A||n -> B if B is not an n-type. This makes it desirable to derive more powerful elimination theorems. We show a first general result: If B is an (n+1)-type, then functions ||A||n -> B correspond exactly to functions A -> B which are constant on all (n+1)-st loop spaces. We give one "elementary" proof and one proof that uses a higher inductive type, both of which require some effort. As a sample application of our result, we show that we can construct "set-based" representations of 1-types, as long as they have "braided" loop spaces. The main result with one of its proofs and the application have been formalised in Agda., Comment: 15 pages; to appear at CSL'15

This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector fields. We then introduce the formalism of formal derived stacks and prove formal localization and gluing results. These allow us to define shifted Poisson structures on general derived Artin stacks, and prove that the non-degenerate Poisson structures correspond exactly to shifted symplectic forms. Shifted deformation quantization for a derived Artin stack endowed with a shifted Poisson structure is discussed in the last section. This paves the way for shifted deformation quantization of many interesting derived moduli spaces, like those studied in [PTVV] and probably many others., Comment: 111 pages. Minor changes, to appear in Journal of Topology