All arithmetic non-compact ball quotients by Deligne-Mostow's unitary monodromy group arise as sub-ball quotients of either of two spaces called ancestral cases, corresponding to Gaussian or Eisenstein Hermitian forms respectively. In a previous paper, we investigated the compactifications of the Gaussian Deligne-Mostow variety. Here we work on the remaining case, namely the ring of Eisenstein integers. This variety is related to the moduli space of unordered 12 points on $\mathbb{P}^1$. In particular, we show that Kirwan's partial resolution of the moduli space is not a semi-toroidal compactification and Deligne-Mostow's period map does not lift to the unique toroidal compactification. We give two interpretations of these phenomena in terms of the log minimal model program and automorphic forms. As an application, we prove that the above two compactifications are not (stacky) derived equivalent, as the $DK$-conjecture predicts. Furthermore, we construct an automorphic form on the moduli space of non-hyperelliptic curves of genus 4, which is isogenous to the Eisenstein Deligne-Mostow variety, giving another intrinsic proof, independent of lattice embeddings, of a result by Casalaina-Martin, Jensen and Laza.

The matching complex $\mathsf{M}(G)$ of a graph $G$ is a simplicial complex whose simplices are matchings in $G$. These complexes appear in various places and found applications in many areas of mathematics including computational geometry, representation theory, combinatorics, etc. In this article, we consider the matching complexes of the categorical product $P_n \times P_m$ of path graphs $P_n$ and $P_m$. For $m = 1$, $P_n \times P_m$ is a discrete graph and therefore its matching complex is the void complex. For $m = 2$, $\M(P_n \times P_m)$ has been proved to be homotopy equivalent to a wedge of spheres by Kozlov. We show that for $n \geq 2$ and $3 \leq m \leq 5$, the matching complex of $P_n \times P_m$ is homotopy equivalent to a wedge of spheres. For $m =3$, we explicitly compute the number and dimension of spheres appearing in the wedge. Furthermore, for $m \in \{4, 5\}$, we provide the minimum and maximum dimensions of spheres appearing in the wedge in the homotopy type of $\mathsf{M}(P_n \times P_m)$.

We introduce the notion of a contractible subshift. This is a strengthening of the notion of strong irreducibility, where we require that the gluings are given by a block map. We show that a subshift is a retract of a full shift if and only if it is a contractible SFT with a fixed point. For many groups, including virtually polycyclic groups, metabelian Baumslag-Solitar groups and the lamplighter group, contractibility implies dense periodic points. We introduce a ``homotopy theory'' framework for working with this notion, and ``contractibility'' is in fact simply an analog of the usual contractibility in algebraic topology. We also explore the symbolic dynamical analogs of homotopy equivalence and strong contractibility of subshifts (corresponding to the notion of equiconnectedness in topology). Contractibility is implied by the map extension property of Meyerovitch, and among SFTs, it implies the finite extension property of Briceño, McGoff and Pavlov. We include thorough comparisons with these classes. We also encounter some new geometric notions, in particular a periodic variant of Gromov's asymptotic dimension of a group.

We analyze the effects of enforcing vs. exempting access ISP from net neutrality regulations when platforms are present and operate two-sided pricing in their business models. This study is conducted in a scenario where users and Content Providers (CPs) have access to the internet by means of their serving ISPs and to a platform that intermediates and matches users and CPs, among other service offerings. Our hypothesis is that platform two-sided pricing interacts in a relevant manner with the access ISP, which may be allowed (an hypothetical non-neutrality scenario) or not (the current neutrality regulation status) to apply two-sided pricing on its service business model. We preliminarily conclude that the platforms are extracting surplus from the CPs under the current net neutrality regime for the ISP, and that the platforms would not be able to do so under the counter-factual situation where the ISPs could apply two-sided prices.

The elusive polarized microwave signal from the Fermi bubbles is disentangled from the more extended polarized lobes, which similarly emanate from the Galactic plane but stretch farther west of the bubbles. The projected ~20% synchrotron polarization reveals magnetic fields preferentially parallel to the bubble edges, as expected downstream of a strong shock. The projected ~20% polarization of thermal dust emission is similarly oriented, constraining grain alignment in an extreme environment. We argue that the larger lobes arise from an older Galactic-center, likely supermassive black-hole, outburst.

In this research, we generalize the transformation of the vacuum state that generated gravitational waves in the early universe which is usually transformed using a two-mode into a three-mode Bogoliubov transformation. Based on the calculation of quantum discord this transformation allows the universe to be classical when the squeezed parameter is large if only of the three possible modes, only two are considered. We also studied the quantum characteristics of those gravitational waves by calculating an observable quantity named the quantum Poincare sphere. The result will be the same as the two-mode transformation, where quantum characteristics appear if the squeezed parameter is greater than zero. However, if the initial state is coherent, different results will be obtained, the quantum Poincare sphere will not depend on the squeezed parameter and will be non-classical if $\cosθ$ or $\sinθ$ is not zero.

We study the construction of a manifestly covariant worldline action from a coadjoint orbit. A coadjoint orbit is a submanifold in the dual vector space of a Lie algebra, generated by coadjoint actions. Since a coadjoint orbit is a symplectic space, we derive the worldline particle action from the symplectic two-form. One subtlety in formulating worldline particle actions from coadjoint orbits is the choice of a coordinate system that clearly illustrates physical properties of the particles. We introduce Hamiltonian constraints derived from the defining conditions of the isometry. This allows us to write a manifestly covariant worldline action. We demonstrate our method for both massive and massless particles in Minkowski and AdS spacetime.

Given a graph $G$ and a partition $P$ of its vertex set, an independent transversal (IT) is an independent set of $G$ that contains one vertex from each block in $P$. Various sufficient conditions for the existence of an IT have been established, and a common theme for many of them is that the block sizes are sufficiently large compared to the maximum degree of $G$. Consequently, there has been interest in constructing graphs with no IT which demonstrate that these bounds on the block sizes are best possible. We describe a simple systematic method for constructing vertex-partitioned graphs with large block sizes and no IT. Unifying previous constructions, we use our method to derive classical extremal constructions due to Jin (1992), Yuster (1997), and Szabó and Tardos (2006) in streamlined fashion. For our new results, we describe extremal constructions of minimal graphs with maximum degree two and no IT, generalizing a result of Aharoni, Holzman, Howard, and Sprüssel (2015). We construct a family of locally sparse graphs with no IT, complementing an asymptotic result of Loh and Sudakov (2007). We describe new and smaller counterexamples to a list coloring conjecture of Reed (1999), which was originally disproved by Bohman and Holzman (2002). We disprove a conjecture of Aharoni, Alon, and Berger (2016) about IT's in graphs without large induced stars. We answer negatively a question of Aharoni, Holzman, Howard, and Sprüssel (2015) about extremal graphs with no IT, but we also prove that a useful variation of their question does hold.

Systematically biased forecasts are typically interpreted as evidence of forecasters' irrationality and/or asymmetric loss. In this paper we propose an alternative explanation: when forecasts inform policy decisions, and the resulting actions affect the realisation of the forecast target itself, forecasts may be optimally biased even under quadratic loss. The result arises in environments in which the forecaster is uncertain about the policymaker's reaction to the forecast, which is presumably the case in most applications. We motivate our theory by reviewing some stylised properties of Greenbook inflation forecasts. Our results point out that the presence of policy feedback poses a challenge to traditional tests of forecast rationality.

We present the unified computational framework for modeling the sulcal patterns of human brain obtained from the magnetic resonance images. The Wasserstein distance is used to align the sulcal patterns nonlinearly. These patterns are topologically different across subjects making the pattern matching a challenge. We work out the mathematical details and develop the gradient descent algorithms for estimating the deformation field. We further quantify the image registration performance. This method is applied in identifying the differences between male and female sulcal patterns.

OpenCitations Meta is a new database for open bibliographic metadata of scholarly publications involved in the citations indexed by the OpenCitations infrastructure, adhering to Open Science principles and published under a CC0 license to promote maximum reuse. It presently incorporates bibliographic metadata for publications recorded in Crossref, DataCite and PubMed, making it the largest bibliographic metadata source using Semantic Web technologies. It assigns new globally persistent identifiers (PIDs), known as OpenCitations Meta Identifiers (OMIDs) to all bibliographic resources, enabling it both to disambiguate publications described using different external PIDS (e.g., a DOI in Crossref and a PMID in PubMed), and to handle citations involving publications lacking external PIDs. By hosting bibliographic metadata internally, OpenCitations Meta eliminates its former reliance on API calls to external resources and thus enhances performance in response to user queries. Its automated data curation, following the OpenCitations Data Model, includes deduplication, error correction, metadata enrichment and full provenance tracking, ensuring transparency and traceability of data and bolstering confidence in data integrity, a feature unparalleled in other bibliographic databases. Its commitment to Semantic Web standards ensures superior interoperability compared to other machine-readable formats, with availability via a SPARQL endpoint, REST APIs and data dumps.

The complement of plane algebraic curves are well studied from topological and algebro-geometric viewpoints. In this paper, we will describe the explicit handle decompositions and the Kirby diagrams for the complement of plane algebraic curves. The method is based on the notion of braid monodromy. We refined this technique to obtain handle decompositions and Kirby diagrams.

In this paper, a new criterion is given to determine the $p-$rationality of some complex cubic number fields in terms of $ p-$divisibility of certain terms of a third-order recurrence sequence, several illustrated examples are constructed,the relations between generalized $ abc-$conjecture and the $p-$rationality are discussed, from which some explicit fields satisfying Greenberg's Generalized Conjecture (GGC, for short) are obtained.

We study transverse equivariant Hilbert schemes of affine hypertoric varieties equipped with a symplectic action of a Weyl group. In particular, we show that the Coulomb branches of Braverman, Finkelberg, and Nakajima can be obtained either as such Hilbert schemes or Hamiltonian reductions thereof. Furthermore, we propose that the Coulomb branches for representations of non-cotangent type are also obtained in this way. We also investigate the putative complete hyperkähler metrics on these objects. We describe their twistor spaces and, in the case when the symplectic quotient construction of the hypertoric variety is $W$-equivariant (which includes Coulomb branches of cotangent type), we show that the hyperkähler metric can be described as the natural $L^2$-metric on a moduli space of solutions to modified Nahm's equations on an interval with poles at both ends and a discontinuity in the middle, with the latter described by a new object: a hyperspherical variety canonically associated to a hypertoric variety.

It is a long-standing problem in Hodge theory to generalize the Satake--Baily--Borel (SBB) compactification of a locally Hermitian symmetric space to arbitrary period maps. A proper topological SBB-type completion has been constructed, and the problem of showing that the construction is algebraic has been reduced to showing that the compact fibres A of the completion admit neighborhoods X satisfying certain properties. All but one of those properties has been established; the outstanding problem is to show that holomorphic functions on certain divisors "at infinity" extend to X. Extension theorems of this type require that the complex manifold X be pseudoconvex; that is, admit a plurisubharmonic exhaustion function. The neighborhood X is stratified, and the strata admit Hodge norms which are may be used to produce plurisubharmonic functions on the strata. One would like to extend these norms to X so that they may be used to construct the desired plurisubharmonic exhaustion of X. The purpose of this paper is show that there exists a function that simultaneously extends all the Hodge norms along the strata that intersect the fibre A nontrivially.

We study the graph of the function $d(t)$ encoding the Hausdorff dimensions of the classical Lagrange and Markov spectra with half-infinite lines of the form $(-\infty, t)$. For this sake, we use the fact that the Hausdorff dimension of dynamically Cantor sets drop after erasing an element of its Markov partition to determine twelve nontrivial plateaux of $d(t)$. Next, we employ rigorous numerical methods (from our recent joint paper with Pollicott) to produce approximations of the graph of $d(t)$ between these twelve plateaux. As a corollary, we prove that the largest ten non-trivial plateaux of $d(t)$ are exactly those plateaux with lengths $> 0.005$.

We present a microscopic derivation from a nonequilibrium spin-boson model to a $\PT$-symmetric non-Hermitian sine-Gordon (SG) effective theory, via the Keldysh functional-integral formalism, a Lang-Firsov polaron transformation, bosonization, and a Grassmann coherent-state spin trace.The spin trace yields the generic reduced vertex $g_r\cos(λΦ_1)+ig_i\sin(λΦ_1)$, where the imaginary part originates from the nonequilibrium Keldysh distribution asymmetry $δn(ω)=n_+(ω)-n_-(ω)$. We provide an explicit dictionary between the spin-boson microscopic parameters and the NH-SG couplings: $K=v_f/\tilde{J}_\parallel^2$ (Luttinger parameter from $J_\parallel$), $g_r\propto J_\perp^2/Γ$ (from the transverse coupling and impurity width), and $\mathcal{I}=g_i/g_r\proptoμ/v_f$ (bias ratio, an exact RG invariant).One-loop Wilson momentum-shell RG on the NH-SG action gives the closed equations $\diff K/\diff l=-g_r^2(1-\mathcal{I}^2)K^2$ and $\diff g_r/\diff l=(2-K)g_r$, identical to those of Ashida \textit{et al.}\ for the $\PT$-symmetric SG; the present work supplies the microscopic initial conditions from the spin-boson Keldysh reduction. The BKT separatrix $K=2$ (Toulouse line), the EP fixed manifold $\mathcal{I}=1$ ($μ=μ_c$), and the mass gap $m\simΛe^{-c/\sqrt{K_0-2}}$ all follow from this closed system.In the non-relativistic soliton sector near the EP, the effective coupling $\tilde{g}=g_r\sqrt{1-\mathcal{I}^2}$ reduces the S-matrix to the Lieb-Liniger rational form and the Bethe ansatz becomes exact for that auxiliary gas.Within this sector we derive $n$-string bound states with$E_n^{\rm bind}=-n(n^2-1)\tilde{g}^2/12$, identify the EP as the many-body bound-state threshold, and construct the Jordan-partner state from the $ε$-regularised dimer.

We completely characterize triangulations of the projective plane that have a spanning bipartite quadrangulation subgraph. This is an affirmative answer to a question by Kündgen and Ramamurthi (J Combin Theory Ser B 85, 307--337, 2002) for the projective planar case.

We classify birational involutions of the real projective plane up to conjugation. In contrast with an analogous classification over the complex numbers (due to E. Bertini, G. Castelnuovo, F. Enriques, L. Bayle and A. Beauville), which includes 4 different classes of involutions, we discover 12 different classes over the reals, and provide many examples when the fixed curve of an involution does not determine its conjugacy class in the real plane Cremona group.

We give a sufficient condition in order that $n$ closed connected subsets in the $n$-dimensional real projective space admit a common multitangent hyperplane.

We provide an original analysis of historical documents to describe the assignment procedures used to allocate entry-level civil service jobs in China from the tenth to the early twentieth century. The procedures tried to take different objectives into account through trial and error. By constructing a formal model that combines these procedures into a common framework, we compare their effectiveness in minimizing unfilled jobs and prioritizing high-level posts. We show that the problem was inherently complex such that changes made to improve the outcome could have the opposite effect. Based on a small modification of the last procedure used, we provide a new mechanism for producing maximum matchings under constraints in a transparent and public way.

We establish long-range order for discrete nearest-neighbor spin systems on $\mathbb{Z}^d$ satisfying a certain symmetry assumption, when the dimension $d$ is higher than an explicitly described threshold. The results characterize all periodic, maximal-pressure Gibbs states of the system. The results further apply in low dimensions provided that the lattice $\mathbb{Z}^d$ is replaced by $\mathbb{Z}^{d_1}\times\mathbb{T}^{d_2}$ with $d_1\ge 2$ and $d=d_1+d_2$ sufficiently high, where $\mathbb{T}$ is a cycle of even length. Applications to specific systems are discussed in detail and models for which new results are provided include the antiferromagnetic Potts model, Lipschitz height functions, and the hard-core, Widom--Rowlinson and beach models and their multi-type extensions. We also establish a formula conjectured by Jenssen and Keevash for the topological pressure in the high-dimensional limit.

We show that every bipartite planar graph with minimum degree at least 3 has proper orientation number at most 3.

Three-dimensional self-assembly of lithographically patterned ultrathin films opens a path to manufacture microelectronic architectures with functionalities and integration schemes not accessible by conventional two-dimensional technologies. Among other microelectronic components, inductances, transformers, antennas and resonators often rely on three-dimensional configurations and interactions with electromagnetic fields requiring exponential fabrication efforts when downscaled to the micrometer range. Here, the controlled self-assembly of functional structures is demonstrated. By rolling-up ultrathin films into cylindrically shaped microelectronic devices we realized electromagnetic resonators, inductive and mutually coupled coils. Electrical performance of these devices is improved purely by transformation of a planar into a cylindrical geometry. This is accompanied by an overall downscaling of the device footprint area by more than 50 times. Application of compact self-assembled microstructures has significant impact on electronics, reducing size, fabrication efforts, and offering a wealth of new features in devices by 3D shaping.

Given sets $X,Y$ and a regular cardinal $μ$, let $Φ(X,Y,μ)$ be the statement that for any function $f : X \times Y \to μ$, there are functions $g_1 : X \to μ$ and $g_2 : Y \to μ$ such that or all $(x,y) \in X \times Y$, $$f(x,y) \le \max \{ g_1(x), g_2(y) \}.$$ In ZFC, the statement $Φ(ω_1, ω_1, ω)$ is false. However, we show the theory ZF + ``the club filter on $ω_1$ is normal'' + $Φ(ω_1, ω_1, ω)$ (which is implied by ZF + AD) implies that for every $α< ω_1$ there is a $κ\in (α,ω_1)$ such that in some inner model, $κ$ is measurable with Mitchell order $\ge α$. There was an error in Welch's paper ``Characterizing Subsets of $ω_1$ Constructible From a Real'', which he has retracted in a personal communication. Our paper originally referenced that paper. In this version of our paper, we are not using that result. Our consistency strength upper bound has changed accordingly.

Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two flavours: a \emph{kinematic} non-locality -- arising from the structure of the Hilbert space -- and a \emph{dynamical} non-locality -- arising from the quantum equations of motion. Recently, the origin of kinematic non-locality was traced to the uncertainty principle; here we rigorously trace the origin of dynamical non-locality to the superposition principle. We prove, via deformation quantization and Marinov's phase-space path integrals, that the exact Wigner propagator reduces to the classical Liouville propagator if and only if the Hamiltonian has at-most-quadratic Weyl symbol. This unified theorem covers both continuous-variable and finite-dimensional Hilbert spaces, aligning the Gaussian (CV) and Clifford (finite-$d$) boundaries of classical simulability into a single algebraic criterion. We introduce a macroscopic, experimentally accessible measure of dynamical non-locality -- the signed divergence $\mathcal{D}(t)$ -- and show that it governs five phenomena: (i) the dynamical penalty incurred by quantum non-local games under post-measurement evolution; (ii) the quantum corrections to out-of-time-order correlators; (iii) the metrological gain beyond the shot-noise limit; (iv) the generation of non-Gaussian entanglement from product states; and (v) the non-Clifford / magic-state content of finite-dimensional dynamics. A concrete experimental protocol in circuit QED is proposed and complemented by a three-qubit CCZ protocol accessible on current qubit platforms.

We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s<3 have also been previously established. More precisely, we establish that if f : [N] -> [-1,1] is a function with || f ||_{U^{s+1}[N]} > δthen there is a bounded-complexity s-step nilsequence F(g(n)Γ) which correlates with f, where the bounds on the complexity and correlation depend only on s and δ. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity. A 6-page erratum to the original paper was provided in April 2024 and is available as a separate PDF on the webpages of the first and second authors.