This article considers a long-outstanding open question regarding the Jacobian determinant for the relativistic Boltzmann equation in the center-of-momentum coordinates. For the Newtonian Boltzmann equation, the center-of-momentum coordinates have played a large role in the study of the Newtonian non-cutoff Boltzmann equation, in particular we mention the widely used cancellation lemma [1]. In this

We construct two non-semisimple braided ribbon tensor categories of modules for each singlet vertex operator algebra \({\mathcal {M}}(p)\), \(p\ge 2\). The first category consists of all finite-length \({\mathcal {M}}(p)\)-modules with atypical composition factors, while the second is the subcategory of modules that induce to local modules for the triplet vertex operator algebra \({\mathcal {W}}(p)\)

We give a skein-theoretic realization of the \(\mathfrak {gl}_n\) double affine Hecke algebra of Cherednik using braids and tangles in the punctured torus. We use this to provide evidence of a relationship we conjecture between the skein algebra of closed links in the punctured torus and the elliptic Hall algebra of Burban and Schiffmann.

In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted K-theory and higher twisted cohomology over the reals. Finally we compute spherical T-duality in higher twisted K-theory and higher twisted cohomology in very general

We present a novel symmetry of the colored HOMFLY polynomial. It relates pairs of polynomials colored by different representations at specific values of N and generalizes the previously known “tug-the-hook” symmetry of the colored Alexander polynomial (Mishnyakov et al. in Annales Henri Poincaré, 2021. https://doi.org/10.1007/s00023-020-00980-8, arXiv:2001.10596). As we show, the symmetry has a superalgebra

We study the asymptotic speed of a random front for solutions \(u_t(x)\) to stochastic reaction–diffusion equations of the form $$\begin{aligned} \partial _tu=\frac{1}{2}\partial _x^2u+f(u)+\sigma \sqrt{u(1-u)}{\dot{W}}(t,x),~t\ge 0,~x\in {\mathbb {R}}, \end{aligned}$$ arising in population genetics. Here, f is a continuous function with \(f(0)=f(1)=0\), and such that \(|f(u)|\le K|u(1-u)|^\gamma \)

We consider the limiting process that arises at the hard edge of Muttalib–Borodin ensembles. This point process depends on \(\theta > 0\) and has a kernel built out of Wright’s generalized Bessel functions. In a recent paper, Claeys, Girotti and Stivigny have established first and second order asymptotics for large gap probabilities in these ensembles. These asymptotics take the form $$\begin{aligned}

We introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions

We solve the Jang equation with respect to asymptotically hyperbolic “hyperboloidal” initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses on the case when the spatial dimension is equal to three.

We study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators consists of exchanges of pairs of particles on junctions of the graph and of certain circular moves where one particle travels around a simple cycle of the graph. We point out that so defined generators often do not satisfy

We analytically study the long time and large space asymptotics of a new broad class of solutions of the KdV equation introduced by Dyachenko, Zakharov, and Zakharov. These solutions are characterized by a Riemann–Hilbert problem which we show arises as the limit \(N\rightarrow + \infty \) of a gas of N-solitons. We show that this gas of solitons in the limit \(N\rightarrow \infty \) is slowly approaching

In this article, we construct non-compact complete Einstein metrics on two infinite series of manifolds. The first series of manifolds are vector bundles with \({\mathbb {S}}^{4m+3}\) as principal orbit and \({{\mathbb {H}}}{\mathbb {P}}^{m}\) as singular orbit. The second series of manifolds are \({\mathbb {R}}^{4m+4}\) with the same principal orbit. For each case, a continuous 1-parameter family

In this paper, we construct quantum invariants for knotoid diagrams in \({{\mathbb {R}}}^2\). The diagrams are arranged with respect to a given direction in the plane (Morse knotoids). A Morse knotoid diagram can be decomposed into basic elementary diagrams each of which is associated to a matrix that yields solutions of the quantum Yang–Baxter equation. We recover the bracket polynomial, and define

We consider the Navier–Stokes–Fourier system in a bounded domain \(\Omega \subset R^d\), \(d=2,3\), with physically realistic in/out flow boundary conditions. We develop a new concept of weak solutions satisfying a general form of relative energy inequality. The weak solutions exist globally in time for any finite energy initial data and comply with the weak–strong uniqueness principle.

The quantum symmetric simple exclusion process (Q-SSEP) is a model for quantum stochastic dynamics of fermions hopping along the edges of a graph with Brownian noisy amplitudes and driven out-of-equilibrium by injection-extraction processes at a few vertices. We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit by constructing the steady

We use coarse index methods to prove that the Landau Hamiltonian on the hyperbolic half-plane, and even on much more general imperfect half-spaces, has no spectral gaps. Thus the edge states of hyperbolic quantum Hall Hamiltonians completely fill up the gaps between Landau levels, just like those of the Euclidean counterparts.

We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered \(C^1\)-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of

The full 6d Hopf–Wess–Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess–Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis that the C-field is charge-quantized in twisted Cohomotopy theory. The proof follows

We establish rapid mixing of the random-cluster Glauber dynamics on random \(\varDelta \)-regular graphs for all \(q\ge 1\) and \(p2\) the Glauber dynamics on random \(\varDelta \)-regular graphs undergoes an exponential slowdown at \(p_u(q,\varDelta )\). More precisely, we show that for every \(q\ge 1\), \(\varDelta \ge 3\), and \(p

The Rarita–Schwinger operator is the twisted Dirac operator restricted to \(\nicefrac 32\)-spinors. Rarita–Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds

The confinement of quarks is one of the enduring mysteries of modern physics. There is a longstanding physics heuristic that confinement is a consequence of ‘unbroken center symmetry’. This article gives mathematical confirmation of this heuristic, by rigorously defining of center symmetry in lattice gauge theories and proving that a theory is confining when center symmetry is unbroken. Furthermore

We present a new construction of the Euclidean \(\Phi ^4\) quantum field theory on \({\mathbb {R}}^3\) based on PDE arguments. More precisely, we consider an approximation of the stochastic quantization equation on \({\mathbb {R}}^3\) defined on a periodic lattice of mesh size \(\varepsilon \) and side length M. We introduce a new renormalized energy method in weighted spaces and prove tightness of

Consider the relativistic Vlasov–Maxwell–Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works Germain and Masmoudi (Ann Sci Éc Norm Supér 47(3):469–503, 2014), Guo et al. (J Math Phys 55(12):123102, 2014) and Deng et al. (Arch Ration Mech Anal 225(2):771–871, 2017), we establish the global-in-time validity of its Hilbert expansion

In this paper, we study the so-called intermediate disorder regime for a directed polymer in a random environment with heavy-tail. Consider a simple symmetric random walk \((S_n)_{n\ge 0}\) on \(\mathbb {Z}^d\), with \(d\ge 1\), and modify its law using Gibbs weights in the product form \(\prod _{n=1}^{N} (1+\beta \eta _{n,S_n})\), where \((\eta _{n,x})_{n\ge 0, x\in {\mathbb {Z}}^d}\) is a field of

We build a bridge between two algebraic structures in superconformal field theories (SCFT): a vertex operator algebra (VOA) in the Schur sector of 4d \(\mathcal {N}=2\) theories and an associative algebra in the Higgs sector of 3d \(\mathcal {N}=4\). The natural setting is a 4d \(\mathcal {N}=2\) SCFT placed on \(S^3\times S^1\): by sending the radius of \(S^1\) to zero, we recover the 3d \(\mathcal

The asymptotic wave speed for FKPP type reaction-diffusion equations on a class of infinite random metric trees are considered. We show that a travelling wavefront emerges, provided that the reaction rate is large enough. The wavefront travels at a speed that can be quantified via a variational formula involving the random branching degrees \(\vec {d}\) and the random branch lengths \(\vec {\ell }\)

We define and study the totally nonnegative part of the Chow quotient of the Grassmannian, or more simply the nonnegative configuration space. This space has a natural stratification by positive Chow cells, and we show that nonnegative configuration space is homeomorphic to a polytope as a stratified space. We establish bijections between positive Chow cells and the following sets: (a) regular subdivisions

Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonance phenomena, and fluid stability analysis. Similarly, spectral decompositions (into pure point, absolutely continuous and singular continuous parts) often characterise relevant physical properties such as the long-time dynamics of quantum systems. Despite new results on computing spectra, there remains

We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discussed by Bonk–Meyer and is closely related to coarse expanding conformal systems as defined by Haïssinsky–Pilgrim. We prove existence and uniqueness of equilibrium states for a wide class of potentials, as well as statistical

We introduce a symmetric operad whose algebras are the operator product expansion (OPE) Algebras of quantum fields. There is a natural classical limit for the algebras over this operad and they are commutative associative algebras with derivations. The latter are the algebras of classical fields. In this paper we completely develop our approach to models of quantum fields, which come from vertex algebras

We study how conserved quantities such as angular momentum and center of mass evolve with respect to the retarded time at null infinity, which is described in terms of a Bondi–Sachs coordinate system. These evolution formulae complement the classical Bondi mass loss formula for gravitational radiation. They are further expressed in terms of the potentials of the shear and news tensors. The consequences

We study the light ray transform on Minkowski space-time and its small metric perturbations acting on scalar functions which are solutions to wave equations. We show that the light ray transform uniquely determines the function in a stable way. The problem is of particular interest because of its connection to inverse problems of the Sachs–Wolfe effect in cosmology.

For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be characterized as stable manifolds foliating neighborhoods of the limit cycle or as level sets of an isochron map. In recent years, there has been a lively discussion in the

Inspired by the quantum McKay correspondence, we consider the classical ADE Lie theory as a quantum theory over \(\mathfrak {sl}_2\). We introduce anti-symmetric characters for representations of quantum groups and investigate the Fourier duality to study the spectral theory. In the ADE Lie theory, there is a correspondence between the eigenvalues of the Coxeter element and the eigenvalues of the adjacency

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle of functional law of large numbers type are established. Then we consider the small fluctuations of the system around its average. Nine cases of functional central

In this note, we study a simplified variant of the familiar holographic duality between supergravity on \(\hbox {AdS}_3\times S^3\times T^4\) and the SCFT (on the moduli space of) the symmetric orbifold theory \(Sym^N(T^4)\) as \(N \rightarrow \infty \). This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors

We consider the capillary–gravity water wave equation in two dimensions. We assume that the fluid is inviscid, incompressible, irrotational and the air density is zero. We construct an energy functional and prove a local wellposedness result without assuming the Taylor sign condition. When the surface tension \(\sigma \) is zero, the energy reduces to a lower order version of the energy obtained by

We show how to derive asymptotic charges for field theories on manifolds with “asymptotic” boundary, using the BV-BFV formalism. We also prove that the conservation of said charges follows naturally from the vanishing of the BFV boundary action, and show how this construction generalises Noether’s procedure. Using the BV-BFV viewpoint, we resolve the controversy present in the literature, regarding

We describe the structure of ground states and ceiling states for generalized gauge actions on a UHF algebra. It is shown that both sets are affinely homeomorphic to the state space of a unital AF algebra, and that any pair of unital AF algebras can occur in this way, independently of the field of KMS states. In addition we study the subset of the ground states called \({\text {KMS}}_\infty \)-states

We analyze the eigenvalue problem for the semiclassical Dirac (or Zakharov–Shabat) operator on the real line with general analytic potential. We provide Bohr–Sommerfeld quantization conditions near energy levels where the potential exhibits the characteristics of a single or double bump function. From these conditions we infer that near energy levels where the potential (or rather its square) looks

In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any “long-range” bulk gauge

In this paper, we give a generalization of Kitaev’s stabilizer code based on chain complex theory of bicommutative Hopf algebras. Due to the bicommutativity, the Kitaev’s stabilizer code extends to a broader class of spaces, e.g. finite CW-complexes ; more generally short abstract complex over a commutative unital ring R which is introduced in this paper. Given a finite-dimensional bisemisimple bicommutative

In this paper, we first construct the controlling algebras of embedding tensors and Lie–Leibniz triples, which turn out to be a graded Lie algebra and an \(L_\infty \)-algebra respectively. Then we introduce representations and cohomologies of embedding tensors and Lie–Leibniz triples, and show that there is a long exact sequence connecting various cohomologies. As applications, we classify infinitesimal

Inspired by the numerical evidence of a potential 3D Euler singularity by Luo-Hou [30, 31] and the recent breakthrough by Elgindi [11] on the singularity formation of the 3D Euler equation without swirl with \(C^{1,\alpha }\) initial data for the velocity, we prove the finite time singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with \(C^{1,\alpha

We consider directed last passage percolation on \({\mathbb {Z}}^2\) with exponential passage times on the vertices. A topic of great interest is the coupling structure of the weights of geodesics as the endpoints are varied spatially and temporally. A particular specialization is when one considers geodesics to points varying in the time direction starting from a given initial data. This paper considers

We study nonstationary intermittent dynamical systems, such as compositions of a (deterministic) sequence of Pomeau–Manneville maps. We prove two main results: sharp bounds on memory loss, including the “unexpected” faster rate for a large class of measures, and sharp moment bounds for Birkhoff sums and, more generally, “separately Hölder” observables.

In this paper we continue to explore infinitely renormalizable Hénon maps with small Jacobian. It was shown in a previous paper by the authors, joint with A. de Carvalho, (J Stat Phys 121(5/6):611–669, 2005) that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with the one-dimensional Cantor attractor is at most 1/2-Hölder. Another formulation

We consider the geodesic flow for a rank one non-positive curvature closed manifold. We prove an asymptotic version of the Central Limit Theorem for families of measures constructed from regular closed geodesics converging to the Bowen-Margulis-Knieper measure of maximal entropy. The technique expands on ideas of Denker, Senti and Zhang, who proved this type of asymptotic Lindeberg Central Limit Theorem

Rindler wedges are fundamental localization regions in AQFT. They are determined by the one-parameter group of boost symmetries fixing the wedge. The algebraic canonical construction of the free field provided by Brunetti–Guido–Longo (BGL) arises from the wedge-boost identification, the BW property and the PCT Theorem. In this paper we generalize this picture in the following way. Firstly, given a

We propose a formula for the exact central charge of a B-type D-brane that is expected to hold in all regions of the Kähler moduli space of a Calabi–Yau. For Landau–Ginzburg orbifolds we propose explicit expressions for the mathematical objects that enter into the central charge formula. We show that our results are consistent with results in FJRW theory and the hemisphere partition function of the

In this work, we consider self-similar profiles for Smoluchowski’s coagulation equation for kernels which are possibly unbounded perturbations of the constant one. For this model, we show that the self-similar solutions for the perturbed kernel are close in weighted \(L^1\) spaces to the profile of the unperturbed equation, i.e. the profiles are stable with respect to the perturbation. Additionally

In our result about dynamical thermalization, the proof of the upper bound on the time average of the distance between the local evolved state

We study the long-time behavior of the Schrödinger flow in a heterogeneous potential \(\lambda V\) with small intensity \(0<\lambda \ll 1\) (or alternatively at high frequencies). The main new ingredient, which we introduce in the general setting of a stationary ergodic potential, is an approximate stationary Floquet–Bloch theory that is used to put the perturbed Schrödinger operator into approximate

This paper is dedicated to proving the complete integrability of the Benjamin–Ono (BO) equation on the line when restricted to every N-soliton manifold, denoted by \(\mathcal {U}_N\). We construct generalized action–angle coordinates which establish a real analytic symplectomorphism from \(\mathcal {U}_N\) onto some open convex subset of \({\mathbb {R}}^{2N}\) and allow to solve the equation by quadrature

Given a compact Kähler manifold X, there is an equivalence of categories between the completely reducible flat vector bundles on X and the polystable Higgs bundles \((E, \theta )\) on X with \(c_1(E)= 0= c_2(E)\) (Simpson in J Am Math Soc 1(4):867–918, 1988; Corlette in J Differ Geom 28:361–382, 1988; Uhlenbeck and Yau in Commun Pure Appl Math 39:257–293, 1986; Donaldson in Duke Math J 54(1):231–247

A Correction to this paper has been published https://doi.org/10.1007/s00220-019-03374-y.

For a complex finite-dimensional simple Lie algebra \({\mathfrak {g}}\), we introduce the notion of Q-datum, which generalizes the notion of a Dynkin quiver with a height function from the viewpoint of Weyl group combinatorics. Using this notion, we develop a unified theory describing the twisted Auslander–Reiten quivers and the twisted adapted classes introduced in Oh and Suh (J Algebra 535(1):53–132

We obtain an asymptotic formula for \(n\times n\) Toeplitz determinants as \(n\rightarrow \infty \), for non-negative symbols with any fixed number of Fisher–Hartwig singularities, which is uniform with respect to the location of the singularities. As an application, we prove a conjecture by Fyodorov and Keating (Philos Trans R Soc A 372: 20120503, 2014) regarding moments of averages of the characteristic

We investigate the dynamical behaviours of the n-vortex problem with circulation vector \(\varvec{\Gamma }\) on a Riemann sphere \({\mathbb {S}}^2\), equipped with an arbitrary metric g. By mixing perspectives from Riemannian geometry and symplectic geometry, we prove that for any given \(\varvec{\Gamma }\), the Hamiltonian is a Morse function for \({\mathcal {C}}^2\) generic g. If some constraints

We study the two-dimensional rotating shallow-water model describing Earth’s oceanic layers. It is formally analogue to a Schrödinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an odd-viscous term, such a model has a well-defined bulk topological index. However, in presence of a sharp boundary, the number of edge modes depends on the boundary