287 papers
This paper constructs an instanton cochain complex using the eigenspaces of a deformed mapping cone Laplacian and proves its cochain isomorphism to the topologically defined mapping cone Thom-Smale complex, thereby establishing a bridge between analytic and topological approaches to the wedge by a smooth closed form.
This paper classifies differential operators between spaces of weighted densities in the superdimension setting, effectively superizing a previous result on modular forms and identifying open problems in the field.
This paper establishes that the asymptotic accumulation of eigenvalues near unity for convolutions of indicator functions and density operators on locally compact groups occurs if and only if the group is unimodular and the underlying sets form a Følner sequence, thereby extending known results for the Heisenberg group to broader classes such as nilpotent and homogeneous Lie groups.
This paper investigates the irreducible components of fixed point sets within the -character variety of a genus two surface under finite group actions, utilizing the genus two DAHA to identify geometric transitions that yield novel candidates for symmetry-reduced moduli spaces in 4d SCFTs.
This paper constructs the parametrix for elliptic Gevrey pseudodifferential operators by establishing a Banach algebra structure for formal Gevrey symbols, which is then applied to derive estimates for adiabatic projectors in the Gevrey setting.
This paper demonstrates that entropy acts as a driving force in various evolution equations because it characterizes the invariant measure of an underlying stochastic process, thereby unifying diverse examples from stochastic processes, gradient flows, and GENERIC systems under a single principle.
This paper establishes the integrability of a one-parameter family of coupled Dirac-scalar field theories in dimensions that interpolates between the Dirac-sinh-Gordon and Dirac-sine-Gordon systems by constructing an explicit -valued Lax pair, proving the physical non-triviality of the deformation, and deriving associated conserved densities.
This survey reviews the computation of Weil-Petersson and Masur-Veech volumes for moduli spaces of Riemann surfaces, highlighting their profound impact on combinatorial enumeration, intersection theory, and recursion relations, while drawing parallels between the methods used to calculate these two distinct types of volumes.
This paper establishes both Anderson localization and Hölder continuity of the integrated density of states for quasi-periodic Schrödinger operators on with non-constant analytic potentials and fixed Diophantine frequencies in the perturbative regime, utilizing a novel multi-scale analysis approach to control Green's functions.
This paper generalizes the Peter-Weyl Theorem by demonstrating that functions on locally compact groups with large nontrivial compact open subgroups can be approximated by locally representative functions.
This paper develops a wave function renormalization scheme within the Hamiltonian formalism to construct the ground state representation of interacting Hamiltonians for non-relativistic particles coupled to quantized relativistic fields, thereby addressing ultraviolet and infrared singularities in models like the spin-boson and Nelson systems.
This paper classifies central extensions for the loop group of area-preserving diffeomorphisms of the 2-sphere and demonstrates that their associated Lie algebra cocycles emerge as fuzzy sphere limits of Kac-Moody cocycles for large in (twisted) loop algebras of , provided a specific rescaling by $6/k^3$.
This paper establishes a framework for defining self-adjoint realizations of 2d-dimensional canonical systems through symplectic geometry and Lagrangian boundary conditions, demonstrating their critical application in analyzing the spectral stability of traveling waves and solitons in nonlinear partial differential equations.
This paper presents a symplectic Hamiltonian framework for thermodynamics that models equilibrium states as Lagrangian submanifolds and describes both reversible and irreversible processes, such as free expansion and heat transfer, through Hamiltonian dynamics and port-Hamiltonian systems.
This paper provides a learner-focused, methodical exposition on deriving the General Lagrangian Mean (GLM) and pseudo-Lagrangian equations for inviscid, incompressible, homogeneous fluids to describe the interactions between mean flows and waves.
This paper establishes a hydrodynamic framework for force dipoles in compressible membranes with odd viscosity by deriving an exact Green tensor that reveals distinct dynamical regimes and chiral observables, such as transverse drift and relative motion, arising from the interplay of shear, compressional, and odd-viscous modes.
This paper presents two new methods for constructing Lagrangians with specific symmetries by deriving relations from Noether's identity that link the Hessian matrix, symmetry transformations, and constants of motion, and then combining these with Helmholtz's conditions to solve the inverse problem of mechanics.
This paper proposes a classical model of elementary particles where distinguishing between the center of mass and the center of interaction leads to a description of spinning particles whose dynamics, when the center of interaction moves at light speed, yield Dirac's equation upon quantization.
This paper introduces a comprehensive framework that unifies formal group theory and group entropies to create a flexible, infinite family of Mirror Descent optimization algorithms, featuring a novel "mirror duality" mechanism that adapts to diverse data geometries and statistical distributions while enhancing convergence and regularizer design in machine learning.
This paper establishes a general topological framework for understanding the local robustness of bound states in the continuum (BICs) by characterizing them as isolated zeros of a parameter-to-coefficient mapping derived from scattering-matrix eigenvectors, thereby providing both a theoretical explanation for their phase singularities and a practical numerical criterion for their detection.