Guillemin trace formula adapted for group actions.
problem Distributional trace for proper, cocompact group actions.
method Developing an equivariant version of the distributional trace.
result Equivariant Guillemin trace formula for group actions.
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48 results for “Equivariant trace”
Formula for twisted orbital integrals using hypoelliptic Laplacian.
problem Evaluate equivariant trace of Laplacians on compact locally symmetric spaces.
method Using the hypoelliptic Laplacian method and twisted trace formula.
result Explicit geometric formula for twisted orbital integrals.
Defines an equivariant Ruelle dynamical zeta function for flows on manifolds.
problem Defining a zeta function for equivariant flows on manifolds.
method Equivariant generalization of Guillemin's trace formula.
result Computes the equivariant Ruelle zeta function in various examples.
Formula for fixed points on noncompact spaces.
problem Calculating fixed points on noncompact manifolds.
method Equivariant index theorem, localised functional, asymptotically local operators.
result Obtained a new Lefschetz fixed-point formula.
An equivariant Atiyah-Patodi-Singer index theorem for proper actions II: the -theoretic indexmath.KT
New index formula connects numerical and -theoretic indices.
problem Equivariant index for proper group actions on manifolds.
method Developed a trace on group conjugacy classes to relate numerical and -theoretic indices.
result Shows that numerical index equals -theoretic index under certain conditions.
We prove inverse spectral results for differential operators on manifolds and orbifolds invariant under a torus action. These inverse spectral results involve the asymptotic equivariant spectrum, which is the spectrum itself together with "very large" weights of the torus action on eigenspaces. More precisely, we show …
Let O be a symplectic toric 2n-dimensional orbifold with a fixed T^n-action and with a toric Kahler metric g. We previously explored whether, when O is a manifold, the equivariant spectrum of the Laplace operator acting on smooth functions on (O,g) determines the moment polytope of O, and hence by Delzant's theorem det…
Formula derived for Dirac operators on Lie groupoids.
problem Equivariant Dirac operators on Lie groupoids.
method Getzler rescaling method to derive a fixed-point formula.
result Reduces to standard fixed-point formula for closed manifolds.
Consider a proper, isometric action by a unimodular locally compact group on a Riemannian manifold with boundary, such that is compact. For an equivariant, elliptic operator on , and an element , we define a numerical index , in terms of a parametrix for and …
Improves modeling of sets with permutation invariant densities.
problem Challenges in calculating trace limit practicality of current methods.
method Proposes an alternative approach to define permutation equivariant transformations with closed form trace.
result Improves both training and final performance.
Generative adversarial networks fix aliasing issues by making signals continuous.
problem Alias-free generation in GANs to prevent unwanted information leakage.
method Interpreting all signals as continuous, deriving small architectural changes.
result Generative models match FID of StyleGAN2 but have better internal representations.
Formulates a new connection between topological and geometric categories.
problem No specific problem stated; focuses on category formulation.
method Formulates a connection between a topological and geometric category.
result Provides a more precise and improved version of a previous proposal.
Reflection Symmetry, APS Boundary Conditions, and Equivariant Spectral Flow on a Warped Cylindermath-ph
Study reflection symmetry and APS boundary conditions on a warped cylinder.
problem Analyzing reflection symmetry and APS boundary conditions for twisted Dirac operators on a finite warped cylinder.
method Examined reflection symmetry and APS boundary conditions for twisted Dirac operators on a finite warped cylinder, considering both fixed and varying holonomy.
result Reflection symmetry lifts to a unitary symmetry under specific conditions, and the spectral flow admits an RO(O(2))-valued decomposition for fixed holonomy.
Let be a connected compact Lie group. We study the heat operator of a -transversally elliptic operator. After we review the spectral properties of a -transversally elliptic operator, we define the character, that is a distribution on generalizing the trace of the heat operator to the -equivariant case.…
We study the Laplace spectra of the intrinsic instantaneous metrics on the event and cosmological horizons of a Kerr-Newman de Sitter space-time and prove that the spectral data from these horizons uniquely determine the space-time. This is accomplished by exhibiting formulae relating the parameters of the space-time m…
Study quantisation of geometric operators on manifolds with group actions.
problem Quantisation of geometric operators on manifolds with group actions.
method Use maximal versions of equivariant localised Roe algebras to define and compute indices.
result Recover an index defined earlier by integrating over the group action.
This is a sequel to the paper [Cas]. Here, we extend the methods of Farb-Wolfson using the theory of FI_G-modules to obtain stability of equivariant Galois representations of the etale cohomology of orbit configuration spaces. We establish subexponential bounds on the growth of unstable cohomology, and then use the Gro…
We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle $\GR$ of Lie groups. If the fibers of $\GR \to B$ are simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result being given by an Atiyah-Singe…
Geometrically computes sheaves linking HOMFLY-PT homology to Hilbert schemes.
problem Linking HOMFLY-PT homology to geometric structures on Hilbert schemes.
method Geometric sheaf theory, Hochschild homology formality, Hilbert schemes of points.
result Established formalism connecting HOMFLY-PT homology to coherent sheaves on Hilbert schemes.
This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.
Study of torus surgeries on knot traces, finding exotic surfaces and traces.
problem Understanding exotic surfaces and traces through torus surgeries.
method Realizing annulus twisting as torus surgery, using key technical insight.
result Exotic elliptic surfaces and traces discovered, improving known geography.
Classifies knot traces with specific trisection genus limits.
problem Classifying knot traces with specific trisection genus limits.
method Classifying knot traces with specific trisection genus limits.
result Infinitely many knots have traces with trisection genus 3 and 4, and arbitrarily large trisection genus.
Paper derives trace formula for magnetic Laplacian at zero energy.
problem Trace formula for magnetic Laplacian at zero energy.
method Generalizes Gutzwiller trace formula, focuses on zero energy level.
result Derives trace formula at zero energy level.
In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.
New methods derive a generalized Frenkel trace formula for Lie groups.
problem Deriving a generalized Frenkel trace formula for Lie groups.
method Applying supersymmetric localization to quantum mechanical and gauged sigma models.
result Presented two complementary approaches for the derivation of the trace formula.
Examines a new type of analytic torsion on Riemannian manifolds.
problem Analyzing a new trace formula for Riemannian manifolds.
method Uses residue-trace instead of spectral zeta function quasi-trace.
result Defines and examines the residue analytic torsion.
Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.
problem Deriving and generalizing the Selberg trace formula.
method Supersymmetric localization principle and path integral derivation.
result Derives Selberg trace formula on arbitrary compact Riemann surfaces and generic compact locally symmetric spaces.
Introduces a new model for mapping matrices to matrices, subsuming linear regression.
problem Learning matrix-to-matrix mappings from data.
method Partial trace regression model, leveraging quantum information theory.
result Relevance demonstrated in matrix-to-matrix regression and positive semidefinite matrix completion.
CausalSim corrects bias in trace-driven simulations for more accurate results.
problem Bias in trace-driven simulations due to system conditions during trace collection.
method CausalSim learns a causal model of system dynamics and latent factors from an RCT to remove bias from trace data.
result CausalSim reduces simulation errors by 53% and 61% compared to baselines, providing more accurate insights.
L-spaces and knot tracesmath.GT
New findings on knots and their traces, distinguishing L-space knots by their 0-trace.
problem Characterizing knots by their traces and Dehn surgeries.
method Combining Heegaard Floer homology with surface homeomorphisms and dynamics.
result The 0-trace detects every L-space knot, contrasting with characterizing surgeries.
Study of invariants on manifolds with boundary involving equivariant spectral flow and η-invariants.
problem Equivariant invariants on manifolds with boundary.
method Analysis of Dirac operators, winding numbers, spectral flow, Maslov indices, and η-invariants.
result Established relation between equivariant η-invariants and Maslov triple indices.
Group-equivariant subsampling layers improve CNNs' equivariance.
problem Non-translation equivariance in subsampling operations.
method Translation and group-equivariant subsampling/upsampling layers.
result Group-equivariant autoencoders learn equivariant representations.
This paper investigates the strength of the trace field as a commensurability invariant of hyperbolic 3-manifolds. We construct an infinite family of two-component hyperbolic link complements which are pairwise incommensurable and have the same trace field, and infinitely many 1-cusped finite volume hyperbolic 3-manifo…
Clarifies a trace for Heisenberg operators on contact manifolds.
problem Calculating the index of Heisenberg elliptic operators on contact manifolds.
method Introduced a new trace on Heisenberg pseudodifferential operators and constructed a cocycle in periodic cyclic cohomology.
result Simplified the construction of the trace on Heisenberg pseudodifferential operators.
We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.
Study of equivariant ribbon concordance using Khovanov homology.
problem Understanding equivariant ribbon concordance.
method Functoriality of equivariant Khovanov homology under equivariant cobordisms, and induced split injection.
result Equivariant ribbon concordances induce a split injection on equivariant Khovanov homology.
Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.
problem Analyzing the magnetic Laplacian on compact hyperbolic surfaces.
method Computed the trace formula for magnetic Laplacian energies above the Mane critical level.
result Asymptotic behavior of trace formula coefficients near the Mane critical level.
Sharp inequality found on three-balls for fourth order Sobolev traces.
problem Fourth order Sobolev trace inequality on three-balls.
method Established through equivalence to a third order Sobolev inequality on two-spheres.
result Sharp fourth order Sobolev trace inequality on three-balls.
Infinite knots have non-integer trace values.
problem Finding knots with non-integer trace values.
method Proved existence of infinitely many non-homeomorphic hyperbolic knot complements with specific trace properties.
result Infinitely many non-homeomorphic hyperbolic knot complements with non-integer trace values.
Defines a new homomorphism for strongly invertible knots, proving equivariant algebraic concordance.
problem Equivariant algebraic concordance of strongly invertible knots.
method Defining a homomorphism from equivariant concordance group to a new equivariant algebraic concordance group, proving it lifts known homomorphisms and provides new obstructions.
result Obtains a new obstruction to equivariant sliceness and novel lower bounds on equivariant slice genus.
Introduces expected eligibility traces for more efficient credit assignment in reinforcement learning.
problem Efficiently assigning credit to states and actions in reinforcement learning.
method Introduces expected eligibility traces, allowing updates to counterfactual sequences.
result Substantial improvements in temporal-difference learning can be achieved with expected traces.
Quantum trace map defined for 3-manifolds with torus boundaries.
problem Quantifying topological structures of 3-manifolds with torus boundaries.
method Defining a quantum trace map from skein module to a quantum torus module.
result Established a 3D quantum trace map for 3-manifolds with torus boundaries.
New knots found that resist trace detection.
problem Knots not detected by any trace.
method Extended existing results to new knots.
result Knots exist that share traces with infinitely many distinct knots and are not detected by any trace.
Quantum heat tracesmath-ph
We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction formulas expressing these new invariants in terms of some integral transforms of the u…
New hyperbolic manifolds found with same trace ring.
problem Finding non-commensurable hyperbolic manifolds with identical trace rings.
method Proved existence of infinitely many non-commensurable manifolds with same ambient group and trace ring.
result Infinitely many non-commensurable hyperbolic manifolds with the same ambient group and trace ring.
Study of equivariant movie moves for involutive links.
problem Equivariant cobordisms between involutive links.
method Equivariant Morse theory and singularity theory.
result 39 equivariant movie moves for isotopic cobordisms.
Sub-Riemannian Selberg trace formulae for compact quotients of SL(2, R)
problem Computing zeta-regularized determinants of sub-Laplacians
method Using Fourier decomposition and Selberg trace formulae
result Compact determinant formula expressed in terms of base hyperbolic surface and relative Selberg product
We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown to be classified by its equivariant holonomy modulo isomorphisms. We also show t…