Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.
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Universal eigenvarieties, triangu line Galois representations, and p-adic Lang- lands functoriality
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Proves unique stationary law for Clifford random monitored quantum circuits and computes leading asymptotics of steady magic, linear for odd-prime dimension mana and quadratic for qubit 2-stabilizer Rényi entropy.
Dimension corrections in non-semisimple walled Brauer algebras are counted via restricted Bratteli diagrams whose generating functions match the partition function of an infinite tower of simple harmonic oscillators.
Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
A dedicated global model structure for K-linear ∞-local systems is constructed via simplicial chain complexes, monoidal for base 1-types under the external tensor product.
The complexified exceptional Jordan algebra yields fermion mass ratios via a diagonal-action theorem on Sym^3(3) representations after triality breaking, with a universal eigenvalue spectrum fixed by the Jordan cubic.
Proves regular representation must appear in latent space of finite-group equivariant encoders and enforces it via auxiliary loss to match specialized equivariant models without added parameters.
Identifies the canonical |x|^{-2} term in scalar-flat ALE four-manifold metrics and shows the leading Weyl component vanishes precisely on crepant minimal resolutions of quotient singularities.
Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
A local reconstruction scheme for Codazzi defects in 4D Lorentzian branches uses a lexicographic residual and CP1 Toeplitz visibility to select the S(U(3)×U(2))/Z6 form and standard one-generation SM exterior package.
Under a division condition, tangential CR cohomology on compact Lie groups with left-invariant CR structures is finite-dimensional and computable on maximal tori, with necessity shown for a class of structures.
Derives combinatorial expression for degrees of tensor train varieties via integral geometry and releases Julia package TTVarietyDegree.jl.
Computes the right spectrum of the canonical G2-equivariant operator h, yielding slice-independent quartic curves and circles via SU(3) block decomposition after fixing complex slices in O.
Authors compute ring structure, coherent cohomology (via Lie algebra reduction), Poincaré duality compatibility, and Picard groups for supertori defined by odd-parameter translations in superspace.
Geometrizes Poisson summation for quadrics over number fields by relating Braverman-Kazhdan and theta-lift Schwartz spaces.
A unified representation-theoretic approach computes the complete Laplace-Beltrami spectra on homogeneous principal bundles and applies the results to classify scalar stability and Yamabe bifurcations on specific manifold families.
Multivariate super Krawtchouk polynomials are defined via representations of the general linear Lie superalgebra, with proofs of orthogonality, recurrence relations, and links to fermionic Fock-space zonal spherical functions.
The derived category of the even Clifford algebra sheaf embeds fully faithfully into that of the orthogonal Grassmannian fibration, enabling a semiorthogonal decomposition for k=2 up to a residual category computed in the smooth case with a conjecture for pencils.
Lattice QED is established as a quantum error-correcting code beyond stabilizers, with explicit recovery operations constructed via quantum reference frames for gauge and fermionic sectors.
Conjecture expressing asymptotic growth of indecomposable summands in monoid-representation tensor powers via the Brauer character table of the group of units, with a proof under an extra hypothesis plus exact and asymptotic length formulas in good characteristic.
The pushout of entangled and parameterized quantum information in monoidal categories yields the external tensor product on flat K-theory bundles.
Generalizes the perfectoid method to construct overconvergent automorphic sheaves whose global sections are overconvergent Siegel modular forms and establishes an explicit overconvergent Eichler-Shimura morphism.
Explicit computation of the cactus group action via Bender-Knuth generators on the subset of short semi-standard Young tableaux, with comparison to the full set.
A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
citing papers explorer
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Eigenvalue optimization via a first-variation formula
Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.
-
Invariant Measures and Weak-Magic-Injection Asymptotics in Random Monitored Quantum Circuits
Proves unique stationary law for Clifford random monitored quantum circuits and computes leading asymptotics of steady magic, linear for odd-prime dimension mana and quadratic for qubit 2-stabilizer Rényi entropy.
-
Oscillators from non-semisimple walled Brauer algebras
Dimension corrections in non-semisimple walled Brauer algebras are counted via restricted Bratteli diagrams whose generating functions match the partition function of an infinite tower of simple harmonic oscillators.
-
Typical entanglement entropy with charge conservation
Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
-
A Global Model Structure for $\mathbb{K}$-Linear $\infty$-Local Systems
A dedicated global model structure for K-linear ∞-local systems is constructed via simplicial chain complexes, monoidal for base 1-types under the external tensor product.
-
Fermion mass ratios from the exceptional Jordan algebra
The complexified exceptional Jordan algebra yields fermion mass ratios via a diagonal-action theorem on Sym^3(3) representations after triality breaking, with a universal eigenvalue spectrum fixed by the Jordan cubic.
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Algebraic Priors for Approximately Equivariant Networks
Proves regular representation must appear in latent space of finite-group equivariant encoders and enforces it via auxiliary loss to match specialized equivariant models without added parameters.
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Curvature at infinity of scalar-flat ALE four-manifolds
Identifies the canonical |x|^{-2} term in scalar-flat ALE four-manifold metrics and shows the leading Weyl component vanishes precisely on crepant minimal resolutions of quotient singularities.
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Quasi-Classical Braverman--Kazhdan Intertwiners via Quiver Varieties
Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
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Self-Reconstructing Codazzi Defects, $\mathbb{CP}^1$ Quantization, and the Minimal Standard-Model Carrier
A local reconstruction scheme for Codazzi defects in 4D Lorentzian branches uses a lexicographic residual and CP1 Toeplitz visibility to select the S(U(3)×U(2))/Z6 form and standard one-generation SM exterior package.
-
Cohomology of CR structures on compact Lie groups
Under a division condition, tangential CR cohomology on compact Lie groups with left-invariant CR structures is finite-dimensional and computable on maximal tori, with necessity shown for a class of structures.
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Degree of tensor train varieties via integral geometry
Derives combinatorial expression for degrees of tensor train varieties via integral geometry and releases Julia package TTVarietyDegree.jl.
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Octonionic structure operator and its right spectrum
Computes the right spectrum of the canonical G2-equivariant operator h, yielding slice-independent quartic curves and circles via SU(3) block decomposition after fixing complex slices in O.
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Cohomology of complex supertori
Authors compute ring structure, coherent cohomology (via Lie algebra reduction), Poincaré duality compatibility, and Picard groups for supertori defined by odd-parameter translations in superspace.
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Geometrization of summation formulae for quadrics
Geometrizes Poisson summation for quadrics over number fields by relating Braverman-Kazhdan and theta-lift Schwartz spaces.
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Explicit Laplace Spectra of Homogeneous Principal Bundles
A unified representation-theoretic approach computes the complete Laplace-Beltrami spectra on homogeneous principal bundles and applies the results to classify scalar stability and Yamabe bifurcations on specific manifold families.
-
Super Krawtchouk Polynomials via Lie Superalgebras
Multivariate super Krawtchouk polynomials are defined via representations of the general linear Lie superalgebra, with proofs of orthogonality, recurrence relations, and links to fermionic Fock-space zonal spherical functions.
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Semiorthogonal decompositions and components of derived categories of orthogonal Grassmannian fibrations
The derived category of the even Clifford algebra sheaf embeds fully faithfully into that of the orthogonal Grassmannian fibration, enabling a semiorthogonal decomposition for k=2 up to a residual category computed in the smooth case with a conjecture for pencils.
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Error Correction in Lattice Quantum Electrodynamics with Quantum Reference Frames
Lattice QED is established as a quantum error-correcting code beyond stabilizers, with explicit recovery operations constructed via quantum reference frames for gauge and fermionic sectors.
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Growth Problems for Representations of Finite Monoids
Conjecture expressing asymptotic growth of indecomposable summands in monoid-representation tensor powers via the Brauer character table of the group of units, with a proof under an extra hypothesis plus exact and asymptotic length formulas in good characteristic.
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Entanglement of Sections: The pushout of entangled and parameterized quantum information
The pushout of entangled and parameterized quantum information in monoidal categories yields the external tensor product on flat K-theory bundles.
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Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism
Generalizes the perfectoid method to construct overconvergent automorphic sheaves whose global sections are overconvergent Siegel modular forms and establishes an explicit overconvergent Eichler-Shimura morphism.
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On the action of Bender-Knuth generators of cactus group on the set of short semi-standard Young tableaux
Explicit computation of the cactus group action via Bender-Knuth generators on the subset of short semi-standard Young tableaux, with comparison to the full set.
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Generalization of Zeroth-Order Method for Quotients of Quadratic Functions
A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
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Boundary lines and Askey-Wilson type moments
Wilson line defect half-indices for 3d N=2 theories with confining boundaries are exactly Askey-Wilson type moments, obtained via dual vortex defects and effective spin shifts in the index computation.
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De Sitter Horizon Edge Partition Functions
Edge partition functions for totally symmetric tensors in dS_{d+1} are decomposed under so(d), with the linearized gravity case receiving contributions from shift-symmetric fields on S^{d-1} suggesting an embedded brane interpretation.
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Weyl algebras on Braverman-Kazhdan spaces
Studies differential operators on Braverman-Kazhdan spaces P^der backslash G and claims they share structural properties with Weyl algebras while developing D-module theory.