Specialty
An arXiv preprint proves coefficient-by-coefficient blowup identities for local Hirzebruch geometries, then extends the framework conditionally to local P2.
Scientific publication3 min read
A mathematical preprint reports exactly 28 quasi-Galois points on the Fermat quartic, including four Galois points and 24 points that are not Galois. It also gives an algebraic test and a K3-surface correspondence for studying such points on smooth quartic surfaces.
Scientific publication3 min read
A mathematical preprint reports that every actual reduced polar hyperplane of a plane-curve topological zeta function lies in the multivariable Bernstein-Sato zero locus. It also finds matching non-equivariant motivic and topological pole data in that setting, while higher-dimensional examples show the pattern has limits.
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A theoretical mathematics preprint proves that Ramond boundary points occur in even numbers and develops finite measures and recursive volume functions for spin moduli spaces.
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A theoretical preprint establishes a sharp universal lower bound for the magnetic-field norm when a non-trivial Dirac zero mode exists on a sphere, while leaving a related Sobolev constant unresolved.
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An arXiv preprint identifies the order conditions behind derived window convolutions, shows how branching can disrupt their composition, and finds rooted forests where the construction supports an interleaving distance.
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The paper builds arithmetic de Rham and Hyodo-Kato stacks, then proves categorical links to rigid cohomology, isocrystals, D-modules and related arithmetic operations under stated assumptions.
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A mathematical framework reduces symmetric time-dependent Hamiltonian systems while preserving their principal-bundle structure, with results illustrated by two mechanical examples.
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A mathematical construction gives three-dimensional normal Q-Gorenstein varieties with minimal log discrepancy one and Cartier index equal to any chosen positive integer, challenging Shokurov's index conjecture in the non-klt setting.
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A preprint examines the Roberts–Street nerve of the walking coinductive equivalence. It finds the nerve is non-contractible in one formal homotopy theory, while every nonnegative thinification and the left-category reflection are contractible.
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A mathematical preprint reports unusually large-centroid tensor families, conditional minimal-border-rank theorems and lower reported upper bounds from laser-method calculations for matrix multiplication. The results are algebraic and do not include measured runtimes or an implemented speedup.
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A formal mathematical argument says strong local stability passes to the stated Artin–Schreier base-change when every Frobenius base-change in the required range is already strongly locally stable.
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A proof-based study develops a tree-based route into the integral homology of SL2(Z[1/n]) and gives an explicit intermediate description for the subgroup Γ0(n).
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A conditional proof for smooth, closed five-dimensional Riemannian manifolds produces a conformal metric with positive scalar curvature and positive Q-curvature, provided two invariants and an initial metric meet the stated conditions.
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A new geometry preprint gives a universal factor-of-two bound for simple polygons, proves the coefficient cannot be increased, and formally checks its main theorems in Lean 4.
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A mathematical preprint reports that type A Hessenberg varieties have one dimension across each sheet when their Hessenberg function is fixed; a broader Poincaré-polynomial statement remains conjectural.
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A new mathematical preprint develops a two-curve description of the variational equation around a KdV cnoidal wave. It finds compatible solution constructions and a three-dimensional solution space, but leaves a proposed differential-Galois result unproved.
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A mathematical preprint assigns an unknotting number of 3 to named alternating knots in its 11-, 12- and 13-crossing lists. It narrows another group to 3 or 4 and gives a conditional same-sign requirement for a separate group if its unknotting number is 2.
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A mathematical preprint gives an explicit model for the Borromean-rings link Floer complex, shows it is not homotopy equivalent to a free resolution of its homology, and finds eight algebraic involution models.
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A proof-based study establishes local existence and uniqueness for the YMHS flow on compact Riemann surfaces, with Sobolev regularity and energy control under stated geometric assumptions.
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A proof-based mathematical construction gives dense Chern slopes from 1/2 to 3 for surfaces with a prescribed fundamental group, and proves the ample-canonical case from 1/2 to 2.
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A mathematical preprint reports Euclidean-complete affine maximal type hypersurfaces that are not elliptic paraboloids across a stated parameter interval, alongside a conditional three-type classification of two-dimensional Calabi affine surfaces.
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A mathematics preprint describes a sufficient condition for admissibility in generalized Alexander quandles and verifies it in one finite example.
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A mathematical preprint reports that nonzero-degree self-maps of generalized Grassmannians induce either a degree-determined Adams operation or that operation combined with a Dynkin symmetry.
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A proof-based mathematical study identifies the geometric Langlands image of the constant sheaf on BunG and gives a functorial description for arbitrary finite-rank local systems.
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A mathematical preprint develops p-adic models for p-complete spaces, recovers key homotopy operations, and connects finite-realization tests with varieties and Galois representations.
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An analytic geometry paper challenges a proposed boundary-eigenvalue threshold while leaving the best eigenvalue constant and broader boundary-area conjecture unresolved.
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A proof-driven mathematical study turns tautological pushforwards from relative Hilbert schemes into universal κ-class series, with recursive curve formulas and a complete codimension-one surface calculation.
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A new mathematical preprint gives finite algebraic tests for deciding when the Cox ring of a toric point blow-up is generated in Rees multiplicity one. It also classifies several important cases and applies the criteria to 225 canonical Fano tetrahedra.
Scientific publication4 min read
A formal algebraic proof gives an exact multiplicative rule for Bernstein-Sato polynomials of products of non-zero ideals, with a conditional result for the strong monodromy conjecture.
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The preprint studies four Painlevé cases, reporting trivial action for the unextended affine Weyl group where established and matching finite Weyl-group monodromy across analytic, algebraic and combinatorial constructions.
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An analytical study of invariant geometric flows on Lie groups reports soliton limits after rescaling, local stability near standard Bismut-flat metrics and instability in a non-standard example.
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The paper builds rational elliptic surfaces from three Platonic reflection groups and traces their singular fibres, integer sequences, Laurent-polynomial representations and monodromy.
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A mathematical preprint reports a diagram-readable grading bound for colored gl_N link homology and a related lower bound using the Legendrian Thurston–Bennequin number.
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A theoretical mathematics preprint constructs an index-two half-signature extension of the three-dimensional oriented bordism bicategory and classifies its componentwise and global linear representations.
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A theoretical preprint proves a product rule for Goodwillie derivatives and applies the framework to operads, pointed spaces, algebras and sheaves.
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A mathematical preprint studies two singularity configurations in cubic-surface families and proposes a global model built over an elliptic curve. Its smooth-stratum fibers are reported to contain 72 isolated points, while the boundary identification rests on theorem-level arguments in the paper.
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A mathematical preprint reports that reduced Gröbner bases can separate selected links that share the same multivariable Alexander polynomial.
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A new arXiv preprint develops coarse-geometric criteria for deciding when closed subgroups act properly on homogeneous spaces built from invertible upper triangular matrices. The results are sufficient conditions, not universal tests, and are illustrated with contrasting constructed examples.
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A mathematical preprint narrows the topological possibilities for several compact geometries, including three- and four-dimensional solitons and selected BHE structures.
Scientific publication4 min read