Specialty
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.
Scientific publication4 min read
Researchers propose a formal reduction method for time-dependent Hamiltonian systems whose symmetries can translate time, with worked examples showing how its conserved quantities behave.
Scientific publication4 min read
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.
Scientific publication3 min read
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.
Scientific publication4 min read
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).
Scientific publication3 min read
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.
Scientific publication4 min read
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.
Scientific publication4 min read
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.
Scientific publication4 min read
A theoretical mathematics preprint presents finite spin measures, an exact sequence for Ramond points, polynomial boundary-length volumes and recursions, while leaving the hyperbolic equivalence and all-genus even-odd symmetry unresolved.
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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.
Scientific publication3 min read
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.
Scientific publication4 min read
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.
Scientific publication3 min read
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.
Scientific publication3 min read
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.
Scientific publication3 min read
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.
Scientific publication3 min read
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.
Scientific publication4 min read
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.
Scientific publication5 min read
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 mathematical preprint reports coefficient-by-coefficient identities linking stable-pair and framed-sheaf series for local Hirzebruch geometries, while related projective-plane equations remain conjectural.
Scientific publication3 min read
A new mathematical preprint connects non-Galois quasi-Galois points on smooth quartic surfaces with a specific class of K3 surfaces, and reports an exact count for the Fermat quartic.
Scientific publication4 min read
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.
Scientific publication3 min read
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.
Scientific publication3 min read
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.
Scientific publication3 min read
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.
Scientific publication4 min read
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.
Scientific publication5 min read
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.
Scientific publication4 min read
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
A mathematical preprint introduces infinitely many distinct four-manifold structures and narrows the long-term behavior of the quantity Λ_s, while leaving its exact value unproved.
Scientific publication3 min read
A preprint in algebraic geometry gives an exact threshold for odd-dimensional quadrics, bounds the even-dimensional case and constructs uniform bundles that are not homogeneous.
Scientific publication4 min read
A mathematical preprint identifies fixed-evaluation quasimap moduli for Nakajima varieties with an explicit critical-locus stack, while deferring fuller derived details to a companion paper.
Scientific publication3 min read
A theoretical mathematics preprint presents a mixed-Hodge-module framework for studying cyclic covers on smooth and singular algebraic varieties.
Scientific publication4 min read