Specialty
A mathematical preprint connects the diagonal F-threshold of a graph's binomial edge ideal to features such as matchings, independent sets and clique matchings.
Scientific publication4 min read
A version 1 arXiv preprint presents a conditional route for excluding non-trivial solutions of a generalized Fermat equation at sufficiently large prime exponents. Its imaginary quadratic example lists three relevant unit solutions and reports relative density 5/6 among squarefree positive integers.
Scientific publication4 min read
A mathematical preprint shows that associated-prime sets for powers of monomial ideals need not move in one direction: the maximal ideal can appear and later disappear.
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A mathematical preprint reduces operators on two finite groups to named families and adds structural results on centers, bijectivity, constructions and splitting.
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A formal mathematical preprint reports equality between the two constructions and traces it through algebraic factors, modules and knot normalization.
Scientific publication3 min read
A new mathematical preprint gives a conditional route from a well-behaved 2-sphere boundary to a Kleinian group with peripheral subgroups virtually isomorphic to the two-dimensional integer lattice.
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A new mathematical preprint reports a proof of Mühlherr’s Twist Conjecture and an algorithmic answer to the isomorphism problem for Coxeter groups.
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A mathematical preprint describes a chain of algorithms that turns subgroup membership in finite-base wreath products into a decidable problem.
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A mathematical preprint reports unconditional lower and upper certificates for a compact-window version of the Weil quadratic form. Its numerical pattern supports, but does not prove, a Landau–Widom-type law for the true infinite-dimensional profile.
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A theoretical arXiv preprint shows that full multigraded regularity preservation fails for some ideals, then uses lower bounds and colored algebraic shifting to settle two colorful fractional Helly conjectures.
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A preprint constructs one-dimensional hypersurface families where a general reduction bound for generalized Loewy length is exact in some cases and one unit high in others.
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A new mathematical preprint proves that uniform Littlewood counterexamples include positive-dimensional families, including pairs whose first coordinate is badly approximable.
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The paper counts bounded products of integer matrices and finds different asymptotic growth laws for fixed targets with nonzero determinant and for the zero matrix. It also proves an upper bound that applies uniformly to nonsingular integer targets.
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The preprint gives conditional theorems for carrying fine Selmer-group finiteness and pseudonullity from a cyclotomic-like extension to a larger p-adic Lie extension. It also describes a case where the comparison has zero kernel but a non-pseudonull cokernel.
Scientific publication4 min read
A mathematical preprint gives an exact Hausdorff-dimension formula for approximable points on the three-dimensional Veronese curve, with the dominant term changing at λ = 2/3.
Scientific publication3 min read
A formal result in reverse mathematics reports that the thin-set principle RT^n_{<∞,ℓ} implies the matching Σ^0_{n+1}-bounding principle BΣ^0_{n+1} over RCA_0 for every n and ℓ at least 1.
Scientific publication3 min read
A mathematical argument uses a scale-sensitive rapid game and lattice dynamics to calculate the Hausdorff dimension of an intersection involving well-approximable and inhomogeneously badly approximable numbers.
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A version-1 arXiv preprint describes an explicit elliptic K3 surface over Q(t) with exact generic Mordell-Weil rank 17. It also reports selected fibers and base changes with higher rank lower bounds, including at least 28 and at least 19.
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An arXiv preprint sets out a framework for studying abeloid varieties over p-adic fields. Its main results are theorem-level equivalences and constructions linking reduction, monodromy, p-divisible groups and rational-point uniformization.
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A mathematical preprint proposes a shared framework for arithmetic volume, distortion functions and equilibrium measures, with several equivalence results under specific assumptions.
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A new mathematical preprint recasts direct integration of Banach-space families as a functor and proves exactness, local approximation, duality and kernel-representation results under stated assumptions. It also shows that direct-integral sheaves can fail infinite gluing.
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A mathematical preprint classifies contravariantly finite resolving subcategories over henselian local rings, leaving three possible forms, and gives a separate two-way result for finite-type subcategories.
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A formal category-theory analysis gives equivalent criteria for absolute weighted colimits and shows how changing both the diagram and weight can produce a Cauchy form.
Absolute colimits, Applied Categorical Structures 34:43 (dedicated to Bob Paré, 2026)4 min read
A mathematical preprint gives sufficient local conditions for Vietoris-Rips complexes and proves contractibility at parameter 2 for right-angled Artin groups whose defining graphs are triangle-free, using the standard word metric.
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The preprint gives a bijective description of characters of quantum symmetric-pair coideal subalgebras, reducing the problem to torus data and split-part choices.
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A 2026 arXiv preprint derives explicit asymptotic formulas for a mixed second moment of quadratic Dirichlet L-functions over monic irreducible polynomials, with separate results for completed and uncompleted forms.
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A mathematical preprint reports a uniform pointwise bound for short Weyl sums and an asymptotic formula for a constrained Waring representation count. Its stated improvement replaces an earlier lower threshold for H with a larger exponent, allowing the formula to cover shorter intervals under the theorem’s assumptions.
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A new arXiv preprint recasts an alternative Collatz integer map as a Boolean-polynomial operator, links it to finite-support binary sequences and derives explicit formulas for its carry terms, while leaving further analyses open.
Scientific publication3 min read
A theoretical study sets an explicit upper bound on minimally transitive subgroups of S_n and shows that, at prime-power degrees, the same n log(n) growth scale persists after permutational isomorphism classes are counted.
Scientific publication3 min read
A theoretical study connects three properties in rigid tensor-triangulated categories and constructs a Baer category with a universal factorization property.
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An arXiv preprint reports a power-saving asymptotic for a mixed second moment of Dirichlet and twisted modular L-functions at the central point, subject to Selberg’s eigenvalue conjecture and a factorization condition on the modulus.
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A proof-based preprint finds a sharp polynomial-logarithmic scale for the smallest positive sum-of-digits bias at fixed binary weight, and identifies the block patterns that approach it.
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The work recasts the successor and limit stages of transfinite jump iteration as a fixed-point problem in domain theory.
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A mathematical construction gives a family of groups whose first ℓ2-Betti number can be any natural number even though their normal rank is one, contradicting the unrestricted Osin–Thom conjecture.
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A mathematical preprint reports an explicit local formula and a conjectural global identity for degree-2 Siegel cusp forms, with conditional implications for norms, Fourier coefficients and central L-values.
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Explicit constructions show that a one-dimensional local ring with the strong finite type property can have a polynomial extension that is not strong finite type, with related examples in prime, zero and mixed characteristic.
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A mathematical preprint lays out a fully constructive route through conic frames, then establishes equivalences among Esakia locales, Esakia frames, Heyting algebras and Heyting frames.
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A mathematical preprint asserts that one tightly specified three-term pattern cannot occur, while leaving broader cases outside its result.
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A preprint reports a three-way equality among canonical-basis partitions, then derives a Richardson-variety identity and a type-A test for weights in Bruhat interval polytopes.
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A proof-based mathematical study develops an upper bound for the index of Borel subalgebras in gl(m|n) and basic classical Lie superalgebras, excluding psl(2|2). It also shows that several associated module indices vanish, including those for the nilradical, its ideals and duals of abelian ideals.
Scientific publication4 min read