Pure and applied mathematics including algebra, analysis, geometry, topology, and probability. ← all categories
We present new results on hamilton cycles with applications to hypergraphs. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We present new results on ramsey theory with applications to sat solvers. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: derived categories of cubic fourfolds containing a plane are equivalent to k3 surfaces of degree 14. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We establish new results concerning supersingular surfaces in the context of artin invariant, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from crystalline cohomology with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.
We establish a new result in algebraic geometry and combinatorics: the number of antichains in the boolean lattice 2^[n] grows as 2^(1.0000134 * binom(n, n/2)) for large n.
We present new results on sphere packing with applications to energy minimization. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: moduli spaces of stable maps to p^1 x p^1 have picard number exactly 3 for genus g >= 2. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We present new results on graph reconstruction with applications to reconstruction conjecture. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: the hodge conjecture holds for codimension-2 cycles on abelian fourfolds with cm by q(zeta_5). Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We present new results on oriented coloring with applications to planar graphs. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: explicit height bounds for rational points on bielliptic curves of genus 2 over q. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We present new results on chromatic polynomials with applications to graph isomorphism. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: distance-regular graphs with intersection number a_1 = 0 are classified for diameter d >= 7. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We establish new results concerning mirror symmetry in the context of grassmannian, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from bps invariants with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.
We present new results on helly theorem with applications to lattice convexity. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish new results concerning brauer group in the context of purity, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from mixed characteristic with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.
We present new results on extremal combinatorics with applications to hypergraphs. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: the chow ring of the moduli space of spin curves m_g^{1/2} is tautological for g >= 12. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We establish new results concerning non abelian hodge in the context of singular varieties, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from higgs bundles with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.
We establish a new result in algebraic geometry and combinatorics: bridgeland stability conditions on the derived category of p^3 form a connected space. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.