Mantis Discovery
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Papers · 4

Research

Every paper is on Zenodo with a DOI, free to read under CC BY 4.0. Each paper’s page lists what the paper shows and what it does not claim. Further down the page are posters for projects that are not finished yet.

Every line that crosses the square hits this fence. Its length is √2 + √6/2, the shortest known.

Sharp reach bounds and quantitative localization for opaque setsMathematics, discrete geometry

  1. Sharp reach bounds and quantitative localization for opaque sets

    We prove two sharp inequalities for barriers that block every line through the unit square, and show what any barrier shorter than √2 + √6/2 must look like. MathematicsDiscrete geometryZenodo 234846291,433 records in MantisGeometric reasoningTraceabilityCertificates

  2. Clique minors and fractional clique covers in graphs with independence number two

    For graphs with independence number two, we turn clique-minor bounds into chromatic bounds without accumulating error, and apply them to Hadwiger’s conjecture. MathematicsGraph theoryZenodo 234845334,459 records in MantisGeometric reasoningTraceabilityAuditsCertificates

  3. Stationary response and singular limits in a linear zonal gyrokinetic model

    We derive the stationary response of a linear periodic gyrokinetic model without assuming uniform kinetic relaxation, and show that two of its limits do not commute. PhysicsPlasma physicsZenodo 234848001,579 records in MantisGeometric reasoningTraceability

  4. Locality and global information in elliptic solvers

    A local approximation to an elliptic inverse needs on the order of nᵈ/(w + 1)ᵈ shared coordinates of global information, and a linear construction achieves this. Machine learningScientific machine learningZenodo 234844553,122 records in MantisGeometric reasoningTraceability

Work in progress

We are still working on these projects. Each poster describes the problem and the results we have so far.