Joshua Evan Greene

activity

20232026

collaborators

5 papers

math.GT2026

Jordan curves inscribe a positive measure of rectangles

Joshua Evan Greene, Andrew Lobb

Suppose that $γ \subset C$ is a Jordan curve of diameter $2 R$ which encloses a region of area $A$ . We prove that there exists a subset $I \subset (0, π)$ of measure at least…

math.SG2024

Polynomial Inscriptions

Joshua Evan Greene, Andrew Lobb

We prove that for every smooth Jordan curve $γ \subset C$ and for every set $Q \subset C$ of six concyclic points, there exists a non-constant quadratic polynomial…

math.SG2024

Square pegs between two graphs

Joshua Evan Greene, Andrew Lobb

We show that there always exists an inscribed square in a Jordan curve given as the union of two graphs of functions of Lipschitz constant less than $1 + 2$ . We are motivate…

math.SG2024

Floer homology and square pegs

Joshua Evan Greene, Andrew Lobb

We construct a version of Lagrangian Floer homology whose chain complex is generated by the inscriptions of a rectangle into a real analytic Jordan curve. By using its associated s…

math.GT2023

Special Alternating Knots are Band Prime

Joe Boninger, Joshua Evan Greene

We prove that a special alternating knot does not decompose as a non-trivial band sum. This restricts concordances from special alternating knots, and we conjecture that special al…