Outputs (2)

The rectangular peg problem (2021)
Journal Article
Greene, J., & Lobb, A. (2021). The rectangular peg problem. Annals of Mathematics, 194(2), 509-517. https://doi.org/10.4007/annals.2021.194.2.4

For every smooth Jordan curve and rectangle R in the Euclidean plane, we show that there exists a rectangle similar to R whose vertices lie on . The proof relies on the theorem of Shevchishin and Nemirovski that the Klein bottle does not admit a smoo... Read More about The rectangular peg problem.

A refinement of Khovanov homology (2021)
Journal Article
Lobb, A., & Watson, L. (2021). A refinement of Khovanov homology. Geometry & Topology, 25(4), 1861-1917. https://doi.org/10.2140/gt.2021.25.1861

We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this... Read More about A refinement of Khovanov homology.