Cuts and penalties: comment on "The clustering of ultra-high energy cosmic rays and their sources"

In a series of papers we have found statistically significant correlations between arrival directions of ultra-high energy cosmic rays and BL Lacertae objects. Recently, our calculations were partly repeated by Evans, Ferrer and Sarkar with different conclusions. We demonstrate that the criticism of Evans, Ferrer and Sarkar is incorrect. We also present the details of our method.Comment: Replaced with version accepted for publication in Phys. Rev.

An sl_n stable homotopy type for matched diagrams

There exists a simplified Bar-Natan Khovanov complex for open 2-braids. The Khovanov cohomology of a knot diagram made by gluing tangles of this type is therefore often amenable to calculation. We lift this idea to the level of the Lipshitz-Sarkar stable homotopy type and use it to make new computations. Similarly, there exists a simplified Khovanov-Rozansky sl_n complex for open 2-braids with oppositely oriented strands and an even number of crossings. Diagrams made by gluing tangles of this type are called matched diagrams, and knots admitting matched diagrams are called bipartite knots. To a pair consisting of a matched diagram and a choice of integer n >= 2, we associate a stable homotopy type. In the case n = 2 this agrees with the Lipshitz-Sarkar stable homotopy type of the underlying knot. In the case n >= 3 the cohomology of the stable homotopy type agrees with the sl_n Khovanov-Rozansky cohomology of the underlying knot. We make some consistency checks of this sl_n stable homotopy type and show that it exhibits interesting behaviour. For example we find a CP^2 in the sl_3 type for some diagram, and show that the sl_4 type can be interesting for a diagram for which the Lipshitz-Sarkar type is a wedge of Moore spaces.Comment: 62 pages, color figure

‘Genetic Coding’ Reconsidered : An Analysis of Actual Usage

I thank George Pandarakalam for research assistance; Hans-Jörg Rheinberger for hosting my stay at the Max Planck Institute for History of Science, Berlin; and Sahotra Sarkar and referees of this journal for offering detailed comments. Funded by the Wellcome Trust (WT098764MA).Peer reviewedPublisher PD

A combinatorial description of the Heegaard Floer contact invariant

In this short note, we observe that the Heegaard Floer contact invariant is combinatorial by applying the algorithm of Sarkar--Wang to the description of the contact invariant due to Honda--Kazez--Matic. We include an example of this combinatorial calculation.Comment: 6 page

A Simplification of Combinatorial Link Floer Homology

We define a new combinatorial complex computing the hat version of link Floer homology over Z/2Z, which turns out to be significantly smaller than the Manolescu-Ozsvath-Sarkar one.Comment: 20 pages with figures, final version printed in JKTR, v.3 of Oberwolfach Proceeding

Localization in Khovanov homology

We construct equivariant Khovanov spectra for periodic links, using the Burnside functor construction introduced by Lawson, Lipshitz, and Sarkar. By identifying the fixed-point sets, we obtain rank inequalities for odd and even Khovanov homologies, and their annular filtrations, for prime-periodic links in $S^3$