Tootfinder

Hmm, ikke sååå fedt at bo tæt på lufthavnen når russerne skal markere sig …
https://www.dr.dk/nyheder/indland/droner-lukker-koebenhavns-lufthavn

Droner lukker Københavns Lufthavn
Politiet er massivt til stede i Københavns Lufthavn på grund af uidentificerede droner.

Morse matchings and Khovanov homology of 4-strand torus links
Tuomas Kelom\"aki
https://arxiv.org/abs/2507.15060 https://arxiv.org/pdf/2507.15060

Morse matchings and Khovanov homology of 4-strand torus links
Given a link or a tangle diagram, we define algorithmic Morse theoretic simplifications on their Khovanov homology. In contrast to Bar-Natan's scanning algorithm, the cancellations are postponed until the end and performed in one go. Although our novel approach is computationally inferior to Bar-Natan's algorithm, it side-steps the need for a large amount of iterations, making it more fitting for theoretical analysis. Our main application is towards integral Khovanov homology of 4-strand torus …

Continuing to experiment with plotting the #fork network of #QEMU for my talk at #kvmforum2025. I need to figure out a way to filter out normal developer forks from the rest.

Erstmal einen Espresso und Ruhe.

Pandemic preparedness. Staying ahead.
https://open.substack.com/pub/senscience/p/staying-ahead-of-sars-cov-2-inside?r=8k45f&utm_medium=ios

Labeled Chip-Firing on Undirected $k$-ary Trees
Ryota Inagaki, Aaron Lin
https://arxiv.org/abs/2509.17358 https://arxiv.org/pdf/2509.17358

Labeled Chip-Firing on Undirected $k$-ary Trees
We explore labeled chip-firing on undirected $k$-ary trees, trees where every vertex has degree $k+1$. First, we extend known results for binary trees from Musiker and Nguyen, including the endgame and the locations of the smallest and largest chips, as well as relations between chips at different vertices. Then, inspired by recent work on the binary tree by Inagaki, Khovanova, and Luo, we use these properties to construct an upper bound, which we call the zigzag bound, on the number of stable …

Lectures on SL(3) foams and link homology
Mikhail Khovanov, Dmitry Solovyev
https://arxiv.org/abs/2507.17119 https://arxiv.org/pdf/2507.17119

Lectures on SL(3) foams and link homology
These notes are based on the three lectures that one of the authors gave at Tsinghua University in the summer of 2023 as part of the workshop on Geometric Representation Theory and Applications. They contain an introduction to the evaluation of $\mathsf{SL}(3)$ foams and the associated topological theory of trivalent planar graphs and foam cobordisms between them. A categorification of the Kuperberg quantum $\mathfrak{sl}_3$ web and link invariant and the Robert-Wagner $\mathsf{SL}(N)$ foam eva…

Computing Khovanov homology of tangles
Li Shen, Jian Liu, Guo-Wei Wei
https://arxiv.org/abs/2508.14398 https://arxiv.org/pdf/2508.14398

Computing Khovanov homology of tangles
The computation of Khovanov homology for tangles has significant potential applications, yet explicit computational studies remain limited. In this work, we present a method for computing the Khovanov homology of tangles via an arc reduction approach, and we derive the Poincaré polynomial for simple tangles. Furthermore, we compute the Poincaré polynomials of tangles with at most three crossings.

Khovanov homology of tangles: algorithm and computation
Li Shen, Jian Liu, Guo-Wei Wei
https://arxiv.org/abs/2508.14404 https://arxiv.org/pdf/2508.14404

Khovanov homology of tangles: algorithm and computation
Knot, link, and tangle theory is crucial in both mathematical theory and practical application, including quantum physics, molecular biology, and structural chemistry. Unlike knots and links, tangles impose more relaxed constraints, allowing the presence of arcs, which makes them particularly valuable for broader applications. Although Khovanov homology for knots and links has been extensively studied, its computation for tangles remains largely unexplored. In our recent work, we provide a topo…

An Intrinsic $L_{\infty}$-Algebra on the Khovanov-Sano Complex
Takahito Kuriya
https://arxiv.org/abs/2509.15018 https://arxiv.org/pdf/2509.15018

An Intrinsic $L_{\infty}$-Algebra on the Khovanov-Sano Complex
This paper reinterprets the symmetries of equivariant Khovanov homology, discovered by Khovanov and Sano, within the Batalin-Vilkovisky (BV) formalism. We identify the Shumakovitch operator $\hatν$ as a BV Laplacian whose nilpotency, a consequence of the algebra's defining relations, induces an $L_{\infty}$-algebra on homology. We prove this structure is non-trivial through explicit computations of higher brackets. Furthermore, we construct a dual $L_{\infty}$-structure, suggesting a unifying …