I spend a lot of time keeping up with the most recent arXiv papers in the subject classes “Algebraic Topology”, “Combinatorics”, “Category Theory”, “Geometric Topology”, “Quantum Algebra”, and “Representation Theory”. Here I will list those papers which I find particularly interesting, together with a description of how the results fit into the scope of my research. Alternatively, sometimes I may just write posts consisting of new ideas I have which are not yet in article form. Please feel free to contact me if anything here sounds like something you may want to work on. I am always looking for new collaborators.
This paper, by Jacob White, the focus is on the study of Cohen-Macaulay Hopf monoids in the category of species. Some insights from the abstract: "The goal is to apply techniques from topological combinatorics to the study of polynomial invariants… Continue Reading
I found this paper on the arXiv a couple of months ago and from time to time I go back to it to try and understand this new diagrammatic language. I think the abstract is quite informative (more so than… Continue Reading
In this paper by Alexander McCleary and Amit Patel, they build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite lattice, and the output is a persistence diagram defined… Continue Reading