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It is really unusual to find "parsing algorithm" and "direct isometries" in the same paper, so it's a bit of a genre-spanning publication. As the arxiv tags say, the key fields could be described as "algebraic geometry" and "rings and algebras". Things like SE2 refer to familiar groups (with useful geometric interpretations) that mathematicians encounter frequently, so group theory is a prerequisite also. Apart from the geometry, most of this is probably covered by "abstract algebra" for which there are good resources online, including lectures on YouTube.

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