Algebraic properties of linguistic structure (Isabella Senturia, Yale / Caltech)

The recognition that theoretical models of natural language syntax have robust algebraic foundations is longstanding. Both the syntactic structures proposed (trees, semirings, etc.) and metrics developed to understand them (the Chomsky hierarchy, partial orders, and so forth) closely resemble structures and systems familiar to theoretical mathematicians (groups, rings, fields, …). Despite the underlying mathematical tools, rarely do structural properties of language get analyzed at an algebraic level. I use two complementary perspectives, one representational and continuous (spectral graph theory) and one derivational and discrete (Hopf algebras), as lenses to explore mathematical properties of linguistic structure. I will also show a connection between the two approaches through a case study on the problem of learning syntactic parameters.