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, there are properties in syntax and morphology, such as constraints on movement and on spellout, which are asserted, not proven. Do these syntactic and morphological characterizations follow from the results of deeper truths about either the representations or the derivations? This dissertation will use two complementary perspectives, one representational and continuous (spectral graph theory) and one derivational and discrete (Hopf algebras), as mathematical machinery to explore this question. In the presentation, we will introduce these two approaches and then demonstrate their utility as a way of characterizing the nature of syntactic parameters. We will then conclude with a survey of the other topics that dissertation will address.
Past Event: Friday Lunch Talk: The Algebraic Foundations of Syntactic Structure (Isabella Senturia)
