Mathematical structures in generative linguistics - Matilde Marcolli

Mathematics Department Colloquium - March 28, 2024
Stony Brook University

Matilde Marcolli, Caltech

Title: Mathematical structures in generative linguistics
Abstract: Mathematics is the study of structures. While most people associate mathematics with numbers, the reason why numbers are of interest to mathematicians is because they exhibit very deep and interesting structures. More generally, various types of algebraic and geometric structures play a crucial role in many branches of mathematics and have found important applications to other sciences, starting with theoretical physics. It is less widely known that generative linguistics also makes use of a range of interesting mathematical structures, in the study of the production, parsing, variability and universal principles of human languages. I will present an overview of the main mathematical aspects of generative linguistics, from the early development of the theory of formal languages to new methods involving Hopf algebras, and geometric spaces involved in the modeling of semantics and of syntactic variation across languages.