My research develops mathematical frameworks for meaning, reasoning, and abstraction to study symbolic and subsymbolic approaches to language and cognition. My current work applies categorical and relational methods to abstraction and analogy in ARC-style reasoning tasks.

In addition to my work on abstraction and analogy, I am woking on various aspects of meaning representation and grounding problems, including the geometry and topology of representation spaces, time-evolving semiotics, and typologies of writing systems as relevant to semiotics and meaning representation.