Kaya Arro

About me

I am a mathematician working in abstract homotopy theory.

From Fall 2023 - Spring 2025, I was a visiting assistant professor in the Department of Mathematics at the University of California, Riverside. I left left that position in order to be free to emigrate from the United States as soon as possible.

Before working at UCR, I was a PhD student of Tom Goodwillie at Brown University. Before that, I studied with Michael Ching as an undergraduate at Amherst College.

You can reach me by email at kaya [dot] arro [at] gmail [dot] com. Here is my CV. I am currently on the job market.

My name is pronounced /ˈkaɪə ˈɑɹo/. My pronouns are “they” (English), «elle» (español), and «hen» (norsk). My surname used to be “Ferendo”.

Kaya in a tree — Photo credit: Chris Grossack

Research

I am an abstract homotopy theorist/∞-category theorist and am easily excited by most aspects of the field. My specialization is in functor calculus.

I am currently working on two interrelated projects. The first develops a framework for functor calculi in an arbitrary ∞-equipment, providing a unified organizational scheme for studying the many flavors of functor calculus, including functor calculi of enriched or internal ∞-categories. Among other goals, one objective is to generalize the Bauer–Burke–Ching–Goodwillie tangent structure to this setting.

In my second project, I specialize this framework to functor calculi formally similar to the FI-calculus introduced in my dissertation. These "corepresentation functor calculi" provide an ∞-categorical elaboration of the phenomenon of representation stability.

You can read about these projects in greater detail in my research statement.

Teaching

Teaching is an extremely rewarding and joyful part of my profession and I believe I have a great responsibility to my students. I elaborate my thoughts in my teaching statement.

I have taught precalculus, differential, integral, and multivariable calculus, linear algebra (using team-based inquiry learning), and topology. I have supervised undergraduate directed reading projects on category theory, model category theory and ∞-category theory, topos theory, and higher algebra.

I designed a rigorous, 30-hour course introducing high school students to logic, proof-writing, and the foundations of mathematics (focusing on Peano arithmetic and Zermelo-Fraenkel set theory) for the Summer@Brown program and have taught the course five times.

I am a recipient of the Brown University Math Department's Outstanding Teaching Award.

Personal

I grew up in Maryland and spent the first twelve years of my adulthood in New England. After two years in Riverside, I currently reside in Long Beach, California with my life partner of 15 years and our dog, Rascal.

Outside of mathematics, my hobbies include photography, spending time in nature, practicing Norwegian, coding, playing Celtic fiddle music, and writing.

My first significant coding project, sc-simplify, is a tool written in Rust for simplifying large simplicial complexes in order to accelerate homology calculations.

You can also find the source code for this website on GitHub.