## About me

I am a visiting assistant professor in the Department of Mathematics at the University of California, Riverside. My office is room 275A of Skye Hall.

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

Here is my CV.

You can reach me by email at kaya [dot] arro [at] ucr [dot] edu.

My pronouns are "they" (English), «elle» (español), and «hen» (norsk). My surname used to be "Ferendo".

## Research

I am an abstract homotopy theorist/∞-category theorist and am easily excited by almost any aspect of the field, but particularly by the use of ∞-categories as a tool for elucidating structures in homotopy theory.

My current work lies within the field of functor calculus and specifically deals with new flavors of functor calculus bearing certain similarities to Michael Weiss' orthogonal calculus. I also have an interest in the tangent (∞,2)-categories of Bauer, Burke, and Ching, and specifically their tangent structure for the Goodwillie calculus of differentiable ∞-categories.

In my dissertation, I show that representation stability for FI-modules can be fit pleasantly into a larger, ∞-categorical functor calculus framework I call FI-calculus. You can read a preprint of my thesis research and my research statement. There are also slides from a talk on the material.

Some of my current work in progress extends FI-calculus to an axiomatic system for a family of functor calculi that I call corepresentation functor calculi. Slides discussing this generalization of FI-calculus are available.

## 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 am currently teaching Math 7B, integral calculus for life sciences, and Math 10B, integral calculus of several variables.

In the past, I have taught precalculus, differential, integral, and multivariable calculus, linear algebra (using team-based inquiry learning), and undergraduate topology.

During the summer, I teach a rigorous, 30-hour introduction to logic, proof-writing, and the foundations of mathematics for high school students in the Summer@Brown program. The summer of 2024 will be my fifth time teaching the course.

In 2022 I received the Brown University Math Department's Outstanding Teaching Award.

## Personal

I grew up in Maryland and spent my early adulthood in New England. This year is my first time living away from the East Coast.

I live with my life partner of 13 years and our dog, Rascal.

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