Kaya Arro

About me

Since Fall 2023 I have been 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. I am currently on the job market and am interested in jobs in both academe and industry.

You can reach me by email at kaya [dot] arro [at] gmail [dot] com.

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 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. Another project in progress with Michael Ching aims to describe differential bundles in the Goodwillie tangent structure for differentiable ∞-categories of Bauer, Burke, and Ching.

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.

This quarter I am teaching sections 020 and 030 of Math 7B, integral calculus for the life sciences.

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

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.

In 2022 I received 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. This is my first time living away from the East Coast.

I live with my life partner of 14 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. I have also written a version of the same algorithm in Python and am hoping it will be included in Sage.

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