Our Summer Research Associates in 2025
Another year, another cohort of wonderful Summer Research Associates (RAs) at Topos working on exciting projects. As is now the custom, we’ve asked each of them to introduce themselves and write a little bit about what they’ll be working on over the summer, with more detailed blog posts from each one to come soon!
It is, once again, the time of year where we welcome our Summer Research Associates (RAs) to Topos. These early-career researchers bring with them not just technical knowledge and capability, but also their perspectives on the sort of culture that we should be actively cultivating within Topos. We are very lucky to be able to award these positions, which are a key part of our academic community building mission.
Tony Wehbe is a PhD student in Applied Mathematics at the University of Toledo, advised by William Kalies. His research interests are in dynamical systems (specifically hybrid systems), and he also has a strong interest in Category Theory for its use in studying them. At Topos this summer, he is working with Sophie Libkind on understanding the composition of attractor lattices. Specifically, he is exploring how the lattice of attractors in coupled and feedback systems can be characterized in terms of the lattices of attractors of the component systems.
Lucy Horowitz just finished the first year of her PhD in logic up the hill in Evans Hall, and this summer is working with Kristopher Brown on logical expressivism. They are trying to understand the relationship between “implication-space semantics” and phase-space semantics for linear logic, as well as how to do this kind of substructural logic in some kind of category (likely virtual double categories). Previously Lucy has collaborated with Valeria de Paiva on knowledge graphs of mathematics. When not doing logic Lucy likes to go hiking, play soccer, listen to and play music, and read science fiction.
Aaron Fairbanks is working with Kevin and David studying comonads on the category \mathbf{Set}. Several people at Topos are already fans of polynomial comonads on \mathbf{Set}. This means that the comonad endofunctor \mathbf{Set}\to\mathbf{Set} is of the form \sum_{i\in I}y^{X_i}, where y^{X_i} denotes the representable functor homming out of the set X_i. Surprisingly, it turns out that polynomial comonads on \mathbf{Set} are the same thing as categories (shown here). They plan to study general (not necessarily polynomial) comonads on \mathbf{Set}, viewing them as a kind of “generalised category”.
Matt Cuffaro is a programmer visiting Topos as an RA, splitting his time between building features which capture selections from H.T. Odum’s Systems Ecology into CatColab as well as discussing modelling with Dana Scott. Matt has collaborated with Topos on the AlgebraicJulia ecosystem as a programmer in the GATAS lab in Gainesville, FL, but is glad to be here on the other side this Summer!
Ea E T is a first-year math PhD student at the University of Illinois Urbana-Champaign, working in homotopy theory, infinity-categories, and higher algebra. They did their undergrad in Physics and Mathematics at the University of Calgary, Alberta Canada, which inspired their interest in exploring connections and applications of higher categorical methods in the natural sciences. This summer they are working with Sophie Libkind to explore the use of loose bimodules in the study of dynamical systems.
Corinthia Aberle is a 2nd year PhD student in Pure and Applied Logic in the CS Department at Carnegie Mellon. This Summer, she is working with Evan Patterson and Kevin Carlson on double-categorical logic—specifically, extending the framework of Cartesian double theories to include other sorts of double-categorical limits such as tabulators— she is also working with Dana Scott on the side on promoting formalization in Agda (since She’ll be formalizing all of her results on double categories anyway!) Corinthia was an RA here last summer as well (under the name CB, back then), during which time she worked with David Spivak on applications of polynomial functors to the semantics of dependent type theory. Corinthia is also a composer, songwriter, and producer, who just released her first pop album and is currently working on another one in her spare time! Before starting her PhD, Corinthia also did half her undergrad in philosophy, and remains keenly interested in philosophical issues pertaining to math, logic, technology, and their role in society.