My research is in logic, more specifically model theory, more more specifically tame topology. The goal of tame topology is to study structures which satisfy certain "nice" topological conditions. Distinct from other notions of "tame" structures within Model Theory, we are not concerned with structures that satisfy combinatorical properties, nor in counting the number of models. Instead, we study the definable sets of a model from a geometric perspective. The first big discovery within tame topology was the identification of o-minimality. The study of o-minimality has been extremely fruitful, leading to beautiful results such as the monotonicity theorem and cell decomposition as well as applications into number theory and arithmetic geometry. In recent years, researches have begun to identify more tame structures beyond o-minimality. This is where my research lies. I am most interested in studying d-minimal structures, those structures which allow for countably many connected components (in contrast to the finite connected components of an o-minimal structure).
Uniform Bounds in Weakly D-Minimal Structures
with Philipp Hieronymi, in progress
Definability and Decidability in Expansions by Generalized Cantor Sets
with William Balderrama, Alexi Block-Gorman, Philipp Hieronymi, and Sven Manthe (in progress)
Recurrence Relations and Benford’s Law
Farris, M., Luntzlara, N., Miller, S.J. et al. Recurrence relations and Benford’s law. Stat Methods Appl (2020)
Ruth-Aaron Numbers: An Exploration in Analytic Number Theory
Honor's thesis (2019)
Purdue University Model Theory and Applications Seminar
50 minute talk titled "Uniform Bounds in Weakly D-Minimal Structures," Fall 2024
Young Women in Model Theory and its Applications
Contributed talk titled "Uniform Bounds in Weakly D-Minimal Structures", Spring 2024
Graduate Logic Seminar
Organizer, multiple talks on the topics of o-minimality, d-minimality, and ultraproducts, Fall 2022 - Present
Computability Theory Seminar
50 minute expository talk on the history of alpha-PA and current research, Fall 2020