I am a Postdoctoral Fellow at the University of Utah. In 2020, I graduated from UCLA with a PhD. in Mathematics. My advisor was Raphaël Rouquier. From 2020-2023, I was a Visiting Assistant Professor at UC Santa Barbara, where I worked with with Ken Goodearl. I am currently in a teaching-focused Postdoctoral Fellowship at University of Utah.
Research Interests:
I study homological algebra and the representation theory of finite-dimensional algebras. My current research involves the differential graded stable category (a triangulated category that can be associated to a finite-dimensional graded algebra) and triangulated categories of negative Calabi-Yau dimension.
My Ph.D. dissertation describes the dg-stable category, a triangulated category associated to a graded self-injective algebra and studies the theory of perverse equivalences in this setting. Perverse equivalences are tilts of a triangulated category which are performed with respect to a stratification. They translate tools in combinatorics and geometric group theory into the language of homological algebra and should serve as a discrete counterpart to the Bridgeland stability manifold.
The dg-stable category of a graded algebra A is defined to be the quotient of the derived category of dg-modules by the thick subcategory of perfect dg-modules. The dg-stable category is similar to the stable category of graded modules, but features nontrivial interactions between the grading data of the algebra and the homological data of the module category. When A is a symmetric algebra with a non-positive grading, the dg-stable category has negative Calabi-Yau dimension. In this setting, the theory of perverse tilts is closely related to that of simple-minded systems, a negative Calabi-Yau analogue of cluster-tilting subcategories.