Description of Research
Mathematical Research: I work in tensor-triangular geometry. It is a beautiful, interdisciplinary field with links to algebraic geometry, (stable, equivarient, motivic) homotopy theory, and representation theory. In my thesis I proved that certain derived categories of motives, based off recent computations by
Martin Gallauer are stratified, a la Barthel, Heard, and Sanders.
Education Research:
I have experience and interests in the redesign of core lower division courses to refocus the overall course structure to an application-based model that teaches students the necessary math skills to solve real-world scientific problems. This involves the creation of new formative assignments and supplemental instructional curriculum material for these courses. Moreover, I am interested in researching the affects project and inquiry based courses have apropos closing the equity gap in mathematics. For upper division courses, I work on creating active learning worksheets, and incorporating category theory into the classroom. Indeed, since the Grothendieck revolution, a mastery of category theory is essential for future researchers in algebra, geometry and topology. Unfortunately, this knowledge is something students are expected to learn with little to no guidance, and many faculty simply assume graduate students simply know category theory.
Presentations
Publications
In progress....