Research projects.
I am very broadly interested in thinking about topics between algebra, geometry and topology. At the moment, I have been interested in algebraic topology/homotopy theory and algebraic geometry, and have been lucky enough to have some opportunities to explore the fields outside of class.
Undergraduate projects
Summer research, University of Chicago - Math REU and Leadership Alliance SR-EIP, 2022
The classical lambda algebra is a differential graded algebra, whose homology is the \(E_2\) page of the Adams spectral sequence computing the stable homotopy groups of spheres. I investigated generalizations of the Curtis algorithm, an inductive process for computing this homology, to determining motivic Adams \(E_2\) pages.
Summer research, MIT Math Dept., 2021
I studied a 1957 algorithm of E.H. Brown, which can be used to determine the homotopy groups of any space obtained as the realization of a finite simplicial set.
