Virtual Criterion for Generalized Eagon-Northcott Complexes

Preprint 2021

Any matrix gives rise to an associated family of canonical complexes associated to it, including the Eagon-Northcott and Buchsbaum-Rim. Famously, there is a simple criterion for checking the exactness of these complexes. We give generalization of this criterion for these complexes to be virtual resolutions, which are “exact enough” to be relevant to the geometry of toric varieties.

Quarternion-Valued Breather Soliton, Rational, and Periodic QKdV Solutions

John Cobb, Alex Kasman, Albert Serna, Monique Sparkman

The KdV equation is a prototypical example of an exactly solvable PDE, due in part to its admittance of soliton solutions. This paper examines and classifies the dynamics of quaternion-valued solutions of the noncommutative KdV equation.

Aggregate Dispersions to Enhance the Intrachain Order in Surfactant-Stabilized Aqueous Colloids of Poly(3-hexylthiophene)

McKenna Andrews, Anna Smirnova, Devin Sharp, Sarah Taylor, John Cobb, David Boucher

Quaternion-Valued KdV Solutions

My bachelor thesis.