Ashley K. Wheeler's primary work is in principal minors of a generic matrix. The topic was motivated by old questions in Invariant Theory. In her thesis, Wheeler showed that unlike the well-studied determinantal and Pfaffian ideals, principal minor ideals do not arise from rings of invariants. Rather, their structure is less organized and for the most part, mysterious. One strategy has been to restrict their study to matrices of a fixed rank. As a result, parts of the problem can be reduced to projective subvarieties of a Grassmannian. Furthermore, the symmetry of principal minors has allowed for the use of techniques in Matroid Theory.
Wheeler has also recently, along with collaborators at James Madison University and Penn State, become interested in connections between Hilbert's axioms (his modern reworking of Euclid's axioms), the classical Pappus's Theorem in projective geometry, and the Gorenstein property of rings.
Since arriving at MHC she has participated with a handful of other faculty members in a reading group on Algebraic Statistics.