I am interested in matroid theory, especially its interplay with discrete, algebraic, and polyhedral geometry. At the moment I am particularly interested in
- characterizing isomorphism classes of active orders of matroids; and
- the combinatorics of cubical complexes generalizing cubical tilings of the zonotope arising from a representable oriented matroid to the non-representable case.
My up-to-date CV can be viewed here.
- Dall, A. Internally perfect matroids. Electron. J. Combin. 24 (2017), no. 2, Paper 2.35, 31 pp.
- Breuer, F., Dall, A., and Kubitzke, M. “Hypergraph coloring complexes.” Discrete Math. 312, 16 (2012), 2407–2420.
- Breuer, F. & Dall, A. “Bounds on the coefficients of tension and flow polynomials.” J Algebr Comb (2011) 33: 465. doi:10.1007/s10801-010-0254-4. arXiv version
- Breuer, F. & Dall, A. “Viewing counting polynomials as Hilbert functions via Ehrhart theory.” In 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010). Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2010, pp. 545—556. arXiv version.
- Doctoral Thesis (advised by Julian Pfeifle): Matroids: h-vectors, zonotopes and Lawrence polytopes
- Master’s Thesis (advised by Matthias Beck): The flow and tension complexes
- Dall, A. & Pfeifle, J. “A polyhedral proof of the matrix tree theorem.” arXiv preprint arXiv:1404.3876 (2014).
- Dall, A. “MonomialRankFunctions: a package for computations with monomial rank functions”. Version 0.1. A Macaulay2 package available at https://github.com/aarondall/MonomialRankFunctions