Alex McDonough: Signed determinantal tilings

Matroid seminar

Abstract: While working on my thesis, I found a fascinating geometric construction which uses a pair of matrices to give a periodic titling of space. This construction only works for specific pairs of matrices, whose associated oriented matroids have a certain property. However, I have recently been working with Doolittle on the more general case. Instead of a single periodic tiling, we obtain a signed tiling made up of positive and negative tiles. I used a special case of the initial construction to prove a result in higher-dimensional chip-firing, and I believe that there is much more to discover about the general construction.