Jeff Mermin (Oklahoma State)Title: Symmetric resolutions of pinched power idealsAbstract: One of the fundamental difficulties in understanding the resolution of a (monomial) ideal is the choice of a convenient basis: we want the differential matrices to be sparse, or at least nicely structured, so that we can extract some intuition about the maps. My favorite tool for identifying good bases is the idea of a frame, which, when applicable, allows us to think about the resolution in terms of a combinatorial object such as a simplicial complex. I'll review how simplicial, cellular, and polytopal resolutions work, and use these ideas to produce two polytopal resolutions for the minimal resolution of a power of the maximal ideal, one of which (Nagel and Reiner's complex of boxes) will already be familiar to experts. Finally, we'll build a cyclically symmetric polytopal resolution for the "pinched power" obtained by deleting one monomial from the generating set for a power of the maximal ideal. This work is joint with Hoai Dao.
