Commutative Algebra Seminar: Subadditivity of Shifts for Monomial Ideals and Shuffle products in Lattices

We prove that the maximal shifts in the minimal free resolution of a monomial ideal form a subadditive sequence, settling a conjecture of Avramov, Conca and Iyengar. To do so, we develop explicit chain-level models for the homology of posets and lattices, introduce an Eilenberg–Zilber–type shuffle product in the lattice setting, and use it to derive nonvanishing criteria for lattice homology classes that yield the desired subadditivity of maximal shifts. The talk is based on joint work with K. Adiprasito, A. Björner, M. Margaritis, and V. Welker (arXiv:2404.16643).

This is a hybrid talk. Join on zoom: https://umich.zoom.us/j/92232890782 with password commalg.