Adam LaClair: The Non-Lefschetz Locus of Monomial Complete Intersections in Positive Characteristic

Abstract: In the 1980s, Stanley and J. Watanabe proved that over a field of characteristic zero every monomial complete intersection has the strong Lefschetz property. Determining which monomial complete intersections have the weak Lefschetz property in positive characteristic has since been the subject of extensive research. Recently, Kyomuhangi, Marangone, Raicu, and Reed gave a numerical characterization of the weak Lefschetz property for monomial complete intersections in positive characteristic. Independently, I gave a geometric description of the locus of exponent vectors corresponding to monomial complete intersections over a field of positive characteristic which fail the weak Lefschetz property. This locus is described explicitly in terms of translates of positive-orthant lattice balls in the taxicab metric. In this talk, I will explain the proof of this result.