**Speaker:** Emanuela Marangone

University of Notre Dame**Will give a PhD Defense entitled:**

The Non-Lefschetz Locus of Lines and Conics**Abstract:** An Artinian Algebra *A* has the *Weak Lefschetz Property* if there is a linear form, $\ell$, such that the multiplication map $\times \ell$ has maximal rank for each degree. The *non-Lefschetz locus* is the set of linear forms for which maximal rank fails, and it has a natural scheme structure. Boij--Migliore--Miró-Roig--*non-Lefschetz locus for conics* and show that for a general complete intersection of height 3, it has the expected codimension as a subscheme of $\mathbb P^5$. The same does not hold for certain monomial complete intersections. Later, we will generalize the study of the non-Lefschetz locus to modules $M = H^1_*(\mathbb{P}^2, \mathcal{E})$ where $\mathcal{E}$ is a vector bundle of rank 2. In this case, we show that the non-Lefschetz locus is exactly the set of jumping lines of $\mathcal E$, and the expected codimension is achieved when $\mathcal E$ is general. In the case of conics, the same is not true: the non-Lefschetz locus of conics is a subset of the jumping conics, but it can be proper.**Date:** 04-05-2024**Time:** 2:30 pm**Location:** 125 Hayes-Healy Bldg