Filip Jonsson Kling: Gröbner bases, lattice paths and the strong Lefschetz property

Abstract: 

The goal of this talk is to give parts of a new proof that any monomial complete intersection has the strong Lefschetz property by finding suitable Gröbner bases. We will begin with a short introduction to the necessary concepts from commutative algebra, before talking about the combinatorial arguments at the heart of the proof. By translating from monomials to certain lattice paths, we will for example explain how bijections between different families of lattice paths can show that we have fund just the right number of elements for the sought Gröbner bases. Finally, we will say some words connecting the found Gröbner bases to several classical combinatorial sequences. This talk is based on joint work with Samuel Lundqvist, Fatemeh Mohammadi, Matthias Orth and Eduardo Sáenz-de-Cabezón.