Mini-Workshop: Lefschetz properties in algebra

Schedule:

• 13:15-14:15. Talk by Samuel Lundqvist (Stockholm University)
• 14:15-15.00. Fika
• 15.00-16.00. Talk by Mats Boij (KTH)

Room: R3-121

Zoom link: https://mdu-se.zoom.us/j/62755453126 External link.

Titles and abstracts:

Samuel's talk: On the principal ideal generated by a power of a general linear form in the squarefree algebra

Abstract: I will discuss the interplay between Gröbner bases, the Fröberg conjecture, and the Lefschetz properties for ideals generated by a power of a general linear form in the squarefree algebra. This is based on joint work with Filip Jonsson Kling, Fatemeh Mohammadi, Matthias Orth, and Eduardo Sáenz-de-Cabezón.

Mats' talk: Lefschetz properties and the Kähler package

Abstract: Properties of cohomology rings of smooth projective varieties have become important tools in areas outside algebraic geometry. One of the first examples is Stanley’s proof of the g-Theorem for simplicial polytopes and a more recent example is the development of Hodge Theory for Matroids by Adiprasito, Huh and Katz. I will explain what these properties are and I will give an example where we could give an explicit proof of them using basic techniques from linear algebra and representation theory. The last part is joint work with Huang, Huh and Smith.