# Lorenzo Venturello: Flag triangulated spheres and quadratic algebras

**Time: **
Wed 2020-10-28 10.15 - 11.15

**Location: **
F11, KTH

**Lecturer: **
Lorenzo Venturello

Abstract: Let us fix a family of simplicial complexes. Which restrictions does our choice pose on the possible number of faces in each dimension? Let us now fix a family of graded algebras. Which restrictions does our choice pose on the possible Hilbert functions? In the seventies, the idea of mathematicians like Stanley, Reisner and Hochster was to relate this two problems, by associating a graded ring to each simplicial complex. If the associated ring is quadratic, i.e., generated in degree 2, we say the corresponding simplicial complex is flag. After providing the necessary background, I will present some open questions on the face numbers of flag triangulated spheres, as well as some results on a class of quadratic algebras called Koszul algebras I obtained in an ongoing project with Alessio D'Alì.

The seminar will also be given via zoom: https://kth-se.zoom.us/j/67213763918