1:45PM: The N6 property for third Veronese embeddings
Vu ThanhMatching complexes are simplicial complexes defined by a very simple combinatorial recipe. A result of Karaguezian, Reiner and Wachs shows that the rational homology groups of matching complexes are closely related to the syzygies of the Veronese embeddings. I will explain how I used this connection, the theory of representations of the symmetric group, and machine computation with Macaulay2 and Maple to show that the third Veronese embedding of any projective space satisfies a certain condition on its free resolution called N6. This settles a case of a conjecture of Ottaviani and Paoletti.