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Lisa Nicklasson: The Fröberg conjecture and exterior algebras

Tid: Fr 2020-01-17 kl 13.15 - 14.15

Plats: Kräftriket, house 6, room 306 (Cramér-rummet)

Föreläsare: Lisa Nicklasson


Let \(R\) be a polynomial ring, and \(I\) a homogeneous ideal. What is the smallest quotient \(R/I\) we can get, if we fix the number of variables, the number of generators of \(I\) and their degrees? A solution to this problem was conjectured by Fröberg in 1985. Although this is a well studied problem, the conjecture has only been proved in a few special cases. An alternative problem is: What happens if we replace the polynomial ring by the exterior algebra (i.e. "skew-commutative" polynomial ring)? In this situation, already the case when \(I\) has just one generator is unknown.