Algebra & Geometry Seminar
Algebra & Geometry Seminar
Date: 12/11/2026 Time: 14.15 Room: 715
Title: TBD
Abstract: TBD
Date: 05/11/2026 Time: 14.15 Room: 715
Title: A level initial ideal of the 2-minors determinantal ideal
Abstract: For any field K, let X be a m x n matrix of variables and S = K[X]. Let
I be the ideal generated by the 2-minors of X. We find a suitable term
order over S such that J, the initial ideal of I, with respect to that
order, is level, i.e. it is Cohen-Macaulay and the socle of an Artinian
reduction of S/J is concentrated in only one degree.
The combinatorics of the simplicial complex associated to J by the
Stanley-Reisner correspondence allows us to understand the structure of
the canonical module of S/J.
In the end, we compare the Betti tables of I with the tables of its
initial ideals.
Date: 01/10/2026 Time: 14.15 Room: 715
Title: Numerical semigroup tree: type-representation
Abstract: The numerical semigroups can be organized as the nodes of an infinite rooted tree, where
the root corresponds to the set of all nonnegative integers and the more elements we remove from a numerical semigroup, the farther we get from the root. Several conjectures circulate already about the magnitude of the growth of this tree.
We suggest to refine the information by taking into account also the type of the semigroups. We found that the number of semigroups of genus g and type t is constant when t is close to g, while g grows. We also study the unimodality of various sequences, as well as the behavior of the leaves in the semigroup tree. We put forward several conjectures that are supported by various computational experiments.
This is joint work with Jonathan Chappelon and Jorge Ramirez Alfonsin.