Speaker: K.-i. Watanabe, Nihon University, Tokyo, Japan.
Date/Time: 13 August 2021, 5:30pm IST/ 12:00pm GMT / 8:00am EDT (joining
time 5:15pm IST)
Google meet link:
https://meet.google.com/uxn-zmfu-efa
Title: Inverse polynomials of symmetric numerical semigroups.
Abstract: This is a joint work with Kazufumi Eto (Nippon Institute of
Technology). This work was inspired by the talk of M.E. Rossi (Univ.
Genova) at VCAS on Dec. 1, 2020. Let H be a numerical semigroup and K[H]
be its semigroup ring over any field K. If $H = (n_1,...,n_e)$, we express
$K[H]$ as $K[x_1,...,x_e]/I_H$ and we want to express $K[H]/(t^h)$ by
"Inverse polynomials" of Macaulay. We study the defining ideal of a
numerical semigroup ring K[H] using the inverse polynomial attached to the
Artinian ring $K[H]/(t^h)$ for $h \in H_+.$ I believe this method to
express by inverse polynomials is very powerful and can be used for many
purposes. At present, we apply this method for the following cases. (1) To
give a criterion for H to be symmetric or almost symmetric. (2)
Characterization of symmetric numerical semigroups of small multiplicity.
(3) A new proof of Bresinsky’s Theorem for symmetric semigroups generated
by 4 elements.
For more information and links to previous seminars, visit the website of
VCAS:
https://sites.google.com/view/virtual-comm-algebra-seminar