Description

Speaker Name: Prof.Satoshi Murai, Waseda University,

Title: Betti tables of S_n-invariant monomial ideals.

Time: 10:45 am IST (gate opens 10:35 am IST), Wednesday, 16 December.

Google meet link: meet.google.com/qtw-ibbr-qkz.

Phone: (US) +1 505-738-3123 (PIN: 572892305).

Abstract: Let $R_n=K[x_1,\dots,x_n]$ be a polynomial ring with $n$

variables. A monomial ideal in $R_n$ is said to be $S_n$-invariant if it

is fixed by the natural action of the $n$-th symmetric group $S_n$ to

$R_n$. In this talk, I will discuss Betti numbers of $S_n$-invariant

monomial ideals of $R_n$. In particular, I will mainly talk about recent

results relating to the following problem: Fix a sequence of monomials

$u_1,\dots,u_r$ and let $I_n$ be the $S_n$-invariant monomial ideal of

$R_n$ generated by the set of $\{\sigma(u_k):k=1,2,\dots,r, \sigma \in

S_n\}$. In this setting, what can be said about Betti numbers of $I_n$

when $n$ increases?

Title: Betti tables of S_n-invariant monomial ideals.

Time: 10:45 am IST (gate opens 10:35 am IST), Wednesday, 16 December.

Google meet link: meet.google.com/qtw-ibbr-qkz.

Phone: (US) +1 505-738-3123 (PIN: 572892305).

Abstract: Let $R_n=K[x_1,\dots,x_n]$ be a polynomial ring with $n$

variables. A monomial ideal in $R_n$ is said to be $S_n$-invariant if it

is fixed by the natural action of the $n$-th symmetric group $S_n$ to

$R_n$. In this talk, I will discuss Betti numbers of $S_n$-invariant

monomial ideals of $R_n$. In particular, I will mainly talk about recent

results relating to the following problem: Fix a sequence of monomials

$u_1,\dots,u_r$ and let $I_n$ be the $S_n$-invariant monomial ideal of

$R_n$ generated by the set of $\{\sigma(u_k):k=1,2,\dots,r, \sigma \in

S_n\}$. In this setting, what can be said about Betti numbers of $I_n$

when $n$ increases?

Date

Wed, December 16, 2020

Start Time

10:45am IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Tue, December 15, 2020 10:18pm IST