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?