Wed, December 16, 2020
Public Access


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10:00am [10:45am] Prof.Satoshi Murai, Waseda University
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?

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