December 14, 2020 - December 18, 2020
Public Access Category: All |
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- Time:
- 5:15pm-6:30pm
- Description:
- Speaker:* Rajendra V. Gurjar, IIT Bombay *
Date/Time: *15 December 2020, **5:30pm IST/ 12:00 GMT/ 7:00am EST* (joining
time: 5:15 pm IST - 6:30 pm IST)
Google meet link: meet.google.com/pwt-vxdm-gbc
Title:* Zariski-Lipman Conjecture for Module of Derivations*
Abstract: Zariski conjectured that if the module of derivations of a local
ring $R$ at a point on an algebraic variety defined over a field of
characteristic $0$ is a free $R$-module then $R$ is regular. In these two
talks we will survey most of the interesting results proved affirming the
conjecture.
Results of Lipman, Scheja-Storch, Becker, Hochster, Steenbrink-van Straten,
Flenner, Kallstrom, Biswas-Gurjar-Kolte, and some general results which can
be deduced by combining some of these results will be discussed. An
interesting proposed counterexample due to Hochster will be introduced.
Some unsolved cases in the paper of Biswas-Gurjar-Kolte will be mentioned.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar/
- Time:
- 10:45am
- 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?
- Time:
- 5:15pm-6:30pm
- Description:
- Speaker: *Rajendra V. Gurjar, IIT Bombay *
Date/Time: *18 December 2020, **5:30pm IST/ 12:00 GMT/ 7:00am EST* (joining
time: 5:15 pm IST - 6:30 pm IST)
Google meet link: meet.google.com/pwt-vxdm-gbc
Title:* Zariski-Lipman Conjecture for Module of Derivations*
Abstract: Zariski conjectured that if the module of derivations of a local
ring $R$ at a point on an algebraic variety defined over a field of
characteristic $0$ is a free $R$-module then $R$ is regular. In these two
talks we will survey most of the interesting results proved affirming the
conjecture.
Results of Lipman, Scheja-Storch, Becker, Hochster, Steenbrink-van Straten,
Flenner, Kallstrom, Biswas-Gurjar-Kolte, and some general results which can
be deduced by combining some of these results will be discussed. An
interesting proposed counterexample due to Hochster will be introduced.
Some unsolved cases in the paper of Biswas-Gurjar-Kolte will be mentioned.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar/