January 2022
Public Access Category: All |
5:30pm» Dipankar Ghosh, IIT Kharagpur, India- Time:
- 5:30pm
- Description:
- Speaker: Dipankar Ghosh, IIT Kharagpur, India.
Date/Time: 7 January 2022, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/cmp-kofi-zic
Title: (Non) linear behavior of Castelnuovo-Mumford regularity.
Abstract: In the first half, we shall discuss the importance of
Castelnuovo-Mumford regularity and the main motivation to define this
invariant along with examples. This part is aimed for the graduate
students and should be elementary. In the second half, we discuss the
asymptotic behavior of Castelnuovo-Mumford regularity of powers of ideals,
and that of Ext and Tor, with respect to the homological degree, over
graded complete intersection rings. We derive from a theorem of Gulliksen,
a linearity result for the regularity of Ext modules in high homological
degrees. We show a similar result for Tor, under the additional hypothesis
that high enough Tor modules are supported in dimension at most one; we
then provide examples showing that the behavior could be pretty hectic
when the latter condition is not satisfied.
This talk is based on our joint papers with Marc Chardin, Navid Nemati and
Tony Puthenpurakal.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar
- Time:
- 4:00pm
- Description:
- Speaker: Frederic Robert (Institut Elie Cartan, Universite de Lorraine,
France)
Time: 13 January 2022, Thursday, 4pm
Title: Blowing-up solutions for second-order critical elliptic equations:
The impact of the scalar curvature
Google Meet joining info:
Video call link: https://meet.google.com/fub-muxa-eik
Or dial: (US) +1 810-356-7203 PIN: 849 892 565#
https://sites.google.com/math.iitb.ac.in/geometric-analysis/home
- Time:
- 5:30pm
- Description:
- Dear All,
The following are the details.
Speaker: Tony Joseph Puthenpurakal, IIT Bombay, India
Date/Time: 14 January 2022, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining
time 5:15pm IST)
Gmeet link: meet.google.com/zcd-zikn-njv
Title: Itohs conjecture for normal ideals.
Abstract: Let (A,m) be a CM local ring and let I be a normal m-primary
ideal with e_3(I) = 0. Then G_I(A) is CM. (note Itoh only conjectured it
for Gorenstein local rings)
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar
- Time:
- 5:30pm
- Description:
- Speaker: Fatemeh Mohammadi, Ghent University, Belgium.
Date/Time: 21 January 2022, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/iui-gxhk-eeo
Title: Toric degenerations of Grassmannians.
Abstract: Toric varieties are popular objects in algebraic geometry, as
they can be modelled on polytopes and polyhedral fans. This is mainly
because there is a dictionary between their geometric properties and the
combinatorial invariants of their polytopes. This dictionary can be
extended from toric varieties to arbitrary varieties through toric
degenerations.
In this talk, I will introduce the notion of toric degenerations which
generalizes the fruitful correspondence between toric varieties and
polytopes, to arbitrary varieties. There are prototypic examples of toric
degenerations (of Grassmannians) which are related to Young tableaux and
Gelfand-Cetlin polytopes. I will describe how to obtain such degenerations
using the theory of Gröbner fans and tropical geometry, and how their
associated polytopes are connected by mutations.
For more information and links to previous seminars, visit the website of
VCAS:
https://sites.google.com/view/virtual-comm-algebra-seminar
- Time:
- 5:30pm
- Description:
- Speaker: Shinya Kumashiro, Oyama College, Japan.
Date/Time: 28 January 2022, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/txo-mdau-ajk
Title: Graded Bourbaki ideals of graded modules and Ideals of reduction
number two
Abstract: In the first part of this talk, we explore graded Bourbaki
ideals. It is a well-known fact that for torsionfree modules over
Noetherian normal domains, Bourbaki sequences exist. We give criteria in
terms of certain attached matrices for a homomorphism of modules to induce
a Bourbaki sequences. In the second part of this talk, we give an
application of graded Bourbaki sequences to Hilbert functions of m-primary
ideals. We give the inequality of the first three Hilbert coefficients for
ideals of reduction number two. This talk is based on the joint work with
J. Herzog and D. I. Stamate.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar