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