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SUMMARY:Dipankar Ghosh (IIT Kharagpur)
DTSTART:20220107T120000Z
DTEND:20220107T130000Z
DTSTAMP:20260423T021101Z
UID:VCAS/116
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/116/">(
 Non) linear behavior of Castelnuovo-Mumford regularity</a>\nby Dipankar Gh
 osh (IIT Kharagpur) as part of IIT Bombay Virtual Commutative Algebra Semi
 nar\n\n\nAbstract\nIn the first half\, we shall discuss the importance of 
 Castelnuovo-Mumford regularity and the main motivation to define this inva
 riant along with examples. This part is aimed for the graduate students an
 d should be elementary.\nIn the second half\, we discuss the asymptotic be
 havior of Castelnuovo-Mumford regularity of powers of ideals\, and that of
  Ext and Tor\, with respect to the homological degree\, over graded comple
 te 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 provid
 e examples showing that the behavior could be pretty hectic when the latte
 r condition is not satisfied.\nThis talk is based on our joint papers with
  Marc Chardin\, Navid Nemati and Tony Puthenpurakal.\n
LOCATION:https://researchseminars.org/talk/VCAS/116/
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