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SUMMARY:Bernd Ulrich (Purdue University)
DTSTART:20210219T130000Z
DTEND:20210219T140000Z
DTSTAMP:20260423T020957Z
UID:VCAS/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/70/">Ge
 neralized multiplicities and integral dependence-I</a>\nby Bernd Ulrich (P
 urdue University) as part of IIT Bombay Virtual Commutative Algebra Semina
 r\n\n\nAbstract\nThese two talks will give a survey about multiplicity bas
 ed criteria\nfor the integral dependence of ideals. This subject has close
  connections\nwith equisingularity theory and intersection theory\, which 
 will be\ndiscussed as well. The first numerical criterion for integral dep
 endence\nwas proved in the 1960s by Rees who treated the case of zero-dime
 nsional\nideals using the Hilbert-Samuel multiplicity. Criteria for arbitr
 ary\nideals require generalized notions of multiplicities. We will discuss
 \nvarious such notions and talk about how they are used to detect integral
 \ndependence. The most recent results are from joint work with Claudia\nPo
 lini\, Ngo Viet Trung\, and Javid Validashti.\n
LOCATION:https://researchseminars.org/talk/VCAS/70/
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