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SUMMARY:Anthony Iarrobino (Northeastern University\, Boston\, MA)
DTSTART:20201229T130000Z
DTEND:20201229T140000Z
DTSTAMP:20260423T035053Z
UID:VCAS/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/61/">Jo
 rdan type and Lefschetz Properties for Artinian algebras</a>\nby Anthony I
 arrobino (Northeastern University\, Boston\, MA) as part of IIT Bombay Vir
 tual Commutative Algebra Seminar\n\n\nAbstract\nThe Jordan type of a pair 
 $(A\,x)\,$ where $x$ is in the maximum ideal of a standard graded Artinian
  algebra A\, is the partition P giving the Jordan block decomposition of t
 he multiplication map by $x$ on $A.$  When $A$ is Artinian Gorenstein\, we
  say that $(A\,x)$ is weak Lefschetz if the number of parts in the  Jordan
  type $P_x$ is the \nSperner number of $A$ – the highest value of the Hi
 lbert function H(A).   We say that \n$(A\,x)$ is strong Lefschetz if $P_x$
  is the conjugate of the Hilbert function.\n\n  Weak and strong Lefschetz 
 properties of $A$ for a generic choice of $x$ have been studied\, due to t
 he connection with topology and geometry\, where A is the cohomology ring 
 of a\n\ntopological space or a variety $X.$ We discuss some of the propert
 ies of Jordan type\, and its\n\nuse as an invariant of $A\,$ its behavior 
 for tensor products and free extensions (defined by \n\nT. Harima and J. W
 atanabe).\n
LOCATION:https://researchseminars.org/talk/VCAS/61/
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