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SUMMARY:Jason McCullough (Iowa state)
DTSTART:20200604T203000Z
DTEND:20200604T220000Z
DTSTAMP:20260423T035820Z
UID:FOTR/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FOTR/7/">Sub
 additivity of syzygies and related problems</a>\nby Jason McCullough (Iowa
  state) as part of Fellowship of the Ring\n\n\nAbstract\nLet $S = K[x_1\,.
 ..\,x_n]$ be a polynomial ring over a field and  $I$ a graded $S$-ideal.  
 There are many interesting questions about the maximal graded shifts of $S
 /I$\, denoted $t_i$.  In the first part of my talk\, I will discuss two cl
 assical constructions that turn a (graded) S-module into an ideal with sim
 ilar properties\, namely idealizations and Bourbaki ideals\, and what they
  say about maximal graded shifts of ideals.  In the second part of the tal
 k\, I will discuss restrictions on maximal graded shifts of ideals.  In pa
 rticular\, an ideal $I$ is said to satisfy the subadditivity condition if 
 $t_a + t_b ≥ t_(a+b)$ for all $a\,b$.  This condition fails for arbitrar
 y\, even Cohen-Macaulay\, ideals but is open for certain nice classes of i
 deals\, such as Koszul and monomial ideals.  I will present a construction
  (joint with A. Seceleanu) showing that subadditivity can fail for Gorenst
 ein ideals.  \n\nIf time allows\, I will talk about some results that hold
  more generally\, including a linear bound on the maximal graded shifts in
  terms of the first $p-c$ shifts\, where $p = pd(S/I)$ and $c = codim(I)$.
   I hope to include several examples and open questions as well.\n
LOCATION:https://researchseminars.org/talk/FOTR/7/
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