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SUMMARY:Selvi Kara (University of South Alabama)
DTSTART:20201007T150000Z
DTEND:20201007T163000Z
DTSTAMP:20260422T172218Z
UID:UCGEN/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCGEN/9/">Mo
 nomial Ideals of Graphs and Their Syzygies</a>\nby Selvi Kara (University 
 of South Alabama) as part of UCGEN - Uluslararası Cebirsel GEometri Neşe
 si\n\n\nAbstract\nGiven a homogeneous ideal $I$\n in a polynomial ring \n$
 R=k[x_1\,…\,x_n]$\,\n we can describe the structure of $I$\n by using it
 s minimal free resolution. All the information related to the minimal free
  resolution of $I$\n is encoded in its Betti numbers. However\, it is a di
 fficult problem to express Betti numbers of any homogeneous ideal in a gen
 eral way. Due to this difficulty\, it is common to focus on coarser invari
 ants of \n$I$ or particular classes of ideals. \n\nIn this talk\, we consi
 der monomial ideals associated to graphs. We will discuss the Castelnuovo-
 Mumford regularity\, projective dimension\, and extremal Betti numbers of 
 such ideals and provide formulas for these invariants in terms of the comb
 inatorial data of their associated graphs. Results presented in this talk 
 are from joint works with Biermann\, O’Keefe\, Lin\, and Casiday.\n
LOCATION:https://researchseminars.org/talk/UCGEN/9/
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