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SUMMARY:Adam Van Tuyl (McMaster University)
DTSTART:20220204T130000Z
DTEND:20220204T140000Z
DTSTAMP:20260423T021049Z
UID:VCAS/120
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/120/">T
 oric ideals of graphs and some of their homological invariants</a>\nby Ada
 m Van Tuyl (McMaster University) as part of IIT Bombay Virtual Commutative
  Algebra Seminar\n\n\nAbstract\nThe study of toric ideals of graphs lies i
 n the intersection of commutative algebra\, algebraic geometry\, and combi
 natorics.  Formally\, if $G = (V\,E)$ is a finite simple graph with edge s
 et $E =\\{e_1\,\\ldots\,e_s\\}$ and vertex set $V = \\{x_1\,\\ldots\,x_n\\
 }\,$ then the toric ideal of $G$ is the kernel of the ring homomorphism $\
 \varphi:k[e_1\,\\ldots\,e_s] \\rightarrow k[x_1\,\\ldots\,x_n]$ where $\\v
 arphi(e_i) = x_jx_k$ if the edge $e_i = \\{x_j\,x_k\\}$.  Ideally\, one wo
 uld like to understand how the homological invariants (e.g. graded Betti n
 umbers) of $I_G$ are related to the graph $G$.  In this talk I will survey
  some results connected to this theme\, with an emphasis on the Castelnuov
 o-Mumford regularity of these ideals.\n
LOCATION:https://researchseminars.org/talk/VCAS/120/
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