BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Amit Roy (IISER Mohali)
DTSTART:20201104T053000Z
DTEND:20201104T063000Z
DTSTAMP:20260423T021419Z
UID:CATGT/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CATGT/16/">S
 tandard monomials of $1$-skeleton ideal of a graph</a>\nby Amit Roy (IISER
  Mohali) as part of Applications of Combinatorics in Algebra\, Topology an
 d Graph Theory\n\n\nAbstract\nLet $G$ be a (multi) graph on the vertex set
  $V=\\{0\,1\,\\ldots \,n\\}$ with root $0$. The $G$-parking function ideal
  $\\M_G$ is a monomial ideal in the polynomial ring $R=\\mathbb{K}[x_1\,\\
 ldots \,x_n]$ over a field $\\mathbb{K}$ such that dim$_{\\mathbb{K}}\\big
 (\\frac{R}{\\mathcal{M}_G}\\big)$ $=\\det\\left(\\widetilde{L}_G\\right)$\
 , where $\\widetilde{L}_G$ is the truncated Laplace matrix of $G$. In othe
 r words\, standard monomials of the Artinian quotient $\\frac{R}{M_G}$ cor
 respond bijectively with the spanning trees of $G$. For $0\\leq k\\leq n-1
 $\, the $k$-skeleton ideal $\\mathcal{M}_G^{(k)}$ of $G$ is a monomial sub
 ideal $\\mathcal{M}_G^{(k)}=\\left\\langle m_A:\\emptyset\\neq A\\subseteq
 [n]\\text{ and }|A|\\leq k+1\\right\\rangle$ of the $G$-parking function i
 deal $\\mathcal{M}_G=\\left\\langle m_A:\\emptyset\\neq A\\subseteq[n]\\ri
 ght\\rangle\\subseteq R$. In this talk we will focus on the $1$-skeleton i
 deal $\\mathcal{M}_G^{(1)}$ of a graph $G$ and see how the number of stand
 ard monomials of $\\frac{R}{\\mathcal{M}_G^{(1)}}$ is related to the trunc
 ated signless Laplace matrix $\\Q_G$ of $G$. This is based on joint work w
 ith Chanchal Kumar and Gargi Lather.\n
LOCATION:https://researchseminars.org/talk/CATGT/16/
END:VEVENT
END:VCALENDAR