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SUMMARY:Hema Srinivasan (University of Missouri\, Columbia\, MO)
DTSTART:20201208T130000Z
DTEND:20201208T143000Z
DTSTAMP:20260423T021004Z
UID:VCAS/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/42/">Se
 migroup rings</a>\nby Hema Srinivasan (University of Missouri\, Columbia\,
  MO) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstra
 ct\nLet $A = \\{a_{ij}\\}$ be an $n \\times m$ matrix of natural numbers $
 \\mathbb N.$  The $S(A)$ denotes the sub-semigroup of $\\mathbb N^n$ gener
 ated by the columns of $A$. The semigroup ring of $A$ over a field $k$\, d
 enoted by $k[A]$ is the homomorphic image of $\\phi: k[x_1\, \\ldots\, x_m
 ] \\to k[t_1\, \\ldots\, t_n]$ defined by $\\phi (x_j) = \\prod_{i=1}^nt_i
 ^{a_{ij}}$ and hence $k[A]$ is isomorphic to $k[x_1\, \\ldots\, x_m]/I_A$.
   In this talk\, we will discuss various invariants of $k[A]$\, such as de
 pth\, dimension\, Frobenius numbers and homological properties\, such as r
 esolutions\, Betti Numbers\, regularity and Hilbert Series.   Recent work 
 on gluing and its relation to these invariants will be outlined. We will c
 ompare the situation in numerical semigroups (subgroups of $\\mathbb N$) t
 o semigroups of higher dimension and which of the many formulas and struct
 ures generalize to higher dimensions.\n
LOCATION:https://researchseminars.org/talk/VCAS/42/
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