Motives associated to graphs
نویسندگان
چکیده
منابع مشابه
Motives Associated to Graphs
A report on recent results and outstanding problems concerning motives associated to graphs.
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In quantum field theory, the path integral is interpreted perturbatively as a sum indexed by graphs. The coefficient (Feynman amplitude) associated to a graph Γ is a period associated to the motive given by the complement of a certain hypersurface XΓ in projective space. Based on considerable numerical evidence, Broadhurst and Kreimer suggested [4] that the Feynman amplitudes should be sums of ...
متن کاملLine graphs associated to the maximal graph
Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...
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Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$, if no two vertices of $S$ are adjacent.The independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.
متن کاملFeynman Motives of Banana Graphs
We consider the infinite family of Feynman graphs known as the “banana graphs” and compute explicitly the classes of the corresponding graph hypersurfaces in the Grothendieck ring of varieties as well as their Chern–Schwartz–MacPherson classes, using the classical Cremona transformation and the dual graph, and a blowup formula for characteristic classes. We outline the interesting similarities ...
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ژورنال
عنوان ژورنال: Japanese Journal of Mathematics
سال: 2007
ISSN: 0289-2316,1861-3624
DOI: 10.1007/s11537-007-0648-9