A Special Case of Completion Invariance for thec2Invariant of a Graph

Yeats, Karen

doi:10.4153/cjm-2018-006-5

Cited by 7 publications

(15 citation statements)

References 36 publications

(76 reference statements)

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“…The main result of [15] is a very special case of this conjecture and the first major progress towards the conjecture. Theorem 3.1 (Theorem 1.2 of [15]). Let G be a connected 4-regular graph with an odd number of vertices.…”

Section: Past Applications Of This Methodsmentioning

confidence: 91%

“…This conjecture has turned out to be quite difficult. This combinatorial perspective on the c 2 invariant is used in [15] to prove one special case of the conjecture. An overview of the results of [14], [8], and [15] is given below in Section 3 along with an outlook for this approach and connections to topics of particular interest to the CARMA conference.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A study on prefixes of $c_2$ invariants

Yeats

2020

IRMA Lectures in Mathematics and Theoretical Physics

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This paper begins by reviewing recent progress that has been made by taking a combinatorial perspective on the c 2 invariant, an arithmetic graph invariant with connections to Feynman integrals. Then it proceeds to report on some recent calculations of c 2 invariants for two families of circulant graphs at small primes. These calculations support the idea that all possible finite sequences appear as initial segments of c 2 invariants, in contrast to their apparent sparsity on small graphs.Thanks to Oliver Schnetz for goading me into doing the prefix calculation, and for his continued excitement about the c 2 invariant. Thanks to Iain Crump and Freddy Cachazo for discussions. Thanks to NSERC and the Humboldt foundation for support. Thanks to the organizers of the Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) conference for their excellent conference.

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Section: Past Applications Of This Methodsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

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A study on prefixes of $c_2$ invariants

Yeats

2020

IRMA Lectures in Mathematics and Theoretical Physics

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“…This is the completion invariance of the Feynman period. The analogous invariance for the c 2 invariant is conjectural [9], but an approach based on counting edge partitions has enabled a proof when q = 2 and the 4-regular graph has an odd number of vertices [31]. Upcoming work of one of us with Simone Hu will complete the q = 2 proof.…”

Section: ϕ 4 Theorymentioning

confidence: 99%

“…The c 2 has been studied quite deeply in particular in the context of φ 4 quantum field theory (Section 2.7). The focus of these studies can either be the general mathematical structure of the c 2 [10,23,13] or the zoology of the geometries identified by c 2 s [8,9,22,12,24,20]. The nature of this article is more in the latter direction, particularly when we analyze the c 2 s of small kernels in Section 5.…”

Section: Introductionmentioning

confidence: 99%

c2 Invariants of Hourglass Chains via Quadratic Denominator Reduction

Schnetz¹,

Friedrich-Alexander-Universit²,

Yeats³

et al. 2021

SIGMA

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We introduce families of four-regular graphs consisting of chains of hourglasses which are attached to a finite kernel. We prove a formula for the c 2 invariant of these hourglass chains which only depends on the kernel. For different kernels these hourglass chains typically give rise to different c 2 invariants. An exhaustive search for these c 2 invariants for all kernels with a maximum of ten vertices provides Calabi-Yau manifolds with point-counts which match the Fourier coefficients of modular forms whose levels and weights are [3,36], [4,8], [4,16], [6,4], [9,4]. We also confirm the conjecture that curves (weight two modular forms) are absent in c 2 invariants up to level 69.

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Canonical Construction of Invariant Differential Operators: A Review

Dobrev

2024

Symmetry

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In the present paper, we review the progress of the project of the classification and construction of invariant differential operators for non-compact, semisimple Lie groups. Our starting point is the class of algebras which we called earlier ‘conformal Lie algebras’ (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this purpose, we introduced recently the new notion of a parabolic relation between two non-compact, semi-simple Lie algebras G and G′ that have the same complexification and possess maximal parabolic subalgebras with the same complexification.

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A Special Case of Completion Invariance for thec₂Invariant of a Graph

Cited by 7 publications

References 36 publications

A study on prefixes of $c_2$ invariants

A study on prefixes of $c_2$ invariants

c<sub>2</sub> Invariants of Hourglass Chains via Quadratic Denominator Reduction

Canonical Construction of Invariant Differential Operators: A Review

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