1.

Bounded Collection of Feynman Integral CalabiYau Geometries
/ Bourjaily, Jacob L. ; McLeod, Andrew J. ; von Hippel, Matt ; Wilhelm, Matthias
We define the rigidity of a Feynman integral to be the smallest dimension over which it is nonpolylogarithmic. [...]
Published in Physical Review Letters 122 (2019)
10.1103/PhysRevLett.122.031601
arXiv:1810.07689
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2.

Cluster algebras and the subalgebra constructibility of the sevenparticle remainder function
/ Golden, John ; McLeod, Andrew
We review various aspects of cluster algebras and the ways in which they appear in the study of looplevel amplitudes in planar N = 4 $$ \mathcal{N}=4 $$ supersymmetric YangMills theory. [...]
Published in JHEP 1901 (2019) 017
10.1007/JHEP01(2019)017
arXiv:1810.12181
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3.

Rationalizing loop integration
/ Bourjaily, Jacob ; McLeod, Andrew ; Hippel, Matt ; Wilhelm, Matthias
We show that direct Feynmanparametric loop integration is possible for a large class of planar multiloop integrals. [...]
Published in JHEP 1808 (2018) 184
10.1007/JHEP08(2018)184
arXiv:1805.10281
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4.

Traintracks through CalabiYau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms
/ Bourjaily, Jacob L. ; He, YangHui ; McLeod, Andrew J. ; von Hippel, Matt ; et al
We describe a family of finite, fourdimensional, $L$loop Feynman integrals that involve weight($L+1$) hyperlogarithms integrated over ($L1$)dimensional elliptically fibered varieties we conjecture to be CalabiYau manifolds. [...]
Published in Physical Review Letters 121 (2018)
10.1103/PhysRevLett.121.071603
arXiv:1805.09326
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5.

The double pentaladder integral to all orders
/ CaronHuot, Simon ; Dixon, Lance ; Hippel, Matt ; McLeod, Andrew ; et al
We compute dualconformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. [...]
Published in JHEP 1807 (2018) 170
10.1007/JHEP07(2018)170
arXiv:1806.01361
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6.

Elliptic DoubleBox Integrals: Massless Scattering Amplitudes beyond Polylogarithms
/ Bourjaily, Jacob L. ; McLeod, Andrew J. ; Spradlin, Marcus ; von Hippel, Matt ; et al
We derive an analytic representation of the tenparticle, twoloop doublebox integral as an elliptic integral over weightthree polylogarithms. [...]
Published in Phys. Rev. Lett. 120 (2018)
10.1103/PhysRevLett.120.121603
arXiv:1712.02785
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7.

Bootstrapping the QCD soft anomalous dimension
/ Almelid, Øyvind ; Duhr, Claude ; Gardi, Einan ; McLeod, Andrew ; et al
The soft anomalous dimension governs the infrared singularities of scattering amplitudes to all orders in perturbative quantum field theory, and is a crucial ingredient in both formal and phenomenological applications of nonabelian gauge theories. [...]
Published in JHEP 1709 (2017) 073
10.1007/JHEP09(2017)073
arXiv:1706.10162
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8.

Heptagons from the Steinmann cluster bootstrap
/ Dixon, Lance ; Drummond, James ; Harrington, Thomas ; McLeod, Andrew ; et al
We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. [...]
Published in JHEP 1702 (2017) 137
10.1007/JHEP02(2017)137
arXiv:1612.08976
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9.

Multiloop positivity of the planar N $$ \mathcal{N} $$ = 4 SYM sixpoint amplitude
/ Dixon, Lance ; Hippel, Matt ; McLeod, Andrew ; Trnka, Jaroslav
We study the sixpoint NMHV ratio function in planar N $$ \mathcal{N} $$ = 4 SYM theory in the context of positive geometry. [...]
Published in JHEP 1702 (2017) 112
10.1007/JHEP02(2017)112
arXiv:1611.08325
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10.

The fourloop sixgluon NMHV ratio function
/ Dixon, Lance ; Hippel, Matt ; McLeod, Andrew
We use the hexagon function bootstrap to compute the ratio function which characterizes the nexttomaximallyhelicityviolating (NMHV) sixpoint amplitude in planar N = 4 $$ \mathcal{N}=4 $$ superYangMills theory at four loops. [...]
Published in JHEP 1601 (2016) 053
10.1007/JHEP01(2016)053
arXiv:1509.08127
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