The thesis performs the first elliptic symbol bootstrap to obtain the symbol of the two-loop twelve-point double box, and identifies the first Calabi-Yau threefold geometry in post-Minkowskian gravitational-wave integrals.
Calabi--Yau Operators
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abstract
Motivated by mirror symmetry of one-parameter models, an interesting class of Fuchsian differential operators can be singled out, the so-called Calabi--Yau operators, introduced by Almkvist and Zudilin. They conjecturally determine $Sp(4)$-local systems that underly a $\mathbb{Q}$-VHS with Hodge numbers \[h^{3 0}=h^{2 1}=h^{1 2}=h^{0 3}=1\] and in the best cases they make their appearance as Picard--Fuchs operators of families of Calabi--Yau threefolds with $h^{12}=1$ and encode the numbers of rational curves on a mirror manifold with $h^{11}=1$. We review some of the striking properties of this rich class of operators.
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Special Functions and Geometries in Scattering Amplitudes: From Particle Physics to Gravity
The thesis performs the first elliptic symbol bootstrap to obtain the symbol of the two-loop twelve-point double box, and identifies the first Calabi-Yau threefold geometry in post-Minkowskian gravitational-wave integrals.