Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in the Gauss-Manin connection.
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Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
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Integrand Analysis, Leading Singularities and Canonical Bases beyond Polylogarithms
Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in the Gauss-Manin connection.
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Discrete symmetries of Feynman integrals
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
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New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
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From geometry to phenomenology
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.