Tootfinder

The geometric bookkeeping guide to Feynman integral reduction and $\varepsilon$-factorised differential equations
Iris Bree, Federico Gasparotto, Antonela Matija\v{s}i\'c, Pouria Mazloumi, Dmytro Melnichenko, Sebastian P\"ogel, Toni Teschke, Xing Wang, Stefan Weinzierl, Konglong Wu, Xiaofeng Xu
https://arxiv.org/abs/250…

The geometric bookkeeping guide to Feynman integral reduction and $\varepsilon$-factorised differential equations
We report on three improvements in the context of Feynman integral reduction and $\varepsilon$-factorised differential equations: Firstly, we show that with a specific choice of prefactors, we trivialise the $\varepsilon$-dependence of the integration-by-parts identities. Secondly, we observe that with a specific choice of order relation in the Laporta algorithm, we directly obtain a basis of master integrals, whose differential equation on the maximal cut is in Laurent polynomial form with res…

On the zero sets of harmonic polynomials
Ioann Vasilyev
https://arxiv.org/abs/2506.24116 https://arxiv.org/pdf/2506.24116

On the zero sets of harmonic polynomials
In this paper we consider nonzero harmonic functions vanishing on certain subvarieties. Among other things, we give a positive solution to the Problem 151 from the Scottish Book posed by R. Wavre in 1936. In more detail, we construct a nonzero harmonic function in the whole space that vanishes on the edges of the unit cube. Moreover, using harmonic morphisms we construct certain new nontrivial families of harmonic polynomials that vanish at the same set in the unit ball in n-dimensional space f…