Persistent homology analysis, a recently developed computational method in algebraic
topology, is applied to the study of the phase transitions undergone by the so-called mean …

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain
with periodic boundary conditions. We formulate a conjecture for the number of solutions …

Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of
equations, which is an important yet challenging problem. We translate this into an algebraic …

A new basin-sampling scheme is introduced to obtain equilibrium thermodynamic properties
by combining results from global optimisation and parallel tempering calculations. Regular …

Finding vacua for the four‐dimensional effective theories for supergravity which descend
from flux compactifications and analyzing them according to their stability is one of the …

In this review work, we outline a conceptual path that, starting from the numerical
investigation of the transition between weak chaos and strong chaos in Hamiltonian systems …

By using the viewpoint of modern computational algebraic geometry, we explore properties
of the optimization landscapes of deep linear neural network models. After providing …

A bstract We explicitly construct all supersymmetric flux vacua of a particular Calabi-Yau
compactification of type IIB string theory for a small number of flux carrying cycles and a …

In this essay, I provide an overview of the debate on infinite and essential idealizations in
physics. I will first present two ostensible examples: phase transitions and the Aharonov …

A bstract There is a rich interplay between algebraic geometry and string and gauge
theories which has been recently aided immensely by advances in computational algebra …