5 papers
Fast Isotopy Computation for T-Curves
Zoe Geiselmann, Michael Joswig, Lars Kastner +5
A T-curve of degree is given by a regular unimodular triangulation of together with a sign distribution on its lattice points. By Viro's Patchworking Theorem, th…
Limits of combinatorial patchworking
Zoe Geiselmann, Michael Joswig, Lars Kastner +5
It is shown that there are real plane algebraic curves of degree eight that cannot be realized as T-curves, i.e., via combinatorial patchworking. In fact, this holds for several re…
Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?
Konrad Mundinger, Max Zimmer, Aldo Kiem +2
We demonstrate how neural networks can drive mathematical discovery through a case study of the Hadwiger-Nelson problem, a long-standing open problem at the intersection of discret…
Extending the Continuum of Six-Colorings
Konrad Mundinger, Sebastian Pokutta, Christoph Spiegel +1
We present two novel six-colorings of the Euclidean plane that avoid monochromatic pairs of points at unit distance in five colors and monochromatic pairs at another specified dist…
Neural Parameter Regression for Explicit Representations of PDE Solution Operators
Konrad Mundinger, Max Zimmer, Sebastian Pokutta
We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for oper…