28 citations · 30 across the 8 of their papers we have counts for
6 papers · 1 filter
Sampling Triangulations and Calabi-Yau Threefolds with Autoregressive GNNs
Nate MacFadden
We introduce `dualGNN', an autoregressive message-passing GNN for sampling fine, regular triangulations of lattice polytopes. dualGNN operates on a generalization of the dual graph…
Further Bounding the Kreuzer-Skarke Landscape
Nate MacFadden, Stepan Yu. Orevkov, Michael Stepniczka
Batyrev's construction provides a map from fine, regular, star triangulations (FRSTs) of 4D reflexive polytopes to smooth Calabi-Yau threefolds (CYs). We prove that there are at mo…
Calabi-Yau Threefolds from Vex Triangulations
Nate MacFadden, Elijah Sheridan
We study the birational geometry (i.e., Kähler moduli space) of Calabi--Yau (CY) threefold hypersurfaces in toric varieties arising from four-dimensional reflexive polytopes. In pa…
The DNA of Calabi-Yau Hypersurfaces
Nate MacFadden, Andreas Schachner, Elijah Sheridan
We implement Genetic Algorithms for triangulations of four-dimensional reflexive polytopes which induce Calabi-Yau threefold hypersurfaces via Batyrev's construction. We demonstrat…
Counting Calabi-Yau Threefolds
Naomi Gendler, Nate MacFadden, Liam McAllister +4
We enumerate topologically-inequivalent compact Calabi-Yau threefold hypersurfaces. By computing arithmetic and algebraic invariants and the Gopakumar-Vafa invariants of curves, we…
Efficient Algorithm for Generating Homotopy Inequivalent Calabi-Yaus
Nate MacFadden
We present an algorithm for efficiently exploring inequivalent Calabi-Yau threefold hypersurfaces in toric varieties. A direct enumeration of fine, regular, star triangulations (FR…