4 papers
NEXP-Completeness and Exponential Coefficient Growth for Existential Presburger Arithmetic with Divisibility
Ignacio Barros, Michaël Cadilhac, Guillermo A. Pérez
We prove that satisfiability for existential Presburger arithmetic with divisibility (EPAD) is NEXP-hard. Together with the known NEXP upper bound, this establishes NEXP-completene…
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of…
A simple criterion for the uniruledness of an orthogonal modular variety
Ignacio Barros
We exhibit a simple uniruledness criterion for general orthogonal modular varieties in terms of invariants of the corresponding lattice. As an application, we obtain the uniruledne…
Two moduli spaces of Calabi-Yau type
Ignacio Barros, Scott Mullane
We show and have Kodaira dimension zero. Our method relies on the construction of a number of curves via nodal Lefschetz penci…