computer-assistance in proofs; flag algebras in combinatorics; algebraic methods in computation; interactive theorem provers; learning-based heuristics

Exploring optimization, learning, and formal proof verification to advance pure mathematics.

What we are interested in

Computers and Artificial Intelligence have always been an important tool for mathematicians,
allowing one to gather data and extrapolate connections to formulate conjectures, exhaustively
execute case analysis too large to be done by hande, solve underlying optimization problems,
or to formalize and verify proofs. We are interested in exploring the many ways in which computational
tools can be used to advance mathematics and formulate novel results by leveraging our
unique knowledge of and access to the ZIB’s computational resources.

Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2023). Fully Computer-assisted Proofs in Extremal Combinatorics. Proceedings of AAAI Conference on Artificial Intelligence.[arXiv][slides][code][BibTeX]

Rué Perna, J. J., and Spiegel, C. (2023). The Rado Multiplicity Problem in Vector Spaces Over Finite Fields. Proceedings of European Conference on Combinatorics.[arXiv][code][BibTeX]

Braun, G., Pokutta, S., and Weismantel, R. (2022). Alternating Linear Minimization: Revisiting von Neumann’s Alternating Projections.[arXiv][slides][video][BibTeX]

Kamčev, N., and Spiegel, C. (2022). Another Note on Intervals in the Hales-Jewett Theorem. Electronic Journal of Combinatorics, 29(1).DOI: 10.37236/9400[URL][arXiv][BibTeX]

Fabian, D., Rué Perna, J. J., and Spiegel, C. (2021-08). On Strong Infinite Sidon and Bₕ Sets and Random Sets of Integers. Journal of Combinatorial Theory, Series A, 182.DOI: 10.1016/j.jcta.2021.105460[URL][arXiv][BibTeX]