Header Image

Computational Mathematics

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.

Christoph SpiegelGábor Braun

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.

Researchers

Christoph Spiegel
spiegel (at) zib.de
Gábor Braun
braun (at) zib.de
Aldo Kiem
kiem (at) zib.de
Max Zimmer
zimmer (at) zib.de
Yves Etienne Jäckle
yvej99 (at) zedat.fu-berlin.de

Projects

Publications

  1. 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]
    @inproceedings{ppss_ramsey_22,
  year = {2023},
  booktitle = {Proceedings of AAAI Conference on Artificial Intelligence},
  archiveprefix = {arXiv},
  eprint = {2206.04036},
  primaryclass = {math.CO},
  author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
  title = {Fully Computer-assisted Proofs in Extremal Combinatorics},
  code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g},
  slides = {https://pokutta.com/slides/20220705_DMD22_RamseyMultiplicity.pdf}
}
  2. 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]
    @inproceedings{rs_radomult_23,
  year = {2023},
  booktitle = {Proceedings of European Conference on Combinatorics},
  archiveprefix = {arXiv},
  eprint = {2304.00400},
  primaryclass = {math.CO},
  author = {Rué Perna, Juan José and Spiegel, Christoph},
  title = {The Rado Multiplicity Problem in Vector Spaces Over Finite Fields},
  code = {https://github.com/FordUniver/rs_radomult_23}
}
  3. Braun, G., Pokutta, S., and Weismantel, R. (2022). Alternating Linear Minimization: Revisiting von Neumann’s Alternating Projections. [arXiv] [slides] [video]
    [BibTeX]
    @misc{alternating_lmo_2022,
  archiveprefix = {arXiv},
  eprint = {2212.02933},
  primaryclass = {math.OC},
  year = {2022},
  author = {Braun, Gábor and Pokutta, Sebastian and Weismantel, Robert},
  title = {Alternating Linear Minimization: Revisiting von Neumann’s Alternating Projections},
  slides = {https://pokutta.com/slides/20230327-icerm.pdf},
  video = {https://icerm.brown.edu/programs/sp-s23/w2/#schedule-item-4945}
}
  4. 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]
    @article{ks_halesjewett_18,
  year = {2022},
  journal = {Electronic Journal of Combinatorics},
  volume = {29},
  number = {1},
  doi = {10.37236/9400},
  url = {https://combinatorics.org/ojs/index.php/eljc/article/view/v29i1p62},
  archiveprefix = {arXiv},
  eprint = {1811.04628},
  primaryclass = {math.CO},
  author = {Kamčev, Nina and Spiegel, Christoph},
  title = {Another Note on Intervals in the Hales-Jewett Theorem}
}
  5. 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]
    @article{frs_sidon_19,
  year = {2021-08},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {182},
  doi = {10.1016/j.jcta.2021.105460},
  url = {https://sciencedirect.com/science/article/abs/pii/S0097316521000595},
  archiveprefix = {arXiv},
  eprint = {1911.13275},
  primaryclass = {math.CO},
  author = {Fabian, David and Rué Perna, Juan José and Spiegel, Christoph},
  title = {On Strong Infinite Sidon and Bₕ Sets and Random Sets of Integers}
}