Christoph Spiegel

I like using computational tools for theoretical mathematics. Lately, I have used flag algebras, semidefinite programming, machine learning, and discrete optimization to improve some long-standing bounds in extremal combinatorics and discrete geometry. Currently, I am exploring the areas of proof verification and assistance.

📬 Contact

office
Room 3036 at ZIB
e-mail
homepage
christophspiegel.berlin
languages
German, English, and French

🎓 Curriculum vitae

since 2024
Postdoc Representative at MATH+
since 2022
Deputy Department Head at ZIB
since 2020
Member of MATH+
since 2020
Researcher at ZIB
2016 to 2020
Researcher at UPC
Jun 2020
Ph.D. in Applied Mathematics at UPC
2015 to 2016
Member of BMS
2014 to 2015
Research Assistant at ZIB
Mar 2015
M.Sc. in Mathematics at FUB
Dec 2012
B.Sc. in Mathematics at FUB

📝 Publications and preprints

Preprints

  1. Kiem, A., Parczyk, O., and Spiegel, C. (2024). Forcing Graphs to Be Forcing. [arXiv]
    [BibTeX]
    @misc{2024_KiemParczykSpiegel_Forcing,
  archiveprefix = {arXiv},
  eprint = {2412.12904},
  primaryclass = {math.CO},
  year = {2024},
  author = {Kiem, Aldo and Parczyk, Olaf and Spiegel, Christoph},
  title = {Forcing Graphs to Be Forcing},
  date = {2024-12-17}
}
  2. Parczyk, O., and Spiegel, C. (2024). An Unsure Note on an Un-Schur Problem. [arXiv]
    [BibTeX]
    @misc{2024_ParczykSpiegel_UnSchur,
  archiveprefix = {arXiv},
  eprint = {2410.22024},
  primaryclass = {math.CO},
  year = {2024},
  author = {Parczyk, Olaf and Spiegel, Christoph},
  title = {An Unsure Note on an Un-Schur Problem},
  date = {2024-10-29}
}
  3. Zimmer, M., Andoni, M., Spiegel, C., and Pokutta, S. (2023). PERP: Rethinking the Prune-Retrain Paradigm in the Era of LLMs. [arXiv] [code]
    [BibTeX]
    @misc{2023_ZimmerAndoniSpiegelPokutta_PerpPruneRetrain,
  archiveprefix = {arXiv},
  eprint = {2312.15230},
  primaryclass = {cs.LG},
  year = {2023},
  author = {Zimmer, Max and Andoni, Megi and Spiegel, Christoph and Pokutta, Sebastian},
  title = {PERP: Rethinking the Prune-Retrain Paradigm in the Era of LLMs},
  code = {https://github.com/ZIB-IOL/PERP},
  date = {2023-12-23}
}
  4. Combettes, C., Spiegel, C., and Pokutta, S. (2020). Projection-free Adaptive Gradients for Large-scale Optimization. [arXiv] [summary] [code]
    [BibTeX]
    @misc{2020_CombettesSpiegelPokutta_Projectionfreeadaptivegradients,
  archiveprefix = {arXiv},
  eprint = {2009.14114},
  primaryclass = {math.OC},
  year = {2020},
  author = {Combettes, Cyrille and Spiegel, Christoph and Pokutta, Sebastian},
  title = {Projection-free Adaptive Gradients for Large-scale Optimization},
  code = {https://github.com/ZIB-IOL/StochasticFrankWolfe},
  summary = {https://pokutta.com/blog/research/2020/10/21/adasfw.html},
  date = {2020-09-29}
}
  5. Pokutta, S., Spiegel, C., and Zimmer, M. (2020). Deep Neural Network Training with Frank-Wolfe. [arXiv] [summary] [code]
    [BibTeX]
    @misc{2020_PokuttaSpiegelZimmer_Frankwolfeneuralnetworks,
  archiveprefix = {arXiv},
  eprint = {2010.07243},
  primaryclass = {cs.LG},
  year = {2020},
  author = {Pokutta, Sebastian and Spiegel, Christoph and Zimmer, Max},
  title = {Deep Neural Network Training with Frank-Wolfe},
  code = {https://github.com/ZIB-IOL/StochasticFrankWolfe},
  summary = {https://pokutta.com/blog/research/2020/11/11/NNFW.html},
  date = {2020-10-14}
}
  6. Salia, N., Spiegel, C., Tompkins, C., and Zamora, O. (2019). Independent Chains in Acyclic Posets. [arXiv]
    [BibTeX]
    @misc{2019_SaliaSpiegelTompkinsZamora_Independentchainsacyclicposets,
  archiveprefix = {arXiv},
  eprint = {1912.03288},
  primaryclass = {math.CO},
  year = {2019},
  author = {Salia, Nika and Spiegel, Christoph and Tompkins, Casey and Zamora, Oscar},
  title = {Independent Chains in Acyclic Posets},
  date = {2019-12-06}
}

Conference proceedings

  1. Mundinger, K., Zimmer, M., Kiem, A., Spiegel, C., and Pokutta, S. (2025, January 30). Neural Discovery in Mathematics: Do Machines Dream of Colored Planes? Proceedings of the International Conference on Machine Learning. [arXiv]
    [BibTeX]
    @inproceedings{2025_MundingerZimmerKiemSpiegelPokutta_NeuralDiscovery,
  year = {2025},
  booktitle = {Proceedings of the International Conference on Machine Learning},
  archiveprefix = {arXiv},
  eprint = {2501.18527},
  primaryclass = {cs.LG},
  author = {Mundinger, Konrad and Zimmer, Max and Kiem, Aldo and Spiegel, Christoph and Pokutta, Sebastian},
  title = {Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?},
  date = {2025-01-30}
}
  2. Kiem, A., Pokutta, S., and Spiegel, C. (2024). The Four-color Ramsey Multiplicity of Triangles. Proceedings of the Discrete Mathematics Days. [URL] [arXiv] [code]
    [BibTeX]
    @inproceedings{2023_KiemPokuttaSpiegel_4colorramsey,
  year = {2024},
  booktitle = {Proceedings of the Discrete Mathematics Days},
  url = {https://dmd2024.web.uah.es/files/abstracts/paper_3.pdf},
  archiveprefix = {arXiv},
  eprint = {2312.08049},
  primaryclass = {math.CO},
  author = {Kiem, Aldo and Pokutta, Sebastian and Spiegel, Christoph},
  title = {The Four-color Ramsey Multiplicity of Triangles},
  code = {https://github.com/FordUniver/kps_trianglemult}
}
  3. Zimmer, M., Spiegel, C., and Pokutta, S. (2024). Sparse Model Soups: A Recipe for Improved Pruning Via Model Averaging. Proceedings of the International Conference on Learning Representations. [URL] [arXiv]
    [BibTeX]
    @inproceedings{2023_ZimmerSpiegelPokutta_Sparsemodelsoups,
  year = {2024},
  booktitle = {Proceedings of the International Conference on Learning Representations},
  url = {https://iclr.cc/virtual/2024/poster/17433},
  archiveprefix = {arXiv},
  eprint = {2306.16788},
  primaryclass = {cs.LG},
  author = {Zimmer, Max and Spiegel, Christoph and Pokutta, Sebastian},
  title = {Sparse Model Soups: A Recipe for Improved Pruning Via Model Averaging}
}
  4. Kiem, A., Pokutta, S., and Spiegel, C. (2024). Categorification of Flag Algebras. Proceedings of the Discrete Mathematics Days. [URL]
    [BibTeX]
    @inproceedings{2024_KiemPokuttaSpiegel_Categorificationflagalgebras,
  year = {2024},
  booktitle = {Proceedings of the Discrete Mathematics Days},
  url = {https://dmd2024.web.uah.es/files/abstracts/paper_47.pdf},
  author = {Kiem, Aldo and Pokutta, Sebastian and Spiegel, Christoph},
  title = {Categorification of Flag Algebras}
}
  5. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024, April 8). Extending the Continuum of Six-Colorings. Proceedings of the Discrete Mathematics Days. [URL] [arXiv]
    [BibTeX]
    @inproceedings{2024_MundingerPokuttaSpiegelZimmer_SixcoloringsExpansion:1,
  year = {2024},
  booktitle = {Proceedings of the Discrete Mathematics Days},
  url = {https://dmd2024.web.uah.es/files/abstracts/paper_27.pdf},
  archiveprefix = {arXiv},
  eprint = {2404.05509},
  primaryclass = {math.CO},
  author = {Mundinger, Konrad and Pokutta, Sebastian and Spiegel, Christoph and Zimmer, Max},
  title = {Extending the Continuum of Six-Colorings},
  date = {2024-04-08}
}
  6. Zimmer, M., Spiegel, C., and Pokutta, S. (2023). How I Learned to Stop Worrying and Love Retraining. Proceedings of the International Conference on Learning Representations. [URL] [arXiv] [code]
    [BibTeX]
    @inproceedings{2021_ZimmerSpiegelPokutta_Retrainingpruning,
  year = {2023},
  booktitle = {Proceedings of the International Conference on Learning Representations},
  url = {https://iclr.cc/virtual/2023/poster/10914},
  archiveprefix = {arXiv},
  eprint = {2111.00843},
  primaryclass = {cs.LG},
  author = {Zimmer, Max and Spiegel, Christoph and Pokutta, Sebastian},
  title = {How I Learned to Stop Worrying and Love Retraining},
  code = {https://github.com/ZIB-IOL/BIMP}
}
  7. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2023). Fully Computer-assisted Proofs in Extremal Combinatorics. Proceedings of the AAAI Conference on Artificial Intelligence. DOI: 10.1609/aaai.v37i10.26470 [URL] [arXiv] [code]
    [BibTeX]
    @inproceedings{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics:1,
  year = {2023},
  booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence},
  doi = {10.1609/aaai.v37i10.26470},
  url = {https://ojs.aaai.org/index.php/AAAI/article/view/26470},
  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}
}
  8. Rué, J. J., and Spiegel, C. (2023, April 1). The Rado Multiplicity Problem in Vector Spaces Over Finite Fields. Proceedings of the European Conference on Combinatorics, Graph Theory and Applications. DOI: 10.5817/CZ.MUNI.EUROCOMB23-108 [URL] [arXiv] [code]
    [BibTeX]
    @inproceedings{2023_RueSpiegel_Radomultiplicity,
  year = {2023},
  booktitle = {Proceedings of the European Conference on Combinatorics, Graph Theory and Applications},
  doi = {10.5817/CZ.MUNI.EUROCOMB23-108},
  url = {https://journals.muni.cz/eurocomb/article/view/35642},
  archiveprefix = {arXiv},
  eprint = {2304.00400},
  primaryclass = {math.CO},
  author = {Rué, Juan José and Spiegel, Christoph},
  title = {The Rado Multiplicity Problem in Vector Spaces Over Finite Fields},
  code = {https://github.com/FordUniver/rs_radomult_23},
  date = {2023-04-01}
}
  9. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2022, July 1). New Ramsey Multiplicity Bounds and Search Heuristics. Proceedings of the Discrete Mathematics Days. [arXiv] [code]
    [BibTeX]
    @inproceedings{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics:2,
  year = {2022},
  date = {2022-07-01},
  booktitle = {Proceedings of the Discrete Mathematics Days},
  archiveprefix = {arXiv},
  eprint = {2206.04036},
  primaryclass = {math.CO},
  author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
  title = {New Ramsey Multiplicity Bounds and Search Heuristics},
  code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g}
}
  10. Rué, J. J., and Spiegel, C. (2018, February 21). On a Problem of Sárközy and Sós for Multivariate Linear Forms. Proceedings of the Discrete Mathematics Days. [URL] [arXiv]
    [BibTeX]
    @inproceedings{2018_RueSpiegel_Srkzyss:1,
  year = {2018},
  booktitle = {Proceedings of the Discrete Mathematics Days},
  url = {https://congreso.us.es/dmd2018/wp-content/uploads/2018/05/DMD2018_paper_21.pdf},
  archiveprefix = {arXiv},
  eprint = {1802.07597},
  primaryclass = {math.CO},
  author = {Rué, Juan José and Spiegel, Christoph},
  title = {On a Problem of Sárközy and Sós for Multivariate Linear Forms},
  date = {2018-02-21}
}
  11. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2017, November 20). Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games. Proceedings of the European Conference on Combinatorics, Graph Theory and Applications. [URL] [arXiv]
    [BibTeX]
    @inproceedings{2017_KuschRueSpiegelSzabo_Uniformrandomstrategy:1,
  year = {2017},
  booktitle = {Proceedings of the European Conference on Combinatorics, Graph Theory and Applications},
  url = {https://dmg.tuwien.ac.at/eurocomb2017/index.php/accepted-papers/},
  archiveprefix = {arXiv},
  eprint = {1711.07251},
  primaryclass = {math.CO},
  author = {Kusch, Christopher and Rué, Juan José and Spiegel, Christoph and Szabó, Tibor},
  title = {Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games},
  date = {2017-11-20}
}

Full articles

  1. Zimmer, M., Spiegel, C., and Pokutta, S. (2025). Compression-aware Training of Neural Networks Using Frank-Wolfe. Mathematical Optimization for Machine Learning, 137–168. DOI: 10.1515/9783111376776-010 [arXiv]
    [BibTeX]
    @article{2022_ZimmerSpiegelPokutta_Compressionawaretraining,
  year = {2025},
  journal = {Mathematical Optimization for Machine Learning},
  date = {2025-04-22},
  month = apr,
  pages = {137-168},
  doi = {10.1515/9783111376776-010},
  archiveprefix = {arXiv},
  eprint = {2205.11921},
  primaryclass = {cs.LG},
  author = {Zimmer, Max and Spiegel, Christoph and Pokutta, Sebastian},
  title = {Compression-aware Training of Neural Networks Using Frank-Wolfe}
}
  2. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2024). New Ramsey Multiplicity Bounds and Search Heuristics. Foundations of Computational Mathematics. DOI: 10.1007/s10208-024-09675-6 [arXiv] [code]
    [BibTeX]
    @article{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics,
  year = {2024},
  journal = {Foundations of Computational Mathematics},
  date = {2024-08-06},
  doi = {10.1007/s10208-024-09675-6},
  archiveprefix = {arXiv},
  eprint = {2206.04036},
  primaryclass = {math.CO},
  author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
  title = {New Ramsey Multiplicity Bounds and Search Heuristics},
  code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g}
}
  3. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). Extending the Continuum of Six-Colorings. Geombinatorics Quarterly, XXXIV. [URL] [arXiv]
    [BibTeX]
    @article{2024_MundingerPokuttaSpiegelZimmer_SixcoloringsExpansion,
  year = {2024},
  journal = {Geombinatorics Quarterly},
  date = {2024-07-01},
  volume = {XXXIV},
  url = {https://geombina.uccs.edu/past-issues/volume-xxxiv},
  archiveprefix = {arXiv},
  eprint = {2404.05509},
  primaryclass = {math.CO},
  author = {Mundinger, Konrad and Pokutta, Sebastian and Spiegel, Christoph and Zimmer, Max},
  title = {Extending the Continuum of Six-Colorings}
}
  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{2018_KamcevSpiegel_Halesjewettintervals,
  year = {2022},
  journal = {Electronic Journal of Combinatorics},
  date = {2022-03-25},
  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. Cao-Labora, G., Rué, J. J., and Spiegel, C. (2020). An Erdős-Fuchs Theorem for Ordered Representation Functions. Ramanujan Journal, 56, 183–2091. DOI: 10.1007/s11139-020-00326-2 [URL] [arXiv]
    [BibTeX]
    @article{2019_CaolaboraRueSpiegel_Erdosfuchs,
  year = {2021-10},
  journal = {Ramanujan Journal},
  date = {2020-10-28},
  volume = {56},
  pages = {183-2091},
  doi = {10.1007/s11139-020-00326-2},
  url = {https://link.springer.com/article/10.1007/s11139-020-00326-2},
  archiveprefix = {arXiv},
  eprint = {1911.12313},
  primaryclass = {math.NT},
  author = {Cao-Labora, Gonzalo and Rué, Juan José and Spiegel, Christoph},
  title = {An Erdős-Fuchs Theorem for Ordered Representation Functions}
}
  6. Fabian, D., Rué, J. J., and Spiegel, C. (2021). 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{2019_FabianRueSpiegel_Strongsidonsets,
  year = {2021-08},
  journal = {Journal of Combinatorial Theory, Series A},
  date = {2021-04-21},
  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, Juan José and Spiegel, Christoph},
  title = {On Strong Infinite Sidon and Bₕ Sets and Random Sets of Integers}
}
  7. Corsten, J., Mond, A., Pokrovskiy, A., Spiegel, C., and Szabó, T. (2020). On the Odd Cycle Game and Connected Rules. European Journal of Combinatorics, 89. DOI: 10.1016/j.ejc.2020.103140 [URL] [arXiv]
    [BibTeX]
    @article{2019_CorstenEtAl_Oddcyclegame,
  year = {2020-10},
  journal = {European Journal of Combinatorics},
  date = {2020-05-20},
  volume = {89},
  doi = {10.1016/j.ejc.2020.103140},
  url = {https://sciencedirect.com/science/article/abs/pii/S0195669820300615},
  archiveprefix = {arXiv},
  eprint = {1906.04024},
  primaryclass = {math.CO},
  author = {Corsten, Jan and Mond, Adva and Pokrovskiy, Alexey and Spiegel, Christoph and Szabó, Tibor},
  title = {On the Odd Cycle Game and Connected Rules}
}
  8. Rué, J. J., and Spiegel, C. (2020). On a Problem of Sárközy and Sós for Multivariate Linear Forms. Revista Matemática Iberoamericana, 36(7), 2107–2119. DOI: 10.4171/RMI/1193 [URL] [arXiv]
    [BibTeX]
    @article{2018_RueSpiegel_Srkzyss,
  year = {2020},
  journal = {Revista Matemática Iberoamericana},
  date = {2020-03-19},
  volume = {36},
  number = {7},
  pages = {2107-2119},
  doi = {10.4171/RMI/1193},
  url = {https://ems.press/journals/rmi/articles/16818},
  archiveprefix = {arXiv},
  eprint = {1802.07597},
  primaryclass = {math.CO},
  author = {Rué, Juan José and Spiegel, Christoph},
  title = {On a Problem of Sárközy and Sós for Multivariate Linear Forms}
}
  9. Candela, P., Serra, O., and Spiegel, C. (2020). A Step Beyond Freĭman’s Theorem for Set Addition Modulo a Prime. Journal De Théorie Des Nombres De Bordeaux, 32(1), 275–289. DOI: 10.5802/jtnb.1122 [URL] [arXiv]
    [BibTeX]
    @article{2019_CandelaSerraSpiegel_Fremantheorem,
  year = {2020},
  journal = {Journal de Théorie des Nombres de Bordeaux},
  date = {2020-08-21},
  volume = {32},
  number = {1},
  pages = {275-289},
  doi = {10.5802/jtnb.1122},
  url = {https://jtnb.centre-mersenne.org/item/JTNB_2020__32_1_275_0/},
  archiveprefix = {arXiv},
  eprint = {1805.12374},
  primaryclass = {math.CO},
  author = {Candela, Pablo and Serra, Oriol and Spiegel, Christoph},
  title = {A Step Beyond Freĭman's Theorem for Set Addition Modulo a Prime}
}
  10. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2018). On the Optimality of the Uniform Random Strategy. Random Structures & Algorithms, 55(2), 371–401. DOI: 10.1002/rsa.20829 [URL] [arXiv]
    [BibTeX]
    @article{2017_KuschRueSpiegelSzabo_Uniformrandomstrategy,
  year = {2019-09},
  journal = {Random Structures & Algorithms},
  date = {2018-12-10},
  volume = {55},
  number = {2},
  pages = {371-401},
  doi = {10.1002/rsa.20829},
  url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.20829},
  archiveprefix = {arXiv},
  eprint = {1711.07251},
  primaryclass = {math.CO},
  author = {Kusch, Christopher and Rué, Juan José and Spiegel, Christoph and Szabó, Tibor},
  title = {On the Optimality of the Uniform Random Strategy}
}
  11. Freĭman, G. A., Serra, O., and Spiegel, C. (2019). Additive Volume of Sets Contained in Few Arithmetic Progressions. INTEGERS, 19. [URL] [arXiv]
    [BibTeX]
    @article{2018_FreimanSerraSpiegel_Additivevolumearithmeticprogressions,
  year = {2019},
  journal = {INTEGERS},
  date = {2019-06-03},
  volume = {19},
  url = {https://math.colgate.edu/~integers/t34/t34.mail.html},
  archiveprefix = {arXiv},
  eprint = {1808.08455},
  primaryclass = {math.NT},
  author = {Freĭman, Gregory A. and Serra, Oriol and Spiegel, Christoph},
  title = {Additive Volume of Sets Contained in Few Arithmetic Progressions}
}
  12. Rué, J. J., Spiegel, C., and Zumalacárregui, A. (2017). Threshold Functions and Poisson Convergence for Systems of Equations in Random Sets. Mathematische Zeitschrift, 288, 333–360. DOI: 10.1007/s00209-017-1891-2 [URL] [arXiv]
    [BibTeX]
    @article{2012_RueSpiegelZumalacarregui_ThresholdfunctionsPoissonconvergence,
  year = {2018},
  journal = {Mathematische Zeitschrift},
  date = {2017-04-10},
  month = feb,
  volume = {288},
  pages = {333-360},
  doi = {10.1007/s00209-017-1891-2},
  url = {https://link.springer.com/article/10.1007/s00209-017-1891-2},
  archiveprefix = {arXiv},
  eprint = {1212.5496},
  primaryclass = {math.CO},
  author = {Rué, Juan José and Spiegel, Christoph and Zumalacárregui, Ana},
  title = {Threshold Functions and Poisson Convergence for Systems of Equations in Random Sets}
}
  13. Spiegel, C. (2017). A Note on Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems. Electronic Journal of Combinatorics, 24(3). DOI: 10.37236/6730 [URL] [arXiv]
    [BibTeX]
    @article{2017_Spiegel_Sparsesupersaturation,
  year = {2017},
  journal = {Electronic Journal of Combinatorics},
  date = {2017-08-25},
  volume = {24},
  number = {3},
  doi = {10.37236/6730},
  url = {https://combinatorics.org/ojs/index.php/eljc/article/view/v24i3p38},
  archiveprefix = {arXiv},
  eprint = {1701.01631},
  primaryclass = {math.CO},
  author = {Spiegel, Christoph},
  title = {A Note on Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems}
}

🔬 Projects

LEAN on Me: Transforming Mathematics Through Formal Verification, Improved Tactics, and Machine Learning

Formal proof verification can both ensure proof correctness and provide new tools and insights to mathematicians. The goals of this project include creating resources for students and researchers, verifying relevant results, improving proof tactics, and exploring Machine Learning approaches.

MATH+ AA5-9
Jan 2024 to Dec 2025
5
Scaling Up Flag Algebras in Combinatorics

This project aims to obtain new bounds in Extremal Combinatorics through an application of flag algebras. The goal is to both improve the underlying computational aspects for existing problems as well as to further develop the theory of flag algebras to extend it to new areas of application.

MATH+ EF1-21
Oct 2022 to Sep 2025
4
4
Learning Extremal Structures in Combinatorics

Extremal Combinatorics focuses on the maximum or minimum sizes of discrete structures with specific properties, posing significant challenges due to their complexity. Traditional computational approaches often fail due to exponential growth in search spaces, but recent AI advancements, especially in Reinforcement Learning, offer new potential. Applying these AI methods could provide insights into combinatorial problems while also enhancing the understanding of AI techniques in complex, sparse reward environments.

MATH+ EF1-12
Jan 2021 to May 2024
4
14
Adaptive Algorithms Through Machine Learning: Exploiting Interactions in Integer Programming

The performance of modern mixed-integer program solvers is highly dependent on a number of interdependent individual components. Using tools from machine learning, we intend to develop an integrated framework that is able to capture interactions of individual decisions made in these components with the ultimate goal to improve performance.

MATH+ EF1-9
Jan 2021 to Dec 2022
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💬 Talks and posters

Conference and workshop talks

May 2025
Forcing Graphs to Be Forcing
13th HJSDM Conference, Tokyo
May 2025
An Unsure Talk on an Un-Schur Problem
17th Combinatorial and Additive Number Theory Conference (CANT), New York
May 2025
Neural Discovery in Mathematics
7th DOxML Conference, Kyoto
Oct 2024
Extending the Continuum of Six-Colorings
41st Kolloquium über Kombinatorik (KolKom), Heidelberg [PDF]
Sep 2024
The Role of Machine Learning for Mathematics
5th Computational Optimization at Work (CO@Work), Berlin [PDF] [video]
Jul 2024
Extending the Continuum of Six-Colorings
13th Discrete Mathematics Days (DMD), Alcalá de Henares [PDF]
Oct 2023
The Role of Machine Learning for Mathematics
BMS RTA 8 - Practical Course, Berlin [PDF]
Aug 2023
The Rado Multiplicity Problem in Vector Spaces Over Finite Fields
12th EUROCOMB Conference, Prague [PDF]
Aug 2023
Computational Challenges in Flag Algebra Proofs
ICIAM 2023 Minisymposium: Advances in Optimization I, Tokyo [PDF]
Aug 2023
Flag Algebras in Additive Combinatorics
5th DOxML Conference, Tokyo [PDF]
Jun 2023
Towards Flag Algebras in Additive Combinatorics
FoCM 2023 Workshop I.3: Graph Theory and Combinatorics, Paris [PDF]
May 2023
Towards Flag Algebras in Additive Combinatorics
15th Combinatorial and Additive Number Theory Conference (CANT), New York [PDF]
Mar 2023
Computer-assisted Proofs in Extremal Combinatorics
Workshop on Optimization and Machine Learning, Waischenfeld [PDF]
Feb 2023
Fully Computer-assisted Proofs in Extremal Combinatorics
37th AAAI Conference on Artificial Intelligence (AAAI), Washington, DC [PDF]
Jan 2023
Fully Computer-assisted Proof in Extremal Combinatorics
Combinatorial Optimization Workshop (Aussois), Aussois [PDF]
Dec 2022
Leveraging Combinatorial Symmetries in Flag Algebra-based SDP Formulations
Workshop on Recent Advances in Optimization, Toronto [PDF]
Sep 2022
Proofs in Extremal Combinatorics Through Optimization
6th ZIB-IMI-ISM-NUS-RIKEN-MODAL Workshop, Tokyo / Fukuoka [PDF]
Jul 2022
New Ramsey Multiplicity Bounds and Search Heuristics
12th Discrete Mathematics Days (DMD), Santander [PDF]
Jun 2019
Odd Cycle Games and Connected Rules
36th Postgraduate Combinatorial Conference (PCC), Oxford [PDF]
Jun 2019
1st GAPCOMB Workshop, Campelles
Jun 2018
On a Problem of Sárközy and Sós for Multivariate Linear Forms
11th Discrete Mathematics Days (DMD), Sevilla [PDF]
May 2018
Going Beyond 2.4 in Freiman's 2.4k-theorem
10th Combinatorial and Additive Number Theory Conference (CANT), New York [PDF]
Sep 2017
Rado Positional Games
The Music of Numbers Conference, Madrid [PDF]
Jun 2017
Generalized Positional Van Der Waerden Games
Interactions with Combinatorics [PDF]
Mar 2017
Joint TAU-FUB Workshop on Graph and Hypergraph Coloring

Research seminar talks

May 2025
Coloring the Plane with Neural Networks
Advanced Topics in Combinatorics II, Taipei
Jan 2025
An Unsure Talk on an Un-Schur Problem
Research Seminar AG Discrete Mathematics, Karlsruhe
Jan 2025
Forcing Graphs to Be Forcing
Research Seminar TCS, Heidelberg
Dec 2024
Coloring the Plane with Neural Networks
Research Seminar Combinatorics, Berlin [PDF]
Nov 2024
An Unsure Talk on an Un-Schur Problem
Research Seminar Combinatorics, Berlin
Feb 2023
The Four-color Ramsey Multiplicity of Triangles
LIMDA Seminar, Barcelona [PDF]
Apr 2022
New Ramsey Multiplicity Bounds and Search Heuristics
LIMDA Seminar, Barcelona
Nov 2019
A Step Beyond Freiman's Theorem for Set Addition Modulo a Prime
Research Seminar Combinatorics, Berlin
Nov 2019
The Probabilistic Intuition in Positional Games
Research Seminar Large Networks and Random Graphs, Ilmenau
May 2019
Intervals in the Hales-Jewett Theorem
Seminar on Combinatorics, Games and Optimisation, London
May 2019
Intervals in the Hales-Jewett Theorem
Combinatorial Theory Seminar, Oxford
Feb 2019
Extremal Set Theory Seminar, Budapest
Dec 2018
Intervals in the Hales-Jewett Theorem
Research Seminar Combinatorics, Berlin
Mar 2018
Going Beyond 2.4 in Freiman's 2.4k-theorem
GRAPHS at IMPA, Rio de Janeiro
Dec 2017
On a Question of Sárközy and Sós
Research Seminar Combinatorics, Berlin
Oct 2017
Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems
LIMDA Seminar, Barcelona
May 2017
Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games
LIMDA Seminar, Barcelona
Mar 2016
Threshold Functions for Systems of Equations in Random Sets
LIMDA Seminar, Barcelona
Feb 2016
Van Der Waerden Games (II)
Research Seminar Combinatorics, Berlin
Jan 2016
Van Der Waerden Games (I)
Research Seminar Combinatorics, Berlin
Dec 2015
What Is Discrete Fourier Analysis?
"What is ...?" seminar [video]
Oct 2015
Threshold Functions for Systems of Equations in Random Sets
Research Seminar Combinatorics, Berlin

Poster presentations

Mar 2023
A Fully Computer-assisted Proof in Extremal Combinatorics
Workshop on Optimization and Machine Learning, Waischenfeld [PDF]
Feb 2023
A Fully Computer-assisted Proof in Extremal Combinatorics
37th AAAI Conference on Artificial Intelligence (AAAI), Washington, DC [PDF]

🌍 Research Stays and Visits

May 2025
National Taiwan University hosted by Shagnik Das
Aug 2024
Institute of Science Tokyo hosted by Katsuki Fujisawa
May 2024
Institute of Science Tokyo hosted by Katsuki Fujisawa
Aug 2023
National Taiwan University hosted by Shagnik Das
Jul 2022
Universitat Politècnica de Catalunya hosted by Juan José Rué
Apr 2022
Universitat Politècnica de Catalunya hosted by Juan José Rué
Jul 2019
Freie Universität Berlin hosted by Tibor Szabó
May 2019
University of Oxford hosted by David Conlon
Feb 2019
Alfréd Rényi Institute of Mathematics hosted by Ervin Győri
Jul 2017
Freie Universität Berlin hosted by Tibor Szabó

📅 Event Attendance

Sep 2025
Open Problems in Combinatorics and Graph Theory, Zamárdi
Aug 2025
13th EUROCOMB Conference, Budapest
Jul 2025
8th International Conference on Continuous Optimization (ICCOPT), Los Angeles
Jul 2025
42nd International Conference on Machine Learning (ICML), Vancouver
Jun 2025
6th GAPCOMB Workshop, Poblet
May 2025
13th HJSDM Conference, Tokyo
May 2025
17th Combinatorial and Additive Number Theory Conference (CANT), New York
May 2025
7th DOxML Conference, Kyoto
Oct 2024
41st Kolloquium über Kombinatorik (KolKom), Heidelberg
Aug 2024
Open Problems in Combinatorics and Graph Theory, Wilhelmsaue
Jul 2024
5th GAPCOMB Workshop, Montserrat
Jul 2024
13th Discrete Mathematics Days (DMD), Alcalá de Henares
Sep 2023
5th Computational Optimization at Work (CO@Work), Berlin
Aug 2023
12th EUROCOMB Conference, Prague
Aug 2023
Open Problems in Combinatorics and Graph Theory, Wilhelmsaue
Aug 2023
ICIAM 2023 Minisymposium: Advances in Optimization I, Tokyo
Aug 2023
5th DOxML Conference, Tokyo
Jun 2023
FoCM 2023 Workshop I.3: Graph Theory and Combinatorics, Paris
May 2023
15th Combinatorial and Additive Number Theory Conference (CANT), New York
Mar 2023
Workshop on Optimization and Machine Learning, Waischenfeld
Feb 2023
37th AAAI Conference on Artificial Intelligence (AAAI), Washington, DC
Jan 2023
Combinatorial Optimization Workshop (Aussois), Aussois
Sep 2022
6th ZIB-IMI-ISM-NUS-RIKEN-MODAL Workshop, Tokyo / Fukuoka
Sep 2022
DMV Annual Meeting, Berlin
Aug 2022
Open Problems in Combinatorics and Graph Theory, Wilhelmsaue
Jul 2022
3rd GAPCOMB Workshop, Montserrat
Jul 2022
12th Discrete Mathematics Days (DMD), Santander
Sep 2021
11th EUROCOMB Conference, Barcelona
Aug 2021
Open Problems in Combinatorics and Graph Theory, Wilhelmsaue
Oct 2019
MFO Seminar 1943a, Oberwolfach
Sep 2019
Open Problems in Combinatorics and Graph Theory, Wilhelmsaue
Jun 2019
1st GAPCOMB Workshop, Campelles
Jun 2019
36th Postgraduate Combinatorial Conference (PCC), Oxford
May 2019
21st One-Day Meeting in Combinatorics
Feb 2019
Graphs and Randomness, Rio de Janeiro
Sep 2018
Open Problems in Combinatorics and Graph Theory, Wilhelmsaue
Jun 2018
11th Discrete Mathematics Days (DMD), Sevilla
May 2018
10th Combinatorial and Additive Number Theory Conference (CANT), New York
May 2018
Georgia Discrete Analysis Conference, Athens
Oct 2017
1st BMS-BGSMath Junior Meeting, Barcelona
Sep 2017
The Music of Numbers Conference, Madrid
Sep 2017
Open Problems in Combinatorics and Graph Theory, Wilhelmsaue
Jun 2017
Interactions with Combinatorics
May 2017
BGSMath course: Random Discrete Structures, Barcelona
Apr 2017
Interactions of harmonic analysis, combinatorics and number theory, Barcelona
Mar 2017
Joint TAU-FUB Workshop on Graph and Hypergraph Coloring
Jan 2017
14th analytic algorithmics and combinatorics (ANALCO), Barcelona
Jan 2017
28th symposium on discrete algorithms (SODA), Barcelona
Sep 2016
Open Problems in Combinatorics and Graph Theory, Wilhelmsaue
Jul 2016
7th European Congress of Mathematics (ECM), Berlin
Jul 2016
Symposium Diskrete Mathematik
Jul 2016
10th Discrete Mathematics Days (DMD), Barcelona
Feb 2016
Joint FUB-TAU Workshop on Ramsey Theory
Jan 2016
Combinatorial and Additive Number Theory
Sep 2015
Cargèse Fall School on Random Graphs, Cargèse
Sep 2015
Open Problems in Combinatorics and Graph Theory, Jetrichovice
May 2015
Berlin-Poznań Seminar in Discrete Mathematics, Berlin
Oct 2014
Methods in Discrete Structures: Polynomial Freimann-Ruzsa

🧑‍🏫 Teaching

winter 2024
Lecturer for Formal Proof Verification at FUB
summer 2024
Lecturer for Discrete Optimization (ADM II) at TUB
winter 2023
Lecturer for Introduction to Linear and Combinatorial Optimization (ADM I) at TUB
summer 2023
Lecturer for Analysis I und Lineare Algebra für Ingenieurwissenschaften at TUB
autumn 2018
Assistant for Discrete Mathematics and Optimization at UPF
autumn 2017
Assistant for Discrete Mathematics and Optimization at UPF
winter 2013
Tutor for Analysis I (Lehramt) at FUB
summer 2012
Tutor for Analysis II (Lehramt) at FUB
summer 2011
Tutor for Analysis I (Lehramt) at FUB

📝 Organization and outreach

Jun 2024
Lange Nacht der Wissenschaften at Zuse Institute Berlin
2024
Organization of the Zuse Research Seminar and Zuse Research Colloquium
2024
Creation and maintenance of the Berlin Math Seminars overview page
2024
Organization of ZIB40 events
Jun 2023
Lange Nacht der Wissenschaften at Zuse Insittute Berlin
2023
Organization of the Zuse Research Seminar
2023
Member of the organizing committee of the MATH+ Thematic Einstein Semester in Berlin
Nov 2022
Assisted in the organization of the Festkolloquium for Martin Aigner in Berlin
Apr 2022
Girls’ Day at Freie Universität Berlin
Sep 2021
Member of the organizing committee of the EUROCOMB conference in Barcelona
Apr 2021
Girls’ Day at Freie Universität Berlin
Sep 2020
Organised exercise session on Robust Machine Learning for CO@Work summer school in Berlin
Oct 2017
Member of the organizing committee of the BMS-BGSMath Junior Meeting in Barcelona
Jul 2016
Assisted in the organization of the Symposium Diskrete Mathematik in Berlin
Jun 2016
Assisted in the organization of the Discrete Mathematics Days in Barcelona

🎈 Miscellaneous

You can find some of my photography on instagram:

Some of my photography I also like designing the occasional conference poster: A collection of conference posters that I have made