Christoph Spiegel

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

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Preprints

1. Zimmer, M., Spiegel, C., and Pokutta, S. (2022). Compression-aware Training of Neural Networks Using Frank-Wolfe. [arXiv]
   [BibTeX]

   @misc{zsp_deepsparsefw_22,
     archiveprefix = {arXiv},
     eprint = {2205.11921},
     primaryclass = {cs.LG},
     year = {2022},
     author = {Zimmer, Max and Spiegel, Christoph and Pokutta, Sebastian},
     title = {Compression-aware Training of Neural Networks Using Frank-Wolfe}
   }

2. Combettes, C., Spiegel, C., and Pokutta, S. (2020). Projection-free Adaptive Gradients for Large-scale Optimization. [arXiv] [summary] [code]
   [BibTeX]

   @misc{csp_adafw_20,
     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}
   }

3. Pokutta, S., Spiegel, C., and Zimmer, M. (2020). Deep Neural Network Training with Frank-Wolfe. [arXiv] [summary] [code]
   [BibTeX]

   @misc{zsp_deepfw_20,
     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}
   }

4. Salia, N., Spiegel, C., Tompkins, C., and Zamora, O. (2019). Independent Chains in Acyclic Posets. [arXiv]
   [BibTeX]

   @misc{sstz_poset_19,
     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}
   }

Conference proceedings

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 = {http://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. Zimmer, M., Spiegel, C., and Pokutta, S. (2023). How I Learned to Stop Worrying and Love Retraining. Proceedings of International Conference on Learning Representations. [arXiv] [code]
   [BibTeX]

   @inproceedings{zsp_retrain_21,
     year = {2023},
     booktitle = {Proceedings of International Conference on Learning Representations},
     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}
   }

4. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2022). New Ramsey Multiplicity Bounds and Search Heuristics. Proceedings of Discrete Mathematics Days. [arXiv] [code]
   [BibTeX]

   @inproceedings{ppss_ramsey_22:1:,
     year = {2022},
     booktitle = {Proceedings of 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}
   }

5. Rué Perna, J. J., and Spiegel, C. (2018). On a Problem of Sárközy and Sós for Multivariate Linear Forms. Proceedings of Discrete Mathematics Days. [arXiv]
   [BibTeX]

   @inproceedings{rs_sarkozysos_18:1:,
     year = {2018},
     booktitle = {Proceedings of Discrete Mathematics Days},
     archiveprefix = {arXiv},
     eprint = {1802.07597},
     primaryclass = {math.CO},
     author = {Rué Perna, Juan José and Spiegel, Christoph},
     title = {On a Problem of Sárközy and Sós for Multivariate Linear Forms}
   }

6. Kusch, C., Rué Perna, J. J., Spiegel, C., and Szabó, T. (2017). Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games. Proceedings of European Conference on Combinatorics. [URL] [arXiv]
   [BibTeX]

   @inproceedings{krss_randomstrategy_17:1:,
     year = {2017},
     booktitle = {Proceedings of European Conference on Combinatorics},
     url = {https://www.dmg.tuwien.ac.at/eurocomb2017/index.php/accepted-papers/},
     archiveprefix = {arXiv},
     eprint = {1711.07251},
     primaryclass = {math.CO},
     author = {Kusch, Christopher and Rué Perna, Juan José and Spiegel, Christoph and Szabó, Tibor},
     title = {Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games}
   }

Full articles

1. 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://www.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}
   }

2. Cao-Labora, G., Rué Perna, J. J., and Spiegel, C. (2021-10). An Erdős-Fuchs Theorem for Ordered Representation Functions. Ramanujan Journal, 56, 183–2091. DOI: 10.1007/s11139-020-00326-2 [URL] [arXiv]
   [BibTeX]

   @article{crs_erdosfuchs_19,
     year = {2021-10},
     journal = {Ramanujan Journal},
     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 Perna, Juan José and Spiegel, Christoph},
     title = {An Erdős-Fuchs Theorem for Ordered Representation Functions}
   }

3. 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://www.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}
   }

4. Corsten, J., Mond, A., Pokrovskiy, A., Spiegel, C., and Szabó, T. (2020-10). On the Odd Cycle Game and Connected Rules. European Journal of Combinatorics, 89. DOI: 10.1016/j.ejc.2020.103140 [URL] [arXiv]
   [BibTeX]

   @article{cmpss_oddcyclegame_19,
     year = {2020-10},
     journal = {European Journal of Combinatorics},
     volume = {89},
     doi = {10.1016/j.ejc.2020.103140},
     url = {https://www.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}
   }

5. 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{css_freiman_18,
     year = {2020},
     journal = {Journal de Théorie des Nombres de Bordeaux},
     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}
   }

6. Rué Perna, 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{rs_sarkozysos_18,
     year = {2020},
     journal = {Revista Matemática Iberoamericana},
     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 Perna, Juan José and Spiegel, Christoph},
     title = {On a Problem of Sárközy and Sós for Multivariate Linear Forms}
   }

7. Kusch, C., Rué Perna, J. J., Spiegel, C., and Szabó, T. (2019-09). On the Optimality of the Uniform Random Strategy. Random Structures & Algorithms, 55(2), 371–401. DOI: 10.1002/rsa.20829 [URL] [arXiv]
   [BibTeX]

   @article{krss_randomstrategy_17,
     year = {2019-09},
     journal = {Random Structures & Algorithms},
     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 Perna, Juan José and Spiegel, Christoph and Szabó, Tibor},
     title = {On the Optimality of the Uniform Random Strategy}
   }

8. Freĭman, G. A., Serra, O., and Spiegel, C. (2019). Additive Volume of Sets Contained in Few Arithmetic Progressions. INTEGERS, 19. [URL] [arXiv]
   [BibTeX]

   @article{fss_additivevolume_18,
     year = {2019},
     journal = {INTEGERS},
     volume = {19},
     url = {http://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}
   }

9. Rué Perna, J. J., Spiegel, C., and Zumalacárregui, A. (2018). 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{rsz_threshold_12,
     year = {2018},
     journal = {Mathematische Zeitschrift},
     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 Perna, Juan José and Spiegel, Christoph and Zumalacárregui, Ana},
     title = {Threshold Functions and Poisson Convergence for Systems of Equations in Random Sets}
   }

10. 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{spiegel_supersaturation_17,
      year = {2017},
      journal = {Electronic Journal of Combinatorics},
      volume = {24},
      number = {3},
      doi = {10.37236/6730},
      url = {https://www.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}
    }

Conference and workshop talks

Research seminar talks

Poster presentations