Christoph Spiegel
I like using computational tools for theoretical mathematics. Lately, I have utilized flag algebras, semidefinite programming, and discrete optimization to improve some longstanding bounds in extremal combinatorics. Currently, I am exploring the areas of proof verification and assistance.
📬 Contact
office  Room 3036 at ZIB 

spiegel (at) zib.de spiegel (at) campus.tuberlin.de 

homepage  christophspiegel.berlin 
languages  German, English, and French 
🎓 Curriculum vitae
since 2022  deputy department head at ZIB 

since Aug 2020  postdoctoral researcher at ZIB 
Jun 2020  Ph.D. in Applied Mathematics at UPC 
Mar 2015  M.Sc. in Mathematics at FUB 
Dec 2012  B.Sc. in Mathematics at FUB 
📝 Publications and preprints
Preprints
 Zimmer, M., Andoni, M., Spiegel, C., and Pokutta, S. (2023). PERP: Rethinking the PruneRetrain Paradigm in the Era of LLMs.
[arXiv]
[code]
[BibTeX]
 Zimmer, M., Spiegel, C., and Pokutta, S. (2022). Compressionaware Training of Neural Networks Using FrankWolfe.
[arXiv]
[BibTeX]
 Combettes, C., Spiegel, C., and Pokutta, S. (2020). Projectionfree Adaptive Gradients for Largescale Optimization.
[arXiv]
[summary]
[code]
[BibTeX]
 Pokutta, S., Spiegel, C., and Zimmer, M. (2020). Deep Neural Network Training with FrankWolfe.
[arXiv]
[summary]
[code]
[BibTeX]
 Salia, N., Spiegel, C., Tompkins, C., and Zamora, O. (2019). Independent Chains in Acyclic Posets.
[arXiv]
[BibTeX]
Conference proceedings
 Kiem, A., Pokutta, S., and Spiegel, C. (2024). Categorification of Flag Algebras. Proceedings of Discrete Mathematics Days.
[BibTeX]
 Kiem, A., Pokutta, S., and Spiegel, C. (2024). The 4color Ramsey Multiplicity of Triangles. Proceedings of Discrete Mathematics Days.
[arXiv]
[code]
[BibTeX]
 Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). Extending the Continuum of SixColorings. Proceedings of Discrete Mathematics Days.
[arXiv]
[BibTeX]
 Zimmer, M., Spiegel, C., and Pokutta, S. (2024). Sparse Model Soups: A Recipe for Improved Pruning Via Model Averaging. Proceedings of International Conference on Learning Representations.
[arXiv]
[BibTeX]
 Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2023). Fully Computerassisted Proofs in Extremal Combinatorics. Proceedings of AAAI Conference on Artificial Intelligence.
[arXiv]
[slides]
[code]
[BibTeX]
 Rué, 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]
 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]
 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]
 Rué, J. J., and Spiegel, C. (2018). On a Problem of Sárközy and Sós for Multivariate Linear Forms. Proceedings of Discrete Mathematics Days.
[arXiv]
[BibTeX]
 Kusch, C., Rué, 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]
Full articles
 Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). Extending the Continuum of SixColorings. Geombinatorics Quarterly, XXXIV.
[arXiv]
[BibTeX]
 Kamčev, N., and Spiegel, C. (2022). Another Note on Intervals in the HalesJewett Theorem. Electronic Journal of Combinatorics, 29(1).
DOI: 10.37236/9400
[URL]
[arXiv]
[BibTeX]
 CaoLabora, G., Rué, J. J., and Spiegel, C. (202110). An ErdősFuchs Theorem for Ordered Representation Functions. Ramanujan Journal, 56, 183–2091.
DOI: 10.1007/s11139020003262
[URL]
[arXiv]
[BibTeX]
 Fabian, D., Rué, J. J., and Spiegel, C. (202108). 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]
 Corsten, J., Mond, A., Pokrovskiy, A., Spiegel, C., and Szabó, T. (202010). On the Odd Cycle Game and Connected Rules. European Journal of Combinatorics, 89.
DOI: 10.1016/j.ejc.2020.103140
[URL]
[arXiv]
[BibTeX]
 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]
 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]
 Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (201909). On the Optimality of the Uniform Random Strategy. Random Structures & Algorithms, 55(2), 371–401.
DOI: 10.1002/rsa.20829
[URL]
[arXiv]
[BibTeX]
 Freĭman, G. A., Serra, O., and Spiegel, C. (2019). Additive Volume of Sets Contained in Few Arithmetic Progressions. INTEGERS, 19.
[URL]
[arXiv]
[BibTeX]
 Rué, 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/s0020901718912
[URL]
[arXiv]
[BibTeX]
 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]
🔬 Projects
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.
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.
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.
The performance of modern mixedinteger 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.
💬 Talks and posters
Conference and workshop talks
 Jul 2024
 Extending the Continuum of SixColorings, DMD Conference, Alcalá de Henares
 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]
View More / Less
 Jun 2023
 Towards Flag Algebras in Additive Combinatorics, FoCM 2023 Workshop I.3 Workshop, Paris [PDF]
 May 2023
 Towards Flag Algebras in Additive Combinatorics, CANT Conference, New York [PDF]
 Mar 2023
 Computerassisted Proofs in Extremal Combinatorics, Optimization and ML Workshop, Waischenfeld [PDF]
 Feb 2023
 Fully Computerassisted Proofs in Extremal Combinatorics, 37th AAAI Conference, Washington, DC [PDF]
 Jan 2023
 Fully Computerassisted Proof in Extremal Combinatorics, Aussois Workshop, Aussois [PDF]
 Dec 2022
 Leveraging Combinatorial Symmetries in Flag Algebrabased SDP Formulations, Recent Advances in Optimization Workshop, Toronto [PDF]
 Sep 2022
 Proofs in Extremal Combinatorics Through Optimization, 6th RIKENMODAL Workshop, Tokyo / Fukuoka [PDF]
 Jul 2022
 New Ramsey Multiplicity Bounds and Search Heuristics, DMD Conference, Santander [PDF]
 Jun 2019
 Odd Cycle Games and Connected Rules, 36th Postgraduate Combinatorial Conference, Oxford [PDF]
 Jun 2019
 GAPCOMB Workshop, Campelles
 Jun 2018
 On a Problem of Sárközy and Sós for Multivariate Linear Forms, DMD Conference, Sevilla [PDF]
 May 2018
 Going Beyond 2.4 in Freiman's 2.4ktheorem, CANT Conference, 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
 FUBTAU Workshop
Research seminar talks
 Feb 2023
 The Fourcolor 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 HalesJewett Theorem, Seminar and PhD Seminar on Combinatorics, Games and Optimisation, London
View More / Less
 May 2019
 Intervals in the HalesJewett Theorem, Combinatorial Theory Seminar, Oxford
 Feb 2019
 Extremal Set Theory Seminar, Budapest
 Dec 2018
 Intervals in the HalesJewett Theorem, Research Seminar Combinatorics, Berlin
 Mar 2018
 Going Beyond 2.4 in Freiman's 2.4ktheorem, 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
 Discrete Fourier Analysis, "What Is ...?" Seminar [video]
 Oct 2015
 Threshold Functions for Systems of Equations in Random Sets, Research Seminar Combinatorics, Berlin
👨🏫Teaching
 winter 2023
 Lecturer for Einführung in die Lineare und Kombinatorische Optimierung (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
 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
 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
 2022
 Member of the organizing committee of a Girls’ Day science outreach event in Berlin
 Sep 2021
 Member of the organizing committee of the EUROCOMB conference in Barcelona
 2021
 Member of the organizing committee of a Girls’ Day science outreach event in 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 BMSBGSMath 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:
I also like designing the occasional conference poster: