# 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
- spiegel (at) zib.de

spiegel (at) campus.tu-berlin.de - homepage
- christophspiegel.berlin
- languages
- German, English, and French

## 🎓 Curriculum vitae

- since 2022
- Deputy Department Head at ZIB
- since 2020
- Researcher at ZIB
- 2016 to 2020
- Researcher at UPC
- Jun 2020
- Ph.D. in Applied Mathematics at UPC
- 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

- Zimmer, M., Andoni, M., Spiegel, C., and Pokutta, S. (2023).
*PERP: Rethinking the Prune-Retrain Paradigm in the Era of LLMs*. [arXiv] [code]## [BibTeX]

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

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

- Pokutta, S., Spiegel, C., and Zimmer, M. (2020).
*Deep Neural Network Training with Frank-Wolfe*. [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*. [URL]## [BibTeX]

- Kiem, A., Pokutta, S., and Spiegel, C. (2024). The 4-color Ramsey Multiplicity of Triangles.
*Proceedings of Discrete Mathematics Days*. [URL] [arXiv] [code]## [BibTeX]

- Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). Extending the Continuum of Six-Colorings.
*Proceedings of Discrete Mathematics Days*. [URL] [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*. [URL] [arXiv]## [BibTeX]

- Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2023). Fully Computer-assisted Proofs in Extremal Combinatorics.
*Proceedings of AAAI Conference on Artificial Intelligence*. DOI: 10.1609/aaai.v37i10.26470 [URL] [arXiv] [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*. DOI: 10.5817/CZ.MUNI.EUROCOMB23-108 [URL] [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*. [URL] [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*. [URL] [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 Six-Colorings.
*Geombinatorics Quarterly*,*XXXIV*. [URL] [arXiv]## [BibTeX]

- 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]

- 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]

- Cao-Labora, G., Rué, 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]

- Fabian, D., Rué, 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]

- 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]

- 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. (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]

- 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/s00209-017-1891-2 [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 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.

## 💬 Talks and posters

### Conference and workshop talks

- Sep 2024
*The Role of Machine Learning for Mathematics*

5th CO@Work, Berlin- Jul 2024
*Extending the Continuum of Six-Colorings*

13th DMD Conference, 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]

## View More / Less

- 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 Workshop, Paris [PDF]- May 2023
*Towards Flag Algebras in Additive Combinatorics*

15th CANT Conference, New York [PDF]- Mar 2023
*Computer-assisted Proofs in Extremal Combinatorics*

Optimization and ML Workshop, Waischenfeld [PDF]- Feb 2023
*Fully Computer-assisted Proofs in Extremal Combinatorics*

37th AAAI Conference, Washington, DC [PDF]- Jan 2023
*Fully Computer-assisted Proof in Extremal Combinatorics*

Combinatorial Optimization Workshop, Aussois [PDF]- Dec 2022
*Leveraging Combinatorial Symmetries in Flag Algebra-based SDP Formulations*

Recent Advances in Optimization Workshop, Toronto [PDF]- Sep 2022
*Proofs in Extremal Combinatorics Through Optimization*

6th RIKEN-MODAL Workshop, Tokyo / Fukuoka [PDF]- Jul 2022
*New Ramsey Multiplicity Bounds and Search Heuristics*

12th 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*

11th DMD Conference, Sevilla [PDF]- May 2018
*Going Beyond 2.4 in Freiman's 2.4k-theorem*

10th 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
- FUB-TAU Workshop

### Research seminar talks

- 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 and PhD Seminar on Combinatorics, Games and Optimisation, London

## View More / Less

- 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

## 👨🏫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 Insittute 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:

I also like designing the occasional conference poster: