About me
I am a tenure-track professor for Applied Discrete Mathematics at University of Technology Nuremberg. My research interests span various topics across discrete mathematics, theoretical computer science, and machine learning, with an emphasis on applying techniques from polyhedral geometry and combinatorial optimization to neural network theory. See this recent survey talk for some of my favorite open problems and results.
Previously, in 2023/24, I was a postdoc at Université libre de Bruxelles advised by Samuel Fiorini and partially funded through my own Marie Skłodowska-Curie fellowship. I paused my stay in Brussels when I acted as a substitute professor for discrete mathematics at Goethe-Universität Frankfurt in the winter semester 2023/24. Furthermore, in 2022/23, I was a postdoc with László Végh at LSE in London. I completed my PhD with Martin Skutella at TU Berlin (2018-22), and my BSc and MSc with Sven O. Krumke at TU Kaiserslautern (2013-18).
Since February 2025, I am the PhD advisor of Moritz Stargalla at UTN.
My brother Johannes is a postdoc in mathematical image processing, currently working in Paris.
Preprints
Depth-Bounds for Neural Networks via the Braid Arrangement
with Moritz Grillo and Georg Loho (2025)
Preprint
Neural Networks and (Virtual) Extended Formulations
with Georg Loho (2024)
Preprint
Publications
Decomposition Polyhedra of Piecewise Linear Functions
with Marie-Charlotte Brandenburg and Moritz Grillo
Spotlight (top 5 %) at International Conference on Learning Representations (ICLR 2025)
Conference Version |
Preprint
Mode Connectivity in Auction Design
with Yixin Tao and László A. Végh
Accepted for Mathematics of Operations Research (2025)
Conference Version at Conference on Neural Information Processing Systems (NeurIPS 2023)
Conference Version |
Preprint
ReLU Neural Networks of Polynomial Size for Exact Maximum Flow Computation
with Leon Sering
Mathematical Programming (2024)
Conference version at Conference on Integer Programming and Combinatorial Optimization (IPCO 2023)
Journal Version |
Conference Version |
Preprint
A First Order Method for Linear Programming Parameterized by Circuit Imbalance
with Richard Cole, Yixin Tao, and László A. Végh
Conference on Integer Programming and Combinatorial Optimization (IPCO 2024)
Conference Version |
Preprint
Training Neural Networks is NP-Hard in Fixed Dimension
with Vincent Froese
Conference on Neural Information Processing Systems (NeurIPS 2023)
Conference Version |
Preprint
Training Fully Connected Neural Networks is ER-Complete
with Daniel Bertschinger, Paul Jungeblut, Tillmann Miltzow, and Simon Weber
Conference on Neural Information Processing Systems (NeurIPS 2023)
Conference Version |
Preprint
Towards Lower Bounds on the Depth of ReLU Neural Networks
with Amitabh Basu, Marco Di Summa, and Martin Skutella
SIAM Journal on Discrete Mathematics (2023)
Conference version at Conference on Neural Information Processing Systems (NeurIPS 2021)
Journal Version |
Conference Version |
Preprint |
Video
Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size
with Martin Skutella
INFORMS Journal on Computing (2023)
Conference Version at AAAI 2021 Conference on Artificial Intelligence
Journal Version |
Conference Version |
Preprint |
Video
Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes
with Christian Haase and Georg Loho
International Conference on Learning Representations (ICLR 2023)
Conference Version |
Preprint
The Computational Complexity of ReLU Network Training Parameterized by Data Dimensionality
with Vincent Froese and Rolf Niedermeier
Journal of Artificial Intelligence Research (2022)
Journal Version |
Preprint
Online Algorithms to Schedule a Proportionate Flexible Flow Shop of Batching Machines
with Christian Weiß, Heiner Ackermann, Sandy Heydrich, and Sven O. Krumke
Journal of Scheduling (2022)
Journal Version |
Preprint
Coloring Drawings of Graphs
with Felix Schröder and Raphael Steiner
Electronic Journal of Combinatorics (2022)
Journal Version |
Preprint
Scheduling a Proportionate Flow Shop of Batching Machines
with Christian Weiß, Heiner Ackermann, Sandy Heydrich, and Sven O. Krumke
Journal of Scheduling (2020)
Journal Version |
Preprint
Decision Support for Material Procurement
with Heiner Ackermann, Erik Diessel, Michael Helmling, Neil Jami, and Johanna Schneider
Operations Research Proceedings 2019
Conference Version
Sweep Algorithms for the Capacitated Vehicle Routing Problem with Structured Time Windows
with Philipp Hungerländer and Christian Truden
Operations Research Proceedings 2018
Conference Version |
Preprint
Theses
Facets of Neural Network Complexity
PhD Thesis, TU Berlin (2022)
Scheduling a Proportionate Flow Shop of Batching Machines
Master Thesis, TU Kaiserslautern (2018)
Received an award from the German Operations Research Society (GOR)
Summary published in OR Proceedings 2019
A Parametric View on Robust Graph Problems
Bachelor Thesis, TU Kaiserslautern (2016)