Christoph Hertrich

Christoph Hertrich is a tenure-track professor for Applied Discrete Mathematics at University of Technology Nuremberg, where he conducts research at the intersection of discrete mathematics, theoretical computer science, and machine learning. His work particularly focuses on applying polyhedral geometry and combinatorial optimization techniques to neural network theory, with significant contributions to understanding the computational complexity and expressivity of neural networks.

Hertrich received his BSc and MSc degrees from TU Kaiserslautern (2013-2018) working with Sven O. Krumke, followed by his PhD at TU Berlin (2018-2022) under the supervision of Martin Skutella. His doctoral thesis, titled "Facets of Neural Network Complexity," laid foundational work for his current research direction. Prior to joining UTN, he held postdoctoral positions at Université libre de Bruxelles (2023-2024) with a Marie Skłodowska-Curie fellowship under Samuel Fiorini, and at LSE London (2022-2023) with László Végh. He also served as a substitute professor for discrete mathematics at Goethe-Universität Frankfurt during the winter semester of 2023/24.

Hertrich's research interests center on the mathematical foundations of neural networks, with particular emphasis on polyhedral geometry approaches. His work explores computational complexity questions related to neural network training and architecture, expressivity bounds, and connections to combinatorial optimization problems. He has made significant contributions to understanding the relationship between neural network depth and function representation, the complexity of counting linear regions in ReLU networks, and the application of extended formulations to neural network theory. His approach combines rigorous theoretical analysis with practical implications for neural network design and optimization.

His recent publication record reveals a strong trend toward establishing fundamental theoretical limits and connections between deep learning and discrete mathematics. A significant portion of his work examines computational complexity of various neural network problems, often proving hardness results or establishing bounds on expressivity. He has also developed novel connections between polyhedral combinatorics and neural network architecture, demonstrating how techniques from operations research can inform deep learning theory.

• Marie Skłodowska-Curie fellowship

Since February 2025, Hertrich has been supervising PhD student Moritz Stargalla at UTN. His research has been supported by prestigious fellowships including a Marie Skłodowska-Curie fellowship during his postdoctoral period in Brussels. He is organizing a workshop on "Polyhedral Geometry for Neural Networks" in March 2026 in Nuremberg, highlighting his leadership in this emerging interdisciplinary field.