Application Areas

The MATH+ Application Areas are tailored toward mathematical research in interdisciplinary application fields. They support cross-institution research projects that involve mathematicians as well as leading experts of the respective field of application. The following list displays the research projects presently running in the five Application Areas. Successfully completed projects can be found on the subsequent websites of the individual Application Areas.

Projects marked with an asterisk (*) are short-term one-year pilot projects.

Mechanisms of Life (AA1)
Scientists in Charge: Edda Klipp, Frank Noé, Christof Schütte

• AA1-6: Data-Driven Modeling from Atoms to Cells
  Frank Noé, Cecilia Clementi, Christof Schütte
• AA1-10: New Methods for Inhibiting Sars-Cov2 Cell Entry
  Frank Noé, Oliver Daumke
• AA1-14: Development of an Ion-Channel Model-Framework for In-vitro Assisted Interpretation of Current Voltage Relations
  Jürgen Fuhrmann, Manuel Landstorfer, Barbara Wagner
• AA1-15: Math-Powered Drug-Design
  Konstantin Fackeldey, Christof Schütte, Vikram Sunkara, Christoph Stein, Marcus Weber, Stefanie Winkelmann
• AA1-17: Beyond Attractors: Understanding the Transient and Modular Behaviour of Boolean Networks
  Elisa Tonello
• AA1-18: Synchronization and Geometric Structures of Stochastic Biochemical Oscillators
  Maximilian Engel, Felix Höfling, Stefanie Winkelmann
  
• AA1-19: Drug Candidates as Pareto Optima in Chemical Space
  Konstantin Fackeldey, Christof Schütte, Vikram Sunkara, Jörg Rademann, Marcus Weber, Stefanie Winkelmann
• AA1-20: Geometric Learning for Single-Cell RNA Velocity Modeling
  Daniel Baum, Tim Conrad, Christof Schütte, Vikram Sunkara, Christoph von Tycowicz

Successfully completed projects of Application Area 1 can be found here.

Nano and Quantum Technologies (AA2)
Scientists in Charge: Uwe Bandelow, Ralf Kornhuber, Barbara Zwicknagl

• AA2-13: Data-Driven Stochastic Modeling of Semiconductor Lasers
  Uwe Bandelow, Markus Kantner, Wilhelm Stannat, Hans Wenzel
• AA2-16: Tailored Entangled Photon Sources for Quantum Technology
  Sven Burger, Stephan Reitzenstein
• AA2-17: Coherent Transport of Semiconductor Spin-Qubits: Modeling, Simulation and Optimal Control
  Tobias Breiten, Markus Kantner, Thomas Koprucki
• AA2-18: Pareto-Optimal Control of Quantum Thermal Devices with Deep Reinforcement Learning
  Paolo Erdman
• AA2-19: Entanglement Detection via Frank-Wolfe Algorithms
  Sébastien Designolle, Sebastian Pokutta
• AA2-20: Coarse-Graining Electrons in Quantum Systems
  Frank Noé, Cecilia Clementi
• AA2-21: Strain Engineering for Functional Heterostructures: Aspects of Elasticity
  Annegret Glitzky, Matthias Liero, Barbara Zwicknagl

Successfully completed projects of Application Area 2 can be found here.

Next Generation Networks (AA3)
Scientists in Charge: Ralf Borndörfer, Martin Skutella

• AA3-12: On the Expressivity of Neural Networks
  Christian Haase, Martin Skutella
• AA3-15: Convex Solver Adaptivity for Mixed-Integer Optimization
  Mathieu Besançon, Ralf Borndörfer, Sebastian Pokutta
• AA3-16: Likelihood Geometry of Max-Linear Bayesian Networks
  Carlos Enrique Améndola Cerón
• AA3-17: Efficient Algorithms for Quickest Transshipment Problems
  Martin Skutella
• AA3-18: Evolution Processes for Populations and Economic Agents
  Max Klimm, Maite Wilke Berenguer
• AA3-19: The Value of Distributional Information
  Franziska Eberle

Successfully completed projects of Application Area 3 can be found here.

Energy Transition (AA4)
Scientists in Charge: Peter Karl Friz, René Henrion, Caren Tischendorf

• AA4-2: Optimal Control in Energy Markets Using Rough Analysis and Deep Networks
  Christian Bayer, Peter Karl Friz, John Schoenmakers, Vladimir Spokoiny
• AA4-7: Decision-Making for Energy Network Dynamics
  Falk Hante, Michael Hintermüller, Sebastian Pokutta
• AA4-9: Volatile Electricity Markets and Battery Storage: A Model-Based Approach for Optimal Control
  Christian Bayer, Dörte Kreher, Manuel Landstorfer
• AA4-10: Modelling and Optimization of Weakly Coupled Minigrids under Uncertainty
  René Henrion, Dietmar Hömberg
• AA4-11: Using Mathematical Programming to Enhance Multiobjective Learning
  Aswin Kannan
• AA4-12: Advanced Modeling, Simulation, and Optimization of Large Scale Multi-Energy Systems
  Volker Mehrmann
• AA4-13: Equilibria for Distributed Multi-Modal Energy Systems under Uncertainty
  Pavel Dvurechenskii, Caroline Geiersbach, Michael Hintermüller, Aswin Kannan
• AA4-14: Data-Driven Prediction of the Band-Gap for Perovskites
  Claudia Draxl, Sebastian Pokutta, Daniel Walter, Andrea Walther

Successfully completed projects of Application Area 4 can be found here.

Variational Problems in Data-Driven Applications (AA5)
Scientists in Charge: Michael Hintermüller, Sebastian Pokutta

AA5 evolved from a merger of selected projects of the Emerging Fields Extracting Dynamical Laws from Complex Data (EF1) and Model-Based Imaging (EF3).

• AA5-2: Robust Multilevel Training of Artificial Neural Networks
  Michael Hintermüller, Carsten Gräser
• AA5-4: Bayesian Optimization and Inference for Deep Networks
  Claudia Schillings, Vladimir Spokoiny
• AA5-5: Wasserstein Gradient Flows for Generalised Transport in Bayesian Inversion
  Martin Eigel, Claudia Schillings, Gabriele Steidl
• AA5-8: Convolutional Brenier Generative Networks
  Hanno Gottschalk, Gabriele Steidl
• AA5-9: LEAN on Me: Transforming Mathematics through Formal Verification, Improved Tactics, and Machine Learning
  Sebastian Pokutta, Christoph Spiegel
• AA5-10: Robust Data-Driven Reduced-Order Models for Cardiovascular Imaging of Turbulent Flows
  Alfonso Caiazzo, Jia-Jie Zhu, Leonid Goubergrits
• AA5-11: Data-Adaptive Discretization of Inverse Problems
  Tim Jahn

Successfully completed projects of Application Area 5 can be found here.