We do research in mathematics, of which we share a broad and dynamic vision. At its center stands the classical core: the mathematics of famous and fruitful conjectures, the mathematics that is in symbiosis with theoretical physics, and which continually reveals to us deep and unexpected connections. Beyond this core, mathematics drives, and is driven by, the successful trend towards quantitative modeling in the natural and social sciences. The steadily improving performance of computers opens new perspectives for model simulations and the direct transfer of mathematics into technological applications.

### Hausdorff School for Advanced Studies in Mathematics (HSM)

The Hausdorff School for Advanced Studies in Mathematics (HSM) supports the research of early career mathematicians by further training through Hausdorff Schools and by other initiatives dedicated to increasing their academic independence and their scientific networks.

### Mathematical Institute (MI)

The Mathematical Institute (MI) has research groups in Algebra and Representation Theory, Analysis and Partial Differential Equations,

Analytic Number Theory and Automorphic Forms, Arithmetic Geometry and Representation Theory, Geometry, Complex Geometry, Mathematical Logic, Mathematics Education, and Topology.

### Institute for Applied Mathematics (IAM)

The Institute for Applied Mathematics (IAM) consists of the following research groups: Applied Analysis, Functional Analysis, PDE and Applications, Probability Theory, Interacting Random Systems, Variational Methods and Mathematical Aspects of Materials Science, Partial Differential Equations and Inverse Problems, Combinatorics.

### Research Institute for Discrete Mathematics (DM)

The Research Institute for Discrete Mathematics (DM) focuses its central research activities on the area of Discrete Mathematics and its applications, particularly Combinatorial Optimization and Chip Design. The institute maintains many international cooperations and third-party projects.

### Max Planck Institute for Mathematics (MPIM)

The Max Planck Institute for Mathematics (MPIM) is a research institute for pure mathematics and belongs to the Max Planck Society. With its well known guest program the institute aims at stimulating the exchange of ideas within the international mathematics community.

- Collaborative Research Center (SFB) 1060 "The Mathematics of Emergent Effects"
- Gottfried Wilhelm Leibniz Prize (Catharina Stroppel)
- ERC Synergy Grant "Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties" (Daniel Huybrechts)
- ERC Advanced Grant "Automorphic Forms and Arithmetic" (Valentin Blomer)
- ERC Consolidator Grant "Integrated Mechanistic Modelling and Analysis of Large-scale Biomedical Data" (Jan Hasenauer)
- ERC Starting Grant "p-adic groups, Representations and the Langlands Program" (Jessica Fintzen)
- ERC Starting Grant "Satisfiability and group rings" (Giles Gardam)
- ERC Starting Grant "Spectral Geometry of higher symmetric spaces" (Tobias Barthel)
- ERC Starting Grant "Interplay of structures in conformal and universal random geometry" (Eveliina Peltola)
- DFG Emmy Noether Project "Numerical methods for nonlinear, random, and dynamic multiscale problems" (Barbara Verfürth)
- Otto Toeplitz Memorial Foundation
- Industrial cooperation with IBM on "Combinatorial Optimization and Chip Design"
- Industrial cooperation with Greenplan on "Combinatorial Optimization for Applications in Pickup and Delivery Services”

Further participation in:

- Collaborative Research Center (CRC) TRR 333 “BATenergy: Brown and Beige Fat - Organ Crosstalk, Signalling and Energetics”
- Collaborative Research Center (CRC) SFB 1454 "Metaflammation and Cellular Programming”
- Collaborative Research Center (CRC) TRR 358 "Integral Structures in Geometry and Representation Theory"
- Collaborative Research Center (CRC) SFB 1173 "Wave phenomena: analysis and numerics"