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The ALGA cluster (Algorithms, Geometry, and Applications) studies the design and analysis of algorithms and data structures, one of the core areas within computer science. Research in ALGA ranges from curiosity-driven to motivated by concrete applications, and from purely theoretical to experimental. In all cases, the goal is to understand the underlying principles of the developed solutions and to formally prove their properties. Our approaches frequently combine the rigorous methods from algorithmic theory – which give performance guarantees with respect to both the quality of solutions and the running time of algorithms – with efficient engineering to achieve results of both theoretical and practical significance.

The FSA (Formal System Analysis) cluster focusses on theories, techniques and tools for modelling and analyzing the behavior of (concurrent) systems. Among others, we study the foundations and applications of process algebras, semantics, concurrency theory, model checking, logics, rewriting, and satisfiability solving. Application areas include, but are not limited to hardware designs, industrial control systems and smart mobility.

The research focus of the Interconnected Resource-aware Intelligent Systems (IRIS) cluster is on the design, analysis, development, and evaluation of concepts, models, algorithms, protocols, and tools that optimize (distributed embedded) systems performance in terms of timing behavior, dependability, programmability, reliability, robustness, scalability, accuracy, energy and data computation efficiency, and trustworthiness.

The mission of the Security cluster (SEC) is to realize a more secure and privacy-preserving digital infrastructure. SEC’s approach to system security covers offensive and defensive aspects of system security, targeting concrete security problems and addressing the underlying, fundamental issues at their core.

The objective of Software Engineering is to develop and maintain, in a time- and cost-efficient manner, high-quality software systems. In support of this, the Software Engineering and Technology (SET) cluster studies people, methods and tools for the development and maintenance of software. Research in SET includes curiosity-driven research, various types of empirical studies (in industry and experiments in labs), and also tool-building.

The research objective of CASA is to develop new and improve existing mathematical (both analytical and numerical) methods for a wide range of applications in science and engineering. Mathematics research within CASA is often driven by models from science and engineering, for instance by mathematical expressions of physical laws. Stimulated by the immense growth in the availability and use of data, mathematics in CASA is also becoming data- driven, with a crucial role in this for machine learning. There is enormous potential for the use of data and machine learning in analysis and scientific computing, in combination with the use of first-principles models. CASA will continue its longstanding expertise and success in, for instance, variational calculus, functional analysis, numerical methods for partial differential equations and linear algebra and model-order reduction methods, while extending its research into the direction of data science, machine learning and uncertainty quantification.

The Statistics, Probability, and Operations Research (SPOR) cluster focuses on the development of foundational understanding and methodologies for the analysis and optimization of complex systems and large-scale networks. The development of sound mathematical models for highly complex systems plays a central role in the research activities within SPOR and serves as an enabler for the creation of effective techniques for inference, performance analysis and optimization of these systems, which are commonly subject to intrinsic randomness and uncertainty. 

Discrete Mathematics is concerned with finite structures and their properties. It is an exciting growth area in the modern information age. Just as continuous mathematics led to major scientific developments in the 19th and 20th century, Discrete Mathematics with its various subfields such as algebra, geometry, number theory, combinatorics, graph theory, discrete optimization, coding theory, cryptography, machine learning, computational algebra, information theory etc., underlies much of the developments in modern fields such as computer technology, communication networks and e-commerce.