The research of the five Institutes of Mathematics focuses on Discrete Mathematicsand Analysis. Mathematics also provides the fundamental basis for the joint interdisciplinary focus on Computational Science and Engineering.
The research focus Discrete Mathematics and Analysis comprises a large portfolio of topics which range from Combinatorics, Graph theory, stochastics, discrete optimisation, analysis of algorithms, applied and computer assisted geometry, and operator theory to modelling problems in economics and technology. It also comprises number theory and its applications in financial mathematics, coding, cryptography and statistical simulation
With respect to the research focus Computational Science and Engineering, key research areas of the Mathematics department are partial differential equations, numeric methods, dynamic systems, constructive approximation, statistics, and financial mathematics. The mathematics institutes collaborate intensively with other faculties of the Graz University of Technology in the areas of robotics, signal processing, big data, mechanical and electrical engineering.
The scientific work of this department is integrated into the Field of Expertise Information, Communication and Computing at Graz University of Technology. Other research highlights include the doctoral school Discrete Mathematics and work groups participating in the SFB (special research area) Quasi Monte Carlo Methods – Theory and Applications. International networking in the framework of guest professorships and the regular exchange of visiting researchers is an essential feature of this faculty.
The five physics institutes of the faculty and their research portfolios are closely interlinked in the joint research focus Nano and Quantum materials. They provide an important contribution to the joint interdisciplinary focus Computational Science and Engineering.
Research on Nano and Quantum Materials is performed in cooperation with the department of physics of the Karl-Franzens-University of Graz in the framework of the NAWI Graz. It is also part of the Field of Expertise Advanced Materials Science. The physics institutes have a broad spectrum of materials characterization equipment that include a state-of-the-art laboratory for ultra-short time spectroscopy and advanced electron microscopes at the Austrian Centre for Electron Microscopy and Nanoanalysis. The latter is in great demand for collaborators from other faculties and industrial partners.
The research focus Nano and Quantum Materials involves experimental and theoretical studies - of nanoscale and heterogeneous solid-state systems with novel functionalities, sensor concepts, and nanoanalytical diagnosis tools in which quantum effects play a dominant role. These new methods and materials are needed to address challenges facing society such as providing clean energy and environmentally sustainable manufacturing processes.
The research focus Computational Science and Engineering exploits the synergies between Mathematics and Physics (Mathematical Physics, Computational Physics) to advance the digitalization of science, e.g., in the field of computer assisted materials development (so-called ab-initio materials design).
The research of the two institutes of geodesy focuses on Change Monitoring of System Earth and, beyond that, the institutes make essential contributions to the common and interdisciplinary focus Computational Science and Engineering.
The research program Change Monitoring of System Earth involves a wide range of size scales. On the global scale, sensor data from satellites is evaluated, e.g., for measuring the rise of the sea level or assessing climate change. On the macro scale, remote sensing using aircraft or drones is used to monitor natural disaster events, glaciers, and permafrost. On the local scale, automated monitoring systems are used to evaluate critical infrastructure such as bridges. Three-dimensional imaging systems are also used to document the form of structures important for our cultural heritage. These activities are integrated into the Fields of Expertise Sustainable Systems; Mobility & Production; and Information, Communication & Computing. In addition, these institutes play a leading role in the Disaster Competence Network Austria.
As part of the research focus Computational Science and Engineering, thematic overlaps and synergies between Mathematics and Geodesy (Sensor Systems, Data Processing) are exploited to study issues in geo informatics technology and large scale differential equation systems.