Research Projects
Current Research Projects at the Department of Mathematics
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
In recent years, the Tomita-Takesaki theory of modular flows of von Neumann algebras has been extensively used both in high energy and condensed matter physics, as a tool for studying energy, entropy and entanglement in quantum field theory (QFT) and semiclassical gravity. The central object in modular theory, the modular or entanglement Hamiltonian associated to a given quantum state and spacetime region, is however only known in a handful of examples. These mainly include theories and regions…
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Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
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Funding source: Bayerisches Staatsministerium für Wirtschaft, Landesentwicklung und Energie (StMWi) (seit 2018)
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Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
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Magnetic Drug Targeting unter Einsatz von superparamagnetischen Eisenoxid-Nanopartikeln (SPIONs) ist eine wirksame Methode, um in der Krebstherapie die Wirkstoffapplikation im Tumorgewebe zu steigern, bei gleichzeitiger Reduktion der Gesamtwirkstoffmenge und der mit der Therapie einhergehenden Nebenwirkungen. Während die Wirksamkeit des Ansatzes bereits in Studien nachgewiesen werden konnte, fehlen allerdings bislang Ansätze, um diese Methode an den jeweiligen Behandlungsfall anzupassen und z…
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
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Topological invariants and their index theory, the bulk-boundary correspondence and the more recently introduced spectral localizer are well-established mathematical concepts for disordered topological insulators and are also influential for numerical studies of such materials. This proposal is about extending prior results and techniques to systems with crystalline defects, disordered semimetals and topological metals, as well as non-hermitian topological systems stemming from (leaky and driven) photonics and metamaterials. Another part of the proposal aims at a deeper understanding of scattering on such topological systems.
Funding source: EU - 8. Rahmenprogramm - Horizon 2020
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The ModConFlex consortium comprises a group of 10 academics and 4 senior researchers in industry (ORE Catapult) with expertise in control theory, artificial intelligence, complex dynamical systems, distributed parameter systems, fluid dynamics, aeroelasticity, power electronics, power systems, swimming theory and marine engineering. Our aim is to train the next generation of researchers on the modelling and control of flexible structures interacting with fluids (water and air), contributing to the latest advances in control theory, artificial intelligence and energy-based modelling. Our main applications are in the control of floating wind turbines (the prime renewable energy source of the future), and in the control of highly flexible aircraft, aircraft with very high aspect ratio. Our research plans are organized into three scientific work packages, which cover mathematical systems theory (modelling and model reduction, boundary control systems, port-Hamiltonian systems, exact beam theory), relevant aspects of control theory (internal model controllers with anti-windup, nonlinear model predictive control, robust control), reinforcement learning, aeroelasticity, stochastic algorithms. We believe that science and technology in Europe will greatly benefit from this research, and from the education and knowledge that we will impart to a new generation of researchers. Key strengths of this consortium include a research environment that brings together mathematicians and engineers to provide the project’s young researchers with a unique training environment, and a network of associated industrial partners that will allow all the young researchers to participate in industrial secondments. We have the critical mass to cover all aspects of training, and we have an excellent track record of past collaboration and of training young researchers.
Funding source: Deutscher Akademischer Austauschdienst (DAAD)
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Funding source: DFG / Schwerpunktprogramm (SPP)
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To couple three interwoven areas of rhizosphere research “Processes, Methods and Applications”, we utilize and improve mechanistic, mathematical models in forms of combined cellular automata and PDE/ODE systems on the microscale, offering the opportunity to bridge scales by homogenization techniques. The
systematic study of the interaction of transformation processes in the rhizosphere focussing on mucilage and root hairs, and its couplings to soil structure, geochemistry, microbiology, and…
Funding source: Deutsche Forschungsgemeinschaft (DFG)
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Funding source: Elitenetzwerk Bayern
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Mountain glaciers and ice caps outside the large ice sheets of Greenland and Antarctica contribute about 41% to the global sea level rise between 1901 to 2018 (IPCC 2021). While the Arctic ice masses are and will remain the main contributors to sea level rise, glacier ice in other mountain regions can be critical for water supply (e.g. irrigation, energy generation, drinking water, but also river transport during dry periods). Furthermore, retreating glaciers also can cause risks and hazards by…
Funding source: Deutsche Forschungsgemeinschaft (DFG)
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Our project deals with various operations research problems for optimal decision making during pandemics. We formulate, solve, and analyze our problems with respect to sensitivity and stability. The common feature of our problems is the stochasticity of inputs --- we deal with one or multi-stage stochastic programming problems. Moreover, the probability distribution of the random inputs very often depends on the decisions, hence stochastic problems with endogenous randomness will be of interest. We a…
Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)
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Funding source: Deutscher Akademischer Austauschdienst (DAAD)
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Funding source: Deutscher Akademischer Austauschdienst (DAAD)
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Funding source: Deutscher Akademischer Austauschdienst (DAAD)
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