Research Projects
Selected Research Projects at the Department of Mathematics

Optimal Decision Making for COVID19
(Third Party Funds Single)
Term: 13072020  29112020
Funding source: andere Förderorganisation 
Stability for doubly nonlinear parabolic equations (C07 intern)
(Third Party Funds Group – Sub project)
Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Term: 01052020  30062022
Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
URL: https://trr154.fau.de/index.php/de/teilprojekte/c07 
Maschinelles Lernen bei korrelativer MR und HochdurchsatzNanoCT
(Third Party Funds Single)
Term: 01042020  31032023
Funding source: Bundesministerium für Bildung und Forschung (BMBF) 
Mechanistische, integrative Mehrskalenmodellierung der Umwandlung von Bodenmikroaggregaten
(Third Party Funds Single)
Term: 01042020  31082024
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH) 
Besov regularity of parabolic partial differential equations on Lipschitz domains
(Third Party Funds Single)
Term: 01042020  30092021
Funding source: Deutsche Forschungsgemeinschaft (DFG) 
Information management and computational science support
(Third Party Funds Group – Sub project)
Overall project: SFB 1411: Design of particulate products
Term: 01012020  31122023
Funding source: DFG / Sonderforschungsbereich (SFB) 
Process optimization for hospital logistics
(Third Party Funds Single)
Term: since 01012020
Funding source: Industrie
URL: https://en.www.math.fau.de/edom/projectsedom/logisticsandproduction/processoptimizationforhospitallogistics/ 
Topology, material and shape optimisation for particle ensembles
(Third Party Funds Group – Sub project)
Overall project: SFB 1411: Design of particulate products
Term: 01012020  31122023
Funding source: DFG / Sonderforschungsbereich (SFB)The objective is the development of a mathematical framework which allows to conclude from desired optical properties to a corresponding optimised configuration of single particles as well as particle assemblies. A structural optimisation approach based on discrete dipole approximations is explored to allow for a design space with sufficiently high resolution and enabling the prediction of structureproperty relations of individual particles. For particle assemblies a structural optimisation method based on a generalised hybrid finite element approach is established. Finally, dispersity and angle independency are taken into account by a new stochastic optimisation method. 
Quality control by robust optimisation
(Third Party Funds Group – Sub project)
Overall project: SFB 1411: Design of particulate products
Term: since 01012020
Funding source: DFG / Sonderforschungsbereich (SFB)The objective is the development, algorithmic design, implementation and validation of robust mathematical optimisation methods for protecting the design of particulate products against uncertainties. Global solution methods will be investigated for optimal robust chromatography as well as synthesis processes, developing methods based on reformulation and decomposition. The obtained results will be validated with the projects. Information on which uncertainties are most relevant and should be reduced, together with recommendations on robust optimum design and quality control, will be returned to the experimental Projects.

Geordnete Dilationsräume und Geometrie von StandardUnterräumen
(Third Party Funds Single)
Term: 01102019  30092022
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH) 
Multiscale modeling with evolving microstructure: An approach to
emergence in the rhizosphere via effective soil functions(Third Party Funds Group – Sub project)
Overall project: DFG Priority Programme 2089 “Rhizosphere Spatiotemporal Organisation – a Key to Rhizosphere Functions”
Term: 01022019  31012022
Funding source: DFG / Schwerpunktprogramm (SPP)
URL: https://www.ufz.de/spprhizosphere/index.php?en=46495The selforganization of the aggregates in the rhizosphere by various
attracting forces influenced by geochemistry, and microbiology shall
be studied by a novel, comprehensive model. This model should
account for processes on the microscale (single roots, pore scale),
and then be upscaled to the root system scale (macroscale) by
mathematical homogenization. This goal exceeds the functional range
of existing models for aggregation and needs the introduction of an
explicit phase of mucilage, and attachment properties of root hairs in
the rhizosheath. The project aims at the development of a mechanistic modeling approach that allows for dynamic structural reorganization of the rhizosphere at the single root scale and couples this evolving microscale model to the root system scale including the inference of soil functions. This means that we do not assume a static rhizosphere but develop a tool that is capable to dynamically track this zone on the basis of the underlying spatiotemporal aggregegate formation and geochemical patterns. The collaboration with experimental groups – analyzing CT images in various moisture and growth conditions  the Central Experiment will allow to derive the properties of the mucilage phase, the pore structure and thus the
influence of root hairs on aggregation mechanisms. 
Teilprojekt P10  Configurational Fracture/Surface Mechanics
(Third Party Funds Group – Sub project)
Overall project: Fracture across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry, and Physics (FRASCAL)
Term: 02012019  30062023
Funding source: DFG / Graduiertenkolleg (GRK)
URL: https://www.frascal.research.fau.eu/home/research/p10configurationalfracturesurfacemechanics/In a continuum the tendency of preexisting cracks to propagate through the ambient material is assessed based on the established concept of configurational forces. In practise crack propagation is however prominently affected by the presence and properties of either surfaces and/or interfaces in the material. Here materials exposed to various surface treatments are mentioned, whereby effects of surface tension and crack extension can compete. Likewise, surface tension in inclusionmatrix interfaces can often not be neglected. In a continuum setting the energetics of surfaces/interfaces is captured by separate thermodynamic potentials. Surface potentials in general result in noticeable additions to configurational mechanics. This is particularly true in the realm of fracture mechanics, however its comprehensive theoretical/computational analysis is still lacking.
The project aims in a systematic account of the pertinent surface/interface thermodynamics within the framework of geometrically nonlinear configurational fracture mechanics. The focus is especially on a finite element treatment, i.e. the Material Force Method [6]. The computational consideration of thermodynamic potentials, such as the free energy, that are distributed within surfaces/interfaces is at the same time scientifically challenging and technologically relevant when cracks and their kinetics are studied.

Teilprojekt P11  Fracture Control by Material Optimization
(Third Party Funds Group – Sub project)
Overall project: Skalenübergreifende Bruchvorgänge: Integration von Mechanik, Materialwissenschaften, Mathematik, Chemie und Physik (FRASCAL)
Term: 02012019  30062023
Funding source: DFG / Graduiertenkolleg (GRK)
URL: https://www.frascal.research.fau.eu/home/research/p11fracturecontrolbymaterialoptimization/In previous works, the dependence of failure mechanisms in composite materials like debonding of the matrixfibre interface or fibre breakage have been discussed. The underlying model was based on specific cohesive zone elements, whose macroscopic properties could be derived from DFT. It has been shown that the dissipated energy could be increased by appropriate choices of cohesive parameters of the interface as well as aspects of the fibre. However due to the numerical complexity of applied simulation methods the crack path had to be fixed a priori. Only recently models allow computing the full crack properties at macroscopic scale in a quasistatic scenario by the solution of a single nonlinear variational inequality for a given set of material parameters and thus model based optimization of the fracture properties can be approached.
The goal of the project is to develop an optimization method, in the framework of which crack properties (e.g. the crack path) can be optimized in a mathematically rigorous way. Thereby material properties of matrix, fibre and interfaces should serve as optimization variables.

Theoretische Grenzen und algorithmische Verfahren verteilter komprimierender Abtastung
(Third Party Funds Single)
Term: 01012019  31122021
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH)The theoretical limits of distributed compressive sensing are studied bytools from both information theory and statistical physics. The investigationscover both noisefree and noisy distributed compressive sensing. The theoretical insightsare utilized to design approximate message passing algorithms for joint recovery of large distributed compressive sensing networks with feasible computational complexity. These algorithms enable us to verify the nonrigorous results obtained by the replica method from statistical mechanics, and also, to propose theoretically optimal approaches for sampling and low complexity. The proposed research will lead to improved performance of reconstruction algorithms for distributed compressive sensing, e.g. higher compression rates and/or higher fidelity of reconstruction. 
PPP Frankreich 2019 Phase I
(Third Party Funds Single)
Term: 01012019  31122020
Funding source: Deutscher Akademischer Austauschdienst (DAAD) 
Nonlocal Methods for Arbitrary Data Sources
(Third Party Funds Group – Sub project)
Overall project: Nonlocal Methods for Arbitrary Data Sources
Term: 01102018  28022022
Funding source: EU  8. Rahmenprogramm  Horizon 2020 
Integriertes und an RaumZeitMessungsskalen angepasstes Global Random Walk  Modell für reaktiven Transport im Grundwasser
(Third Party Funds Single)
Term: 01102018  30092021
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH) 
Holistische Optimierung von Trajektorien und Runway Scheduling
(Third Party Funds Group – Sub project)
Overall project: Holistische Optimierung von Trajektorien und Runway Scheduling
Term: 01092018  31082021
Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)
URL: https://www.mso.math.fau.de/edom/projects/hotrun/Efficient runway utilization is a major issue in airport operation, as capacities are (nearly) reached in many aiports. But planing is highly affected by uncertainties arising from weather changes or disruptions in the operative business. Furthermore, the planing of flight trajectories in the terminal region is by now often neglected in runway scheduling, as time efficient solution methods are mathematically challenging. The overall goal of this project is to combine trajectory and runway schedule computation including resilience against uncertainties in order to obtain stable optimal solutions.

Parity Sheaves on Kashiwara's flag manifold
(Third Party Funds Group – Overall project)
Term: 01092018  31122019
Funding source: Deutscher Akademischer Austauschdienst (DAAD)The project is located in pure mathematics and deals with a problem in geometric representation theory. Parity sheaves and moment graph techniques have proven to be extremely effective in answering questions in modular representation theory. In the finitedimensional case a hypercohomology functor establishes a connection between parity sheaves and sheaves on moment graphs. However the geometry controlling representation theoretic phenomena in this case is often infinitedimensional. We plan to study the category of parity sheaves on Kashiwara's infinitedimensional thickflag variety Y, to define a hypercohomology functor, to interpret its image as a category of moment graph sheaves and to establish an equivalence between parity sheaves and canonical sheaves on the moment graph. In a second phase, we intend to study base change and torsion phenomena in the category of parity sheaves on the thick flag manifold, in order to establish an equivalence between the category of projective objects in the category O of an affine KacMoody algebra at negative level and parity sheaves on Y.

Implementation of vector operations for SBCL
(Third Party Funds Single)
Term: 10072018  31032019
Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)Ziel des Projekts ist es, AVX2 Vektoroperationen für die Common LispImplementierung SBCL verfügbar zu machen. SBCL ist derpopulärste und am weitesten Entwickelte freie Compiler für CommonLisp. Die Verbesserungen aus diesem Projekt machen es möglichCommon Lisp Programme zu schreiben, deren Ausführungsgeschwindigkeitmit C++ und Fortran Programmen auf Augenhöhe liegt. Dadurchergeben sich interessante Möglichkeiten der Metaprogrammierung imwissenschaftlichen Rechnen. 
Decomposition methods for mixedinteger optimal control (A05) (2018  2022)
(Third Party Funds Group – Sub project)
Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Term: 01072018  30062022
Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)The focus lies on the development of mathematical decomposition methods for mixedinteger nonlinear optimal control problems on networks. On the top level (master) mixedinteger linear problems are in place, whereas in the subproblem only continuous variables are considered. The exchange between the levels is performed not only via cutting planes, but also via the modelling of disjunctions to deal with nonconvex optimal control problems as well. The overall emphasis is the mathematical analysis of structured mixed nonlinear optimization problems based on hierarchical models.

MIP techniques for equilibrium models with integer constraints (B07) (2018  2022)
(Third Party Funds Group – Sub project)
Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Term: 01072018  30062022
Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)In this subproject we will develop techniques to solve equilibrium problems with integer constraints using MIP techniques. To this end, we will consider first mixedinteger linear, then mixedinteger nonlinear problems as subproblems. To solve the resulting problems we will study both complete descriptions as also generalized KKT theorems for mixedinteger nonlinear optimization problems. 
Multilevel mixedinteger nonlinear optimization for gas markets (B08) (2018  2022)
(Third Party Funds Group – Sub project)
Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Term: 01072018  30062022
Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
URL: https://trr154.fau.de/index.php/de/teilprojekte/b08The main goal of this project is the development of mathematical methods for the solution of multilevel, mixedinteger, and nonlinear optimization models for gas markets. To this end, the focus is on a genuine fourlevel model of the entryexit system that can be reformulated as a Bilevel model. The mathematical and algorithmic insights shall then be used to characterize market solutions in the entryexit system and to compare them to system optima. Particular attention is paid to booking prices for entry or exit capacity.

Robustification of Physics Parameters in Gas Networks (B06) (2018  2022)
(Third Party Funds Group – Sub project)
Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Term: 01072018  30062022
Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)The goal of this research project is to study uncertain optimization problems using robust optimization methods. Focusing on transport networks, we aim at the development of tractable robust counterparts for uncertain optimization problems and an analysis of the problem structure. For the arising adjustable robust optimization tasks, good relaxations as well as effective branchandbound implementations shall be developed.

Interfaces, complex structures, and singular limits in continuum mechanics
(Third Party Funds Group – Overall project)
Term: 01042018  30092022
Funding source: DFG / Graduiertenkolleg (GRK) 
Free boundary propagation and noise: analysis and numerics of stochastic degenerate parabolic equations
(Third Party Funds Single)
Term: 01042018  31032020
Funding source: Deutsche Forschungsgemeinschaft (DFG), DFGEinzelförderung / Sachbeihilfe (EINSBH)
URL: https://www1.am.unierlangen.de/~gruen/The porousmedium equation and the thinfilm equation are prominent examples of nonnegativity preserving degenerate parabolic equations which give rise to free boundary problems with the free boundary at time t > 0 defined as the boundary of the solution’s support at that time.
As they are supposed to describe the spreading of gas in a porousmedium or the spreading of a viscous droplet on a horizontal surface, respectively, mathematical results on the propagation of free boundaries become relevant in applications. In contrast to, e.g., the heat equation, where solutions to initial value problems with compactly supported nonnegative initial data
instantaneously become globally positive, finite propagation and waiting time phenomena are characteristic features of degenerate parabolic equations.
In this project, stochastic partial differential equations shall be studied which arise from the aforementioned degenerate parabolic equations by adding multiplicative noise in form of source terms or of convective terms. The scope is to investigate the impact of noise on the propagation of free boundaries, including in particular necessary and sufficient conditions for the occurrence
of waiting time phenomena and results on the size of waiting times. Technically, the project relies both on rigorous mathematical analysis and on numerical simulation. 
MixedInteger NonLinear Optimisation: Algorithms and Applications
(Third Party Funds Group – Overall project)
Building upon the achievements of the MarieCurie ITN MixedInteger NonLinear Optimization (MINO) (2012  2016), the goal of the MixedInteger NonLinear Optimisation Applications (MINOA) proposal is to train the next generation of highly qualified researchers and managers in applied mathematics, operations research and computer science that are able to face the modern imperative challenges of European and international relevance in areas such as energy, logistics, engineering, natural sciences, and data analytics. Twelve EarlyStage Researchers (ESRs) will be trained through an innovative training programme based on individual research projects motivated by these applications that due to their high complexity will stimulate new developments in the field. The mathematical challenges can neither be met by using a single optimisation method alone, nor isolated by single academic partners. Instead, MINOA aims at building bridges between different mathematical methodologies and at creating novel and effective algorithmic enhancements. As special challenges, the ESRs will work on dynamic aspects and optimisation in real time, optimisation under uncertainty, multilevel optimization and noncommutativity in quantum computing. The ESRs will devise new effective algorithms and computer implementations. They will validate their methods for the applications with respect to metrics that they will define. All ESRs will derive recommendations, both for optimised MINO applications and for the effectiveness of the novel methodologies. These ESRs belong to a new generation of highlyskilled researchers that will strengthen Europe'e human capital base in R&I in the fast growing field of mathematical optimisation. The ESR projects will be pursued in joint supervision between experienced practitioners from leading European industries and leading optimisation experts, covering a wide range of scientific fields (from mathematics to quantum computing and realworld applications).

Optimierung der Netzeingriffe
(Third Party Funds Group – Sub project)
Overall project: Flächenbezogene Modellierung, Simulation und Optimierung von SolarEinspeisung, Lastfluss und Steuerung für Stromverteilnetze, unter Berücksichtigung von Einspeisungsunsicherheiten
Term: 01012018  31122020
Funding source: Bundesministerium für Bildung und Forschung (BMBF)
URL: https://www.mso.math.fau.de/edom/projects/verteilnetze/ 
Adaptive Verfahren zur Optimierung gekoppelter pHSysteme
(Third Party Funds Group – Sub project)
Overall project: EiFer: Energieeffizienz durch intelligente Fernwärmenetze
Term: 01012018  31122020
Funding source: Bundesministerium für Bildung und Forschung (BMBF) 
Optimierte Prozesse für Trajektorie, Instandhaltung, Management von Ressourcen und Abläufen in der Luftfahrt
(Third Party Funds Single)
Term: 01012018  31122021
Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)
URL: https://www.mso.math.fau.de/edom/projects/opstimal/ 
Reduced Order Modelling, Simulation and Optimization of Coupled systems
(Third Party Funds Group – Sub project)
Overall project: Reduced Order Modelling, Simulation and Optimization of Coupled systems
Term: 01092017  31082021
Funding source: EU  8. Rahmenprogramm  Horizon 2020
URL: https://www.romsoc.eu/ 
Innovationsfonds 2017: Urkunden und Buchgutscheine für gute Leistungen in Anfängervorlesungen
(FAU Funds)
Term: 01072017  30092020Um den Vorlesungs und Prüfungsbetrieb persönlicher zu gestalten, wird bei sehr guten Leistungen in meinen Anfängervorlesungen "Mathematik für Ingenieure" ein wenig symbolisches Lob in der Form von Urkunden und auch ein wenig finanzielles Lob in der Form von Buchgutscheinen ausgeteilt. 
Besov Regularität von parabolischen partiellen Differentialgleichungen auf Lipschitz Gebieten
(Third Party Funds Single)
Term: 01042017  31032019
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH)This project is concerned with partial differential equations (PDEs) of parabolic type on Lipschitz domains. We want to study the regularity of the solutions of such equations and are particularly interested in smoothness estimates in specific scales of Besov spaces, which determine the approximation order of adaptive and other nonlinear numerical approximation schemes. We wish to show that the Besov regularity is high enough to justify the use of adaptive schemes compared to nonadaptive (uniform) schemes. We shall mainly be concerned with approximation schemes based on wavelets.Our starting point is to improve existing results for the heat equation and extend these results to linear parabolic PDEs with variable coefficients and also to nonlinear parabolic PDEs. We also want to show that when restricting ourselves to polygonal and polyhedral domains (compared to general Lipschitz domains) we get even higher Besov regularity.
Since the approximation rates obtained this way still depend on the spatial dimension, we secondly wish to study regularity of parabolic PDEs in generalized dominating mixed smoothness spaces. By using tensorwavelets we want to beat the socalled 'curse of dimension' and obtain convergence rates independent of the underlying dimension of the domain. 
Energiemarktdesign
(Third Party Funds Group – Sub project)
Overall project: Energie Campus Nürnberg (EnCN2)
Term: 01012017  31122021
Funding source: andere Förderorganisation, Bayerische Staatsministerien
URL: http://www.encn.de/en/forschungsthemen/energiemarktdesign/In the project “Energy Markt Design” within EnCN2 a team of researchers from economics, mathematics, and law analyses the economic and regulatory environment for the transformation of the energy system. The main objectives are to enhance the methods in energy market modeling and to contribute with wellgrounded analyses to the policy discourse in Germany and Europe. For the electricity market, the focus is on the steering effect of market designs on regulated transmission expansion and private investments, as well as on the identification of frameworks at the distribution level that provide regional stakeholders with business models for the provision of flexibility measures. In order to address these complex issues, mathematical techniques are developed within the project that allow for solving the respective models. Another key research topic results from the advancing sector coupling in energy markets. Within EMD, gas market models, that are developed within DFG Transregio 154 (Simulation and Optimization of Gas Networks) in cooperation with project partners, are applied to evaluate the European gas market design. The longterm objective of the research group is an integrated assessment of the electricity and gas market design and their combined effects on investment decisions.

Rechenleistungsoptimierte SoftwareStrategien für auf unstrukturierten Gittern basierende Anwendungen in der Ozeanmodellierung
(Third Party Funds Single)
Term: 01012017  30092020
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH)Um akkurate Ozean, Atmosphären oder Klima Simulationen durchzuführen werden sehr effiziente numerische Verfahren und große Rechenkapazitäten benötigt, die in vielen Teilen der Welt und bei vielen Forschungsgruppen in diesen Anwendungsfeldern nicht verfügbar sind. Solche Beschränkungen führen auch dazu, dass Modelle und Softwarepakete basierend auf strukturierten Gittern derzeit in der Ozeanwissenschaft immer noch vorherrschend sind.In diesem Projekt soll zum einen die Rechenzeit für Modelle, die auf unstrukturierten Gittern und einer diskontinuierlichen Galerkin finite Elemente Methode basieren, deutlich reduziert werden, und zum anderen die Produktivität bei der Softwareentwicklung gesteigert werden. Das erste Ziel soll durch einen neuen Ansatz zur parallelen Gebietszerlegung und durch adaptive numerische Verfahren erreicht werden.Für das zweite Ziel kommen moderne Software Design Strategien zum Einsatz, vor allem Codegenerierung und automatische Optimierung von rechenintensiven Programmteilen. Die Fortschritte bei der Rechenzeit und dem Software Design, die aus dem Projekt resultieren, können einen wichtigen Beitrag leisten, um unstrukturierte Gitter für alle Forscher aus den Ozeanwissenschaften nutzbar zu machen, auch wenn sie nur Zugang zu moderat parallelen Systemen und nicht zu Höchstleistungsrechnern haben.

Optimization of medical care in rural environments
(Third Party Funds Group – Overall project)
Term: 01122016  30112019
Funding source: BMBF / Verbundprojekt
URL: https://www.mso.math.fau.de/edom/projects/healthfact/ 
Verbundvorhaben proMT Teilprojekt 2: Modellreduktion zur prognostischen online MRThermometrie
(Third Party Funds Group – Sub project)
Overall project: Verbundvorhaben proMT Teilprojekt 2: Modellreduktion zur prognostischen online MRThermometrie
Term: 01122016  30112019
Funding source: Bundesministerium für Bildung und Forschung (BMBF) 
"Verbundprojekt MED4D: Dynamische Medizinische Bildgebung: Modellierung und Analyse medizinischer Daten für verbesserte Diagnose, Überwachung und Arzneimittelentwicklung"
(NonFAU Project)
Term: 01122016  30112019
Funding source: Bundesministerium für Bildung und Forschung (BMBF) 
Welfare optimal nominations in gas networks and associated equilibria
(Third Party Funds Group – Sub project)
Overall project: SFB TRR 154 “Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzen”
Term: 01102016  30062018
Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
URL: https://trr154.fau.de/index.php/de/teilprojekte/teilprojektephase1/b08phase1The goal of this project is the analysis of the relation between (i) the equilibria of simple models of competitive natural gas markets, using complementarity problems for modeling the behavior of different players, and (ii) the solution of corresponding singlelevel welfare maximization problems. The understanding of this fundamental relation is a prerequisite for an analysis of the current entryexit gas market design in Europe. Similar questions have been studied in detail in the context of electricity market modeling in the past. For natural gas markets, however, the addressed questions are much more complex and not yet well understood for adequate models of gas physics. The reasons for the high level of complexity is twofold: First, gas flow through pipeline systems is inherently nonconvex due to gas physics. This renders classical firstorder optimality conditions possibly insufficient. Second, the operation of gas transport networks comprises the control of active network devices like (control) valves or compressors. These devices introduce binary aspects and thus a further type of nonconvexity to the models of the underlying equilibrium problems. As a result of the project we will obtain a first reference model that combines gas physics and a market analysis in a wellunderstood way. This will lay the ground for multilevel models of entryexit natural gas markets that account for network characteristics. Beyond that, our results will enhance the understanding of binary equilibrium problems.

Mathematische Schlüsselqualifikation für Energienetze im Wandel – Teilprojekt FAU
(Third Party Funds Group – Sub project)
Overall project: Mathematische Schlüsselqualifikation für Energienetze im Wandel – Teilprojekt FAU
Term: 01102016  30042020
Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi) 
Analyse und Anwendung reduzierter Modelle
(Third Party Funds Group – Sub project)
Overall project: MathEnergy — Mathematische Schlüsseltechniken für Energienetze im Wandel
Term: 01042016  30042020
Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)Das Kernziel dieses mathematisch orientierten Teilvorhabens ist die Methodenentwicklung und Analyse reduzierter Modelle bzw. Modellhierarchien und ihrer Anwendung zur dynamischen Zustandsschätzung in einer modellprädiktiven Regelung.

Analysis and Implementation of Highly Compressive Sensing
(Third Party Funds Single)
Term: 01032016  28022019
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH)The project will investigate the performance limits of compressive sensing and propose practical algorithms that approach these performance limits closely.The project will focus on the regime of high compression ratios where L1norm regularization is suboptimal.Compressive sensing will be investigated from the viewpoint of statistical physics and considered as a particular instance of a spin glass system.Both average distortion and minimax distortion will be addressed as objective functions (Hamiltonians).The analysis will rely on the replica method. Particular emphasis will be put on the implications of replica symmetry breaking.The main objectives of the project are:1) to find a system of saddle point equations that describe the replica symmetry breaking solution to the compressive sensing problem,2) to prove rigorous onesided bounds for these solutions by adapting Guerra's arguments for the SherringtonKirkpatrick spin glass model to spin glass model of compressive sensing and, hereby, justifying the correctness of the replica method in compressive sensing,3) to numerically solve the system of saddle point equations, and 4) to determine which practical algorithms work well for compressive sensing at high compression ratios.

Spatial continuum limit of treevalued statedependent spatial branching processes
(Third Party Funds Single)
Term: 01012016  28022019
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH)The project studies the spatial continuum limit of one and multitype branching processes with statedependent branching rates and analyses the characteristics of limit processes. Particular emphasis is placed on genealogies in the corresponding populations, i.e. treevalued processes are studied. Typical examples are branching random walks, catalytic branching random walks, mutually branching random walks, selfcatalytic random walks and logistic branching random walks and the relevant continuous mass limits (interacting branching diffusions). The goal is to show the existence of the limits, the characteristics of their longtime behaviour and the structure on small space and time scales. The question of their stochasticity shall be clarified and in the case of a deterministic limit the asymptotic of ''hotspots'' shall be studied by means of volatility or size biasing and subsequent rescaling. As basis the calculus of infinitely divisible genealogical processes and the description of genealogies of matri and patrilinear ancestor lines are to be developed.

Mechanistic modelling of the formation and consolidation of soil microaggregates
(Third Party Funds Group – Sub project)
Overall project: DFG RU 2179 “MAD Soil  Microaggregates: Formation and turnover of the structural building blocks of soils”
Term: 01012016  31122018
Funding source: Deutsche Forschungsgemeinschaft (DFG) 
Invariant convexity in infinite dimensional Lie algebras
(Third Party Funds Single)
Term: since 01012016
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH)Infinite dimensional Lie groups show up in all areas of mathematics and other sciences, wherever symmetries depending on infinitely many parameters arise. The goal of this project is to develop a systematic understanding of convexity properties of infinite dimensional Lie algebras. More precisely, we are aiming at a classification of open convex cones in an infinite dimensional Lie algebra that are invariant under the adjoint action. In the dual of the Lie algebra we would like to determine those invariant convex subsets which are semiequicontinuous, which means that their support functional is bounded in the neighborhood of some point. A key point of this project is to understand closed convex hulls of projections of adjoint and coadjoint orbits to subalgebras; results of this type are called convexity theorems. Classically convexity theorems mostly concern orbit projections onto abelian subalgebras, where they are often convex hulls of Weyl group orbits. The convexity theorems of SchurHorn, Kostant, AtiyahPressley and KacPeterson are of this type. We are aiming at a systematic extension of these results to larger classes of Lie algebras and to projections onto more general subalgebras. This project is motivated to a large extent by its applications to unitary representations, where knowledge on open invariant cones is crucial to determine spectral bounds of operators from the derived representation. The set of all elements represented by operators bounded from below is an invariant convex cone. That it has interior points means that the representation is semibounded. Semiboundedness is a stable version of the positive energy condition which characterizes many representations arising in quantum mechanics. Typical Lie algebras we plan to study in this context are direct limits of finite dimensional Lie algebras and their completions, hermitian Lie algebras (corresponding to automorphism groups of symmetric Hilbert domains) and socalled double extensions of HilbertLie algebras (close infinite dimensional relatives of compact Lie algebras) and of twisted loop algebras with infinite dimensional target groups. The latter lead to infinite rank generalizations of affine KacMoody Lie algebras. The focus of the present project lies on combining structural properties on infinite dimensional Lie algebras with functional analytic and geometric methods to obtain a concrete description of invariant convex cones and semiequicontinuous coadjoint orbits.

Applied index theory for quantum and classical systems
(Third Party Funds Single)
Term: 01012016  31122018
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH)The first goal of index theory is to relate topological invariants to indices of Fredholm operators. The most famous result in this direction is the AtiyahSinger index theorem, but there exist far reaching noncommutative generalizations. While there is a general theory, such index theorems have to be established case by case in applications. The second goal of index theory is to connect invariants and indices of problems related via exact sequences. For example, this allows to read off the topology of boundary states or point defects from bulk invariants. The proposal aims to implement this program in situations which have not been tackled before like interacting spin systems, photonic crystals and lattices of classical springs, and also to further develop the index approach to scattering systems and topological materials. 
GermanNorwegian collaborative research support scheme
(Third Party Funds Single)
Term: 01012016  31122017
Funding source: Deutscher Akademischer Austauschdienst (DAAD)Homogenisierung reaktiven Transports in variablen Mikrostrukturen

Modellreduktion zur prognostischen online MRThermometrie
(Third Party Funds Group – Sub project)
Overall project: proMT — Prognostische modellbasierte online MRThermometrie bei minimalinvasiver Thermoablation zur Behandlung von Lebertumoren
Term: 01012016  31122019
Funding source: Bundesministerium für Bildung und Forschung (BMBF)In Hinblick auf die angestrebte prognostische OnlineSimulationsfähigkeit zielt dieses Teilprojekt auf die Entwicklung und Analyse reduzierter Modelle mittels Techniken der Modellordnungsreduktion (MOR). Die Kombination von MOR und SpaceMapping lässt eine weitere Steigerung der Performance erhoffen, die für die konkrete Anwendung der MRThermometrie qualitativ und quantitativ bewertet wird.

Scientific Computing for Improved Detection and Therapy of Sepsis
(NonFAU Project)

EXISTGründerstipendium: FoodOptimizer ist ein wissenschaftliches Ernährungs und Symptomtagebuch
(Third Party Funds Single)
Term: 01102015  30092016
Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)FoodOptimizer ist ein wissenschaftliches Ernährungs und Symptomtagebuch, das eine systematische Analyse und Diagnoseunterstützung zur Aufdeckung von Nahrungsmittelallergien und unverträglichkeiten anbietet.

Verteiltes Höchstleistungsrechnen in Common Lisp
(Third Party Funds Single)
Term: 01102015  31032016
Funding source: Bayerisches Staatsministerium für Wissenschaft, Forschung und Kunst (StMWFK) (bis 09/2013)The Message Passing Interface\cite{mpistandard} (MPI) is the de facto
standard for distributed programming on all modern compute clusters and
supercomputers. It features a large number of communication patterns with
virtually no overhead. Our work on bringing MPI functionality to Common
Lisp resulted in vast improvements to the message passing library CLMPI
and the development of severaly new approaches to distributed computing.

DAAD Exchange Service: PPP Finnland 2017: Bayesian Inverse Problems in Banach Space
(NonFAU Project)
Term: 25012015  31122017
Funding source: Deutscher Akademischer Austauschdienst (DAAD) 
Modeling, simulation and optimization of process chains
(Third Party Funds Group – Sub project)
Overall project: SPP 1679: Dynamic Simulation of Interconnected Solids Processes
Term: since 01012015
Funding source: DFG / Schwerpunktprogramm (SPP)The projected research aims at the simulationbased optimization of predictive models of coupled process chains. This makes it possible to optimize both the conditions of the single processes and the configuration of the entire process chain integrated into an MRT with respect to the desired particle properties. The methods and algorithms to be developed during the funding period build up a general toolbox for simulation and optimization of dynamic processes relevant to the SPP, thereby generalizing from the exemplary applications provided by batch processes, as nucleation and ripening, to process chains. This is made possible by integrating mathematical models including processes of more general but structurally equivalent type. 
Existence and regularity for parabolic quasi minimizers on metric measure spaces
(Third Party Funds Single)
Term: 01012015  31122018
Funding source: DFGEinzelförderung / Sachbeihilfe (EINSBH)The aim of this project is to make a substantial contrubution to existence and regularity theory for solutions of nonlinear parabolic minimization problems on general metric measure spaces. It is intended to establish a systematic approach to the generalization of a result by A. Grigor'yan and L. SaloffCoste on the relation between solutions of the heat equation on Riemannian manifolds and the validity of Harnack estimates. The interest is to generalize this result in two ways: Firstly, one intends to consider metric measure spaces, supporting a doubling property of the measure and a Poincaré inequality, instead of a Riemannian manifold. Secondly, instead of the (linear) heat equation, nonlinear problems should be investigated.Main difficulties of the project consist on one hand in the very general concept of metric measure spaces, on the other hand in the nonlinearity of the partial differential equations and integral functionals under consideration. On general metric measure spaces it is not possible to speak of "direction" or "integration by parts" and consequently there's a lack of a suitable form of derivative. This makes it necessary to work with socalled "upper gradients" which are defined according to a characterization of Sobolev functions in the Euklidean space by to the power p integrable vector fields. This concept does not allow to introduce a reasonable definition of a partial differential equation, however it helps to generalize minimization problems to the context of metric measure spaces. The nonlinearity of the problem causes a number of further severe difficulties, which are basically already known from the theory of nonlinear parabolic differential equations in the n dimensional Euklidean space. These difficulties have to be overcome on the level of pure minimization problems  without any associated partial differential equation behind.