Main Content
Completed projects (selection)
TRR 45: Periods, Moduli Spaces and Arithmetic of Algebraic Varieties
Subproject: Moduli Spaces, Symplectic and Calabi-Yau Manifolds (M08 (C5/C7))
Moduli spaces of various sorts are a common theme inside the Transregio. The central topics in this project are the geometry of moduli spaces of varieties and vector bundles, with a special emphasis on moduli of Calabi-Yau varieties, moduli of vector bundles, and the theory of holomorphic symplectic varieties. New working packages include cubic fourfolds, stability conditions for stacks, tautological sheaves, moduli spaces of vector bundles on higher-dimensional varieties, and the birational geometry of hyperkähler manifolds.
Subproject Manager: Prof. Dr. Sönke Rollenske bis 8/2011;
Funded by: DFG (Transregios)
Funding: from 2011 until 2019SFB 647: Space - Time - Matter: Analytic and Geometric Structures
Subproject: Special Geometries and Fermionic Field Equations (A02)
Subproject Manager: Professorin Dr. Ilka Agricola
Funded by: DFG (Sonderforschungsbereiche)
Funding: from 2005 until 2008SFB 701: Spectral Structures and Topological Methods in Mathematics
Subproject: Algebraic and analytic aspects of holomorphic Lagrangian fibrations (C11*)
We consider various aspects of a class of manifolds called, depending on the point of view, hyperkähler manifolds or irreducible holomorphic-symplectic manifolds. An important subclass is formed by those manifolds which additionally admit a holomorphic Lagrangian fibration. On the complement of singular fibers we get an actual holomorphic fibering by smooth Lagrangian tori. In this situation we want to study, among other things, integrally affine structures on the basis, special Riemannian metrics on the basis and total space, and mappings into the moduli space of abelian varieties, in order to better understand the global geometry of hyperkähler manifolds.
Subproject Manager: Prof. Dr. Sönke Rollenske, Prof. Dr. Andriy Haydys
Funded by: DFG (Sonderforschungsbereiche)
Funding: from 2013 until 2017Adaptive Wavelet and Frame Techniques for Acoustic BEM
In BIOTOP, we will develop new methods to model 3D acoustic wave problems, especially the calculation of head related transfer functions (HRTFs), which play an important role in the localization of sound sources in 3D. Head related transfer functions describe the filtering effect of the head, the torso, and especially the outer ear (pinna) on incoming sounds and can be used to describe and simulate spatial hearing in virtual acoustics. For the simulation of acoustic problems, the boundary element method (BEM) is an important tool. Unfortunately, the matrices generated by the boundary element method are dense and their dimension grows with the wavenumber/frequency. To overcome this obstruction, we will design efficient variants of the boundary element method based on adaptive wavelet methods and the concept of frames. They will be particularly tuned to the requirements in acoustics, thus allowing an efficient computation of sound fields also for high frequencies. We will combine wavelet compression strategies with adaptive techniques and design new frames adapted to the problem at hand, and investigate the mathematical and numerical properties. BIOTOP is a multi-disciplinary project by necessity, involving mathematics, numerics and acoustical modeling. As a D-A-CH project, it combines the expertise of the research groups from Germany (adaptive schemes, regularity theory), Austria (frames, calculation of HRTFs, acoustic modeling) and Switzerland (wavelet BEM, adaptivity).
Applicant: Prof. Dr. Stephan Dahlke
Funded by: DFG (Sachbeihilfen)
Funding: from 2013 until 2015Methods and tools for computational media analysis
The proposed project will address the following tasks: First, an e-Service Media Grid will be developed to enable the media studies research community to easily and flexibly use and combine analysis algorithms, data sets, and results via the World Wide Web. Second, new analysis methods for multimedia (social) web content are being explored to support media studies research activities; new methods are being developed for semantic analysis of videos. Thirdly, a software solution for archiving the data holdings of the expiring Research College 615 and the Package Group is being designed in cooperation with the relevant institutions of the University of Siegen (University Library, Center for Information and Media Technology (ZIMT), Institute for Media Research (IfM)).
Participating: Prof. Dr.-Ing. Bernd Freisleben
Applicant: Prof. Dr. Manfred Grauer
Funded by: DFG (Sachbeihilfen)
Funding: from 2010 until 2012Algebra and Lie Theory
Applicant: Prof. Dr. István Heckenberger
Funded by: DFG (Heisenberg-Professuren)
Funding: from 2010 until 2013Nilmanifolds with left invariant complex structure
The aim of the research project is a better understanding of the geometry of nilmanifolds with left-invariant complex structure. On the one hand, these geometric objects are easily described by methods of Lie theory, and on the other hand, they have a rich geometric structure, for the study of which methods from differential geometry, algebraic geometry and harmonic analysis are necessary. Many important (counter)examples in symplectic topology, complex geometry, and differential geometry have been constructed using nilmanifolds, and a further goal of the project is to generalize these constructions and thus obtain new construction methods for complex manifolds with exotic properties.
Applicant: Prof. Dr. Sönke Rollenske
Funded by: DFG (Forschungsstipendien)
Funding: from 2007 until 2009Preliminary work on the creation of a concept for securing biodiversity data: Analysis of existing initiatives and elicitation of motivation and acceptance issues.
The project proposed here serves to develop a concept for the sustainable safeguarding and provision of primary collected biodiversity research data in Germany in the general consensus of the community. During the proposed project period, an inventory of existing infrastructures that hold biodiversity-relevant primary data is planned, as well as a technical analysis of existing systems. This will be done through targeted internet and literature research, source evaluations and interviews. A further step will be the user analysis, which will focus on the acceptance of a centralized/decentralized data storage as well as the motivation of scientists to save and hand over primary data and will evaluate the required service offer. To narrow down the complexity of the project, the biodiversity projects funded by the DFG since 2003 will be analyzed. Project leaders and staff will be interviewed about their primary data storage using an Internet-based telephone survey. If necessary, personal interviews will be conducted with selected project leaders. The results lead to a final needs assessment for a national umbrella structure for primary data storage in biodiversity research. The final report includes recommendations for future planning.
Co-applicant: Prof. Dr. Bernhard Seeger
Funded by: DFG (Forschungsdaten und Software (Wiss. Literaturversorgung und Informationssysteme))
Funding: from 2010 until 2012Regularity Theory of Stochastic Partial Differential Equations in (Quasi-)Banach Spaces
This project is concerned with regularity estimates for stochastic partial differential equations (SPDEs, for short) on bounded Lipschitz domains. We use specific (quasi-)Banach spaces to measure the smoothness of the solution. Our analysis is motivated by some fundamental problems arising in the context of the numerical treatment of SPDEs. We divide our investigations into three parts which are closely related to each other. In the first two parts we use a specific scale of Besov spaces to measure the spatial regularity of the solution process. This scale determines the convergence order that can be achieved by adaptive (wavelet) schemes and other non-linear approximation methods. It consists mostly of Besov spaces with summability parameter less than one, thus, of quasi-Banach spaces. In the first part we want to derive refined regularity results in weighted Sobolev spaces which yield the desired Besov regularity results by embedding strategies. In the second part, we strive for a more direct approach. To this end, the well-known theory of stochastic integration in UMD-Banach spaces has to be generalized as far as possible to quasi-Banach spaces. In the third part of the project, we want to derive regularity estimates in tensor products of weighted Sobolev spaces which would justify the use of anisotropic full space-time adaptive tensor wavelet methods.
Applicant: Prof. Dr. Stephan Dahlke
Funded by: DFG (Sachbeihilfen)
Funding: from 2013 until 2015Harmonic analysis on affine G-varieties
The present research project aims at the study of algebraic group actions on affine varieties and the development of a corresponding representation and spectral theory. The study of group actions has a history of more than 150 years and has its origin in the classical invariant theory, which developed out of problems in mechanics, geometry and number theory. Modern invariant theory goes back to considerations of Klein and Hilbert at the end of the 19th century. Together with the representation and spectral theory, as well as the theory of partial differential equations, it occupies a central position in mathematics and is also of great importance for modern physics. However, while the representation theory of groups and the spectral theory on the one hand, and the study of algebraic group actions on the other hand, are well developed, the representation theory of an affine variety on which a group acts has been little studied, and the spectral properties of invariant operators on such a variety are largely unknown. The related issues will be addressed in the present project and range from harmonic analysis and operator and spectral theory to algebraic geometry and number theory.
Applicant: Prof. Dr. Pablo Ramacher
Funded by: DFG (Emmy Noether-Nachwuchsgruppen)
Funding: from 2006 until 2014Big cones of algebraic varieties
Ample line bundles are fundamental objects in modern Algebraic Geometry, which enjoy many geometric, numerical and cohomological properties. By contrast, due to well-known pathologies, line bundles satisfying the more general property of bigness were for a long time considered difficult to treat and geometrically hard to grasp. Very recently, however, there were substantial break-throughs showing that from an asymptotic point of view, big line bundles display quite predictable behaviour analogous to that of ample line bundles -- in this way their geometric use is now much more obvious and they therefore received a great deal of attention. Due to these developments it has become essential to understand the set of big line bundles (the big cone) of an algebraic variety as closely as possible from a structural point of view. In particular, decompositions of the big cone into geometrically and numerically determined subcones are of central importance - they collect line bundles with equivalent geometric behaviour and thus reduce the complexity of the situation drastically. In our group, the following sub-projects in this current area of Algebraic Geometry are to be studied: (A) Big cones of algebraic surfaces, investigation of the chamber numbers and chamber volumes of (in particular) anti-canonical surfaces, geometrical interpretations of the chamber volume and computation of the chamber numbers by algorithmic and combinatorial methods. (B) Big cones of higher dimensional varieties, study of the polyhedral case by methods of the Minimal Model Program, characterization of the sub cones, first treatment of sub cone number and sub cone volume in the non-polyhedral case.
Applicant: Prof. Dr. Thomas Bauer
Funded by: DFG (Sachbeihilfen)
Funding: from 2012 until 2015Adaptive wavelet methods for inverse problems and inverse parabolic equations
In this project, two fields of applied mathematics, which were developed almost independently from each other, will be consolidated. On one hand, adaptive wavelet methods for the numerical treatment of operator equations were examined for many years. However the achieved convergence results refer exclusively to continuously invertible operators.On the other hand, the general convergence theory, at least for linear inverse problems, has been worked out for a long time. However, adaptive wavelet methods and the results of non-linear wavelet approximation schemes have hardly been used so far in this context, with the exception of the recent results in [14, 42]. In this project we would like to analyze different approaches to adaptive wavelet methods for inverse problems: two-step regularization schemes, where the data are pre-smoothed in a first step; regularization methods based on adaptive procedures for the forward operator combined with classical regularization procedures; regularization by wavelet discretization. These methods will be extended to some non-linear operator equations. As a prototypical application an inverse heat conduction problem will be examined.
Applicant: Prof. Dr. Stephan Dahlke, Prof. Dr. Peter Maaß
Funded by: DFG (Sachbeihilfen)
Funding: from 2006 until 2010Systematic development of complex software in distributed teams
One of the major challenges of today's software development is to master the complexity of software systems. The use of a model-driven approach is promising, since models are a good means of abstraction and thus developers are more likely to be able to master complexity. Application implementation is largely replaced by automatic code generation from the model. This can greatly speed up software development. An open problem of the model-driven procedure is the systematic software development by several, distributed developers. A goal of the project is it to compile a conception for distributed model-driven software development based on systematic development steps. Models should be decomposable into submodels and systematically developed through distributed transformation steps that enable cooperative work, synchronization of developments, and flexible distribution structures. For the analysis of conflicts and dependencies between development steps, a formal foundation of this conception by distributed graph transformation is planned. Its technical implementation is to take place within the framework of the Eclipse Modeling Framework and the code generator AndroMDA.
Applicant: Prof. Dr. Gabriele Taentzer
Funded by: DFG (Sachbeihilfen)
Funding: from 2007 until 2012Optimal adaptive finite element and wavelet methods for p-Poisson equations
This project is concerned with the design of adaptive strategies for certain classes of quasilinear problems, in particular p-Poisson equations, their convergence analysis, and the proof of optimality in terms of the number of degrees of freedom and the algebraic complexity, respectively. Our approach is based on an adaptive regularization of so-called Kacanov iterations, whose regularization parameter is tuned according to a posteriori error estimators which have also the function of guiding adaptive discretizations. We shall focus on both, adaptive finite element and wavelet methods.T he motivation is twofold: on the one hand, appropriate reliable error estimators for finite element discretizations have already been defined and studied for the p-Poisson equation, and we expect that we will be able to „port“ this knowledge to wavelet methods for which, in this particular problem, reliable error estimators are not yet available. On the other hand, the strong analytical properties of wavelets can usually be exploited to derive more simply and sometimes more rigorously a convergence and optimality analysis for adaptive wavelet schemes compared to finite element approaches; moreover, the understanding of Besov regularity of solutions of any type of known elliptic equations so far considered has been based on the use of wavelets. Let us stress the fact that Besov regularity of solutions is a fundamental issue when it comes to address the rate of convergence or the complexity of both adaptive finite element and wavelet methods. In addition to the analysis of the adaptive methods for p-Poisson equations, we also plan to perform extensive numerical simulations in order to demonstrate the validity of the theoretical results.
Applicant: Prof. Dr. Stephan Dahlke, Prof. Dr. Lars Diening, Prof. Dr. Massimo Fornasier
Funded by: DFG (Sachbeihilfen)
Funding: from 2012 until 2019Measuring the productivity impact of information technology (IT) using data envelopment analysis (DEA).
The relationship between information technology (IT) and productivity is much discussed, but clear results are rare. Therefore, a specific goal of the research project is to achieve an adequate quantification of the influence of IT, as one of the production factors, by means of Data Envelopment Analysis (DEA). One way to compare the productivity of similar organizational units is to determine the relative efficiency of the units using DEA. As a result, DEA provides both a measure of the relative efficiency of an organizational unit and reference units that decision makers can use to guide performance improvement measures. In order to achieve a further increase in the performance of DEA, various extensions are planned. Great importance is attached to the consideration of temporal aspects for the improved "estimation" of efficiencies and for the analysis of productivity developments, as well as the development of methods for the identification of best practices under inclusion of expert knowledge. The developed methods are tested in empirical studies from the banking sector.
Applicant: Prof. Dr. Paul Alpar
Funded by: DFG (Sachbeihilfen)
Funding: from 1998 until 2002Flexible seamless designs for clinical trials in the development of targeted treatments
Molecular and genetic biomarkers offer the potential to identify highly treatment responsive subsets of patients with diseases which appear phenotypically homogenous. In this project, flexible design methods are developed for the interim selection of sub-populations in randomized clinical trials based on interim results. A typical illustrative application of such designs is a cancer trial in which response to the experimental treatment is expected to depend on molecular markers of the tumour. Initially, patients with all molecular types of the tumour are randomized. After an interim inspection of the data, the researcher may decide to restrict further randomization on selected molecular subtypes for which the experimental treatment appears most promising, according to interim data such as response rates and/or partial survival information. Neither the formal selection rule nor the time point of the interim look has to be pre-specified. Data inspections can be made repeatedly during the course of a trial. We will use a combination of the CRP principle in its recent extensions for survival studies (Irle and Schäfer, JASA 2012) and the closed testing principle to provide full control of the family type I error risk.
Participating: Prof. Dr. Hajo Holzmann
Funded by: DFG (Sachbeihilfen)
Funding: from 2012 until 2014Damping optimization on servo axles using Gröbner bases
The commissioning of automation systems requires the setting and - if possible - optimization of dozens of parameters. Especially for servo axles, there are hardly any efficiently applicable approaches for setting instructions to be found in control theory. The commissioning aids of modern automation components provide almost exclusively empirical and qualitative information or require extensive measurements. Today, due to a lack of commissioning time, systems are often delivered and operated permanently with insufficiently optimized settings - with detrimental effects on productivity and the energy-optimal use of resources. For speed control loops with a dominant structural elasticity, which can be described as a 3rd order system, the applicants have already been able to develop analytical setting rules with the help of Gröbner bases, which are successfully used today. Within the scope of this project, the setting rules are to be extended to 4th and 5th order problems, which will also make distributed drives and modern approaches to state controller augmentation practically adjustable.
Participating: Prof. Dr. Volkmar Welker
Funded by: DFG (Sachbeihilfen)
Funding: from 2010 until 2014Multivariate Algorithmics for Graph and String Problems in Bioinformatics
The current best approach to solving NP-hard problems arising in bioinformatics is the combination of data reduction and formulation as integer linear program (ILP). Parameterized algorithmics has also contributed to the development of efficient algorithms for these problems. The research project MAGZ aims to promote the evolution from parameterized to multivariate algorithmics. This shall result in algorithms that identify and exploit different structural features of biological data. The aim is to establish multivariate algorithmics as an equally powerful alternative to ILPs for solving NP-hard problems in bioinformatics. Eventually, this shall significantly increase the range of solvable instances.
Applicant: Prof. Dr. Christian Komusiewicz
Funded by: DFG (Sachbeihilfen)
Funding: from 2015 until 2022Moduli spaces and classification of algebraic surfaces and nilmanifolds with left invariant complex structure
In the classification of algebraic varieties and compact complex manifolds, the study of moduli spaces is of outstanding importance. The present project aims at contributing to the study of moduli spaces of compact complex surfaces and so-called nilmanifolds. On the one hand, we would like to contribute to the understanding of the moduli space of surfaces of general type, which has been studied for a long time. On the other hand, we would like to extend the question beyond that and consider also the compactification proposed by Kollár and Shepherd-Barron and constructed by Alexeev and others. In doing so, we will both construct new interesting examples and prove general structural statements. Left-invariant complex structures on nilmanifolds are elementarily describable by methods of Lie theory, but may have partly exotic properties, so that many important (counter)examples fall into this class. The goal is to systematically understand and classify such structures.
Applicant: Prof. Dr. Sönke Rollenske
Funded by: DFG (Emmy Noether-Nachwuchsgruppen)
Funding: from 2010 until 2018Adaptive wavelet frame methods for operator equations: Sparse grids, vector-valued spaces and applications to nonlinear inverse parabolic problems
This project is the continuation of the DFG-Rroject 'Adaptive Wavelet Frame Methods for Operator Equations: Sparse Grids, Vector-Valued Spaces and Applications to Nonlinear Inverse Parabolic Problems'. The aim of this project is the development of optimally convergent adaptive wavelet schemes for complex systems. Especially, we are concerned with (nonlinear) elliptic and parabolic operator equations on nontrivial domains as well as with the related inverse parameter identification problems. For the onward problems, we use generalized tensor product approximation techniques that realize dimension independent convergence rates. In the first period of SPP 1324, these tensor wavelet bases have already been provided and associated adaptive wavelet algorithms have been designed, implemented, and tested. The tests performed during the first period Include the numerical solution of a prototypical Inverse parabolic parameter identification problem. In addition, the theoretical prerequisites for applying sparsity constrained Tikhonov regularization to such inverse problems have been proved. These investigations will be systematically continued in the second period. In particular, one central goal will be the generalization of such adaptive wavelet algorithms to nonlinear equations. Furthermore we aim at extending the theoretical investigation of Tikhonov-regularizatlon schemes with sparsity constraints by Incorporating positivity constraints. As a model problem we will study the parameter Identification problem for a parabolic reaction-diffusion system which describes the gene concentrations in embryos at an early state of development (embryogenesis).
Applicant: Prof. Dr. Stephan Dahlke, Prof. Dr. Peter Maaß
Funded by: DFG (Schwerpunktprogramme)
Funding: from 2008 until 2014Adaptive Wavelet Methods for SPDEs
Applicant: Prof. Dr. Stephan Dahlke, Prof. Dr. Klaus Ritter, Prof. Dr. René Leander Schilling
Funded by: DFG (Schwerpunktprogramme)
Funding: from 2008 until 2016Quantum groups and quantum spaces
Applicant: Prof. Dr. István Heckenberger
Funded by: DFG (Heisenberg Fellowships)
Funding: from 2007 until 2011Meta-Modeling and Graph Grammars: Generating Development Environments for Modeling Languages
There is a trend to develop domain-specific modeling languages (DSMLs) with corresponding integrated development environments (IDEs) for model-driven development of software. Such IDEs include but are not limited to model editors as well as interpreters and/or translators of models. Additional tools such as high-level model version management and test support with automatic test case generation and model migrators are of great use. The development of such IDEs, however, is costly and requires tool development experiences. Therefore, meta-tools have been developed which reduce tool development to their domain-specific tasks. But still a lot of manual work and tool-related experiences are needed to use these meta-tools in the right way. The overall aim of this project is to raise the degree of automation w.r.t. tool support for modeling languages, especially DSMLs. Since tool development seems to be the largest obstacle for using modeling languages, we intend to identify core problems and to develop new concepts, methods and meta-tools to make tool development for modeling languages faster and easier. In a certain sense, we consider to lift the specification of domain-specific tool environments to a higher abstraction level, i.e., to make it more model-driven. To reach this aim, inherent problems such as interactively generating and repairing models need to be solved and are best considered on the formal level. We use the theory of graph transformation to systematically tackle them. Solutions found are implemented based on the Eclipse Modeling Project and evaluated at a variety of modeling languages.
Applicants: Prof. Dr. Ernst-Rüdiger Olderog since 4/2020, Prof. Dr. Gabriele Taentzer
Funded by: DFG (Sachbeihilfen)
Funding: from 2012 until 2021Seshadri constants of abelian varieties
Seshadri constants are real numbers which are locally assigned to an algebraic manifold. The interest in Seshadri constants stems on the one hand from the fact that they are of central importance for the local investigation of linear systems. On the other hand, it has become clear in recent years that Seshadri constants in and of themselves are highly interesting invariants whose behavior one would like to understand more precisely.Within the framework of a research grant from the DFG, the applicant, in collaboration with R. Lazarsfeld (Ann Arbor, USA), was able to make substantial progress on the question of bounds for Seshadri constants - in particular for abelian varieties. This work was fundamental for the applicant's habilitation thesis, prepared last year, in which Seshadri constants on surfaces are studied in detail. In particular, explicit and complete results could be obtained for generic ablative surfaces for the first time. The aim of the proposed project is on the one hand to obtain such results for a larger class of surfaces, and on the other hand to find explicit formulas for the important case of higher-dimensional abelian varieties.
Applicant: Prof. Dr. Thomas Bauer
Funded by: DFG (Sachbeihilfen)
Funding: from 1999 until 2000Image and scene research in historical holdings of GDR television in the German Broadcasting Archive using automatic content-based video analysis
The German Broadcasting Archive, located in Babelsberg, is the sole documentation center in Germany dedicated to preserving, cataloging, and providing access to the cultural heritage of radio and television from the former German Democratic Republic (DDR). It serves as the unique resource for scholarly research in this field. The objective of the proposed project is to digitize selected special collections of television content and make the image and scene contents searchable using innovative techniques of content-based image and video analysis. The special collections in question include the DDR television news program "Aktuelle Kamera," television series from the field of public information, and 220 hours of DDR television film archives. By utilizing and advancing automatic methods for the content analysis of videos from the project partner Philipps University of Marburg, the project aims to achieve several outcomes:
- Enable the indexing of image content in the television material at a previously unattainable level of temporal granularity.
- Allow the search of the archive based on image/scene content from individual camera shots.
- Facilitate archive exploration through image-based similarity searches.
- These efforts will provide researchers with entirely new ways to conduct inquiries within this archive. For instance, scholars will be able to search for specific scene motifs and camera shots using textual queries or look for similar motifs using image examples.
Applicant: Prof. Dr.-Ing. Bernd Freisleben, Prof. Dr. Michael Crone
Funded by: DFG (Acquisition and Provision (Scientific Library Services and Information Systems))
Funding: from 2012 until 2016Development of a software system for automatic scene and person indexing in scientific video archives
The German Broadcasting Archive (DRA) is a non-profit foundation under civil law, with offices in Frankfurt am Main and Potsdam-Babelsberg. The collection priorities of the archive at the Frankfurt location are audio recordings of contemporary history and music since the beginning of recording and historical recording media. In 1994, the DRA was extended to include the radio and television broadcasting archives of the former German Democratic Republic (GDR) initially at a location in Berlin, today in Potsdam-Babelsberg. In joint previous work, selected special GDR television broadcasts were digitized, and using innovative methods of content-based image and video analysis, have been made searchable. The material consists of approximately 3,000 hours of video footage, including the newscasts "Aktuelle Kamera", magazine broadcasts and 220 hours of the East German television film tradition. Through the use and development of automated methods for content-based video analysis, scientists have obtained new possibilities to carry out their searches for desired scenes, camera shots and persons, or for similar images. The sustainability of the achieved very good results of scene classification (detection of visual concepts) is intended to be further developed for future use. In the proposed project, a software system usable by archive staff will be developed to enable the DRA and other archives to easily integrate automatic video analysis methods for content-based image search. In this software system, deep learning methods will be employed, thereby making it possible at the same time to improve person and visual concept detection and expand them to other research-intensive parts of the television broadcasts. In particular, the project has the following objectives: 1. development of a sustainable software system for user-friendly expansion of two lexicons (concepts and persons) by archive staff, 2. integration of the software system in the digitalization workflows of the DRA to make automatic video analysis methods applicable to the total stock of television broadcasts in the archive, 3. improvement of the detection rates for concepts and persons by applying deep learning methods, 4. expansion of the visual concept lexicon by about 100 further concepts, 5. expansion of the person lexicon to about 100 persons of the GDR history, 6. improvement of the detection rates for concepts and persons through user feedback and similarity search, 7. development of appropriate visualizations for effective search. In this way, is it not only possible for scientists to carry out search queries on the basis of pre-defined concepts and persons, but they can also easily expand the extensive lexicons for visual concepts and persons for their own research tasks. The developed software tools will be made available to other scientific institutions as open source software.
Applicant: Prof. Dr.-Ing. Bernd Freisleben, Prof. Dr. Ralph Ewerth, Angelika Hörth
Funded by: DFG (Research data and software (Scientific Library Services and Information Systems))
Funding: from 2017 until 2021"New Smoothness Spaces on Domains and Their Discrete Characterization"
Since the discovery of wavelets, the past decades have seen an explosion concerning the design of novel representation systems for functions or distributions. The main intent of that work has been to find representation systems which are optimal for the sparse approximation of various signal classes with the main applications lying in the area of signal processing. As an example we mention the efficient detection of directional information that can be performed by shearlet or curvelet or ridgelet systems which possess vastly superior approximation properties as compared to standard discretization methods such as finite elements or wavelets. Having the various spectacular results concerning the approximation properties of these new representation systems in mind, a natural next step would be to employ them also for the numerical treatment of operator equations. However, the development of numerical methods based on these new representation system is currently facing the bottleneck that to date no useful constructions of these representation systems on bounded domains exist. The aim of this project is to remove this bottleneck by constructing and analyzing new discrete representation systems on finite domains which on the one hand enjoy the same optimal approximation properties as, for example, shearlets while still forming a stable discretization of the energy space for a large class of PDEs (for example Sobolev spaces). Our focus will be on the development of a comprehensive theory for the adaption of function spaces to finite domains. We will be especially interested in the discrete characterization of such spaces, the regularity theory of various PDEs on such spaces and the compressibility properties of Galerkin matrices of various PDEs with respect to these discretizations. These studies are expected to lay the ground work for the subsequent development and implementation of a large class of novel discretization methods for operator equations which outperform current wavelet- or finite-element-based methods for a large class of important problems such as reaction-diffusion equations, linear transport equations or elliptic PDEs with discontinuous diffusion coefficients.
Applicant: Prof. Dr. Stephan Dahlke
Funded by: DFG (Sachbeihilfen)
Funding: from 2017 until 2022Structure, trends and determinants of growth and welfare indices: Cluster analysis of time-dependent and multivariate data
The analysis of monetary and nonmonetary empirical welfare distributions is of central importance both to the theory of welfare as well as to economic growth theory. Basic aspects are the occurrence of subgroups in the welfare distribution, the inter-temporal dynamics as well as the discovery of relevant determinants. To investigate these issues empirically, switching-regime models are basic econometric tools. A major goal of the project Ho 3260/3-1 was to further develop the statistical machinery of regime-switching models which is required for the analysis of welfare distributions. The actual analysis was conducted together with the projects Kl 1260/9-1 and Vo 1592/3-1. A major focus of interdisciplinary applications within the current grant request for extension is on joint modeling and analysis of subgroups within monetary and nonmonetary welfare indices like life expectancy, education or the Human Development Index (HDI). In case of such multivariate data, the form of the mixture component (mainly the multivariate normal distribution) often does not correspond well to the shape of potential clusters which may represent groups in the data. Therefore, the major new methodological goal is to further develop merging methods, i.e. methods which allow to objectively merge components of the mixture or hidden Markov model into joint clusters. A further applied emphasis is on regional convergence, in particular within the context of the eastern expansion of the EU. Here, the time-inhomogeneous hidden Markov models which were developed within the project Ho 3260/3-1 shall be applied. Finally, the developed methodology shall be used for the analysis of the distribution and determinants of growth-rates.
Applicant: Prof. Dr. Hajo Holzmann
Funded by: DFG (Sachbeihilfen)
Funding: from 2009 until 2016Request processing of active data streams
Due to the increasing number of active data sources, such as sensors, large volumes of data are being collected as data streams in various application areas, such as traffic and production monitoring. Processing and analyzing these data streams present an entirely new challenge for query processing. Unlike the classical approach in database systems, these active data streams must be processed instantaneously without any intermediate storage to meet the time requirements of critical applications. This research project addresses the issue of processing active data streams with the goal of handling a dynamic set of queries from different users simultaneously. The following problems are to be solved in this project:
- Development of an algebra of operators for processing active data streams.
- Designing generic algorithms for composite queries on active data streams.
- Creating online methods for calculating inductive statistics with limited size.
These methods will be implemented, documented, tested, and then integrated into the XXL library developed by the research group. They will also be made publicly available. Additionally, query functionality for active data streams will be provided on the internet in the form of graphical and individually expandable components.
Applicant: Prof. Dr. Bernhard Seeger
Funded by: DFG (Sachbeihilfen)
Funding: from 2003 until 2009Distributed model-driven software development
Model-driven development is a promising, increasingly used paradigm in modern software engineering. Modeling of software on a high abstraction level accompanied with largely automatic code generation can speed up software development considerably and can further standardize code. Moreover, the sepration of application-specific and technology-oriented code can succeed in a better way. However, generated software systems are mostly smaller ones, since model-driven development in-the-large has not been supported sufficiently. The aim of this project is a method for distributed model-driven software development. The conceptual and formal base is formed by composite models consisting of model components with explicit import and export interfaces as well as their transformations. The development process is iterative and comprises splitting and merging of models, collaborative model editing, and distributed code generation as core activities. Distributed model-driven development is supported by a tool environment distinguishing clearly the development of domain-specific tools and of applications in a chosen domain. The developed method is evaluated in the domain of data-oriented web applications.
Applicant: Prof. Dr. Gabriele Taentzer
Funded by: DFG (Sachbeihilfen)
Funding: from 2014 until 2020SPP 2037: Scalable Data Management on Future Hardware
Subproject: Energy-Efficient Event Processing on Modern Hardware
During the first phase of the priority programme, we developed a prototypical hybrid event processing and storage system. The system leverages multi-core CPUs and integrated GPUs for low latency processing of continuously arriving event data. Furthermore, we utilized flash-based storage devices to guarantee high ingestion rates needed to store large volume event streams in a specialized database system (ChronicleDB). For the second phase, we intend to continue this line of research while extending our focus towards a more comprehensive architectural approach for event data management on heterogeneous hardware. In particular, this extension aims to address three major aspects: general energy efficiency, energy-efficient GPU-acceleration, and optimizations for spatio-temporal operators. These extensions will result in an overall architecture suitable to handle a wide variety of modern day event applications.
Applicant: Prof. Dr. Bernhard Seeger
Funded by: DFG (Priority Programmes)
Funding: from 2017 until 2021SPP 1324: Mathematical methods for extracting quantifiable information from complex systems
Mathematical models of complex systems form the foundation for further technological developments in science, engineering and computational finance; particularly important but also particularly challenging problems arise in connection with high-dimensional parameter spaces. Motivated by the continuously increasing computer power ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment is facing serious challenges. To overcome these difficulties, a possible approach would be to start with the application at hand and to concentrate on this particular case. However, within this Priority Programme, we propose a different strategy. Recent developments in mathematics suggest that in the long run, much more powerful solution strategies can be derived if the interconnections between the different fields of research are systematically exploited at a conceptual level. In order to do so, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms will be the main goals of this Priority Programme. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics. Since the problem of high-dimensionality appears in many fields of applications, the above mentioned synergy and cross-fertilisation effects are very likely to make a great impact. To be really successful, the following issues have to be kept in mind: theoretical research and practical applications must be developed hand in hand; moreover, it is necessary to combine different fields of mathematics, such as numerical analysis and stochastics. To keep the whole programme sufficiently focussed, we will concentrate on specific, but related fields of applications such as data mining, high-dimensional problems in physics, computational finance and differential equations with random coefficients. All these applications share common characteristics and, therefore, they allow for closely related approaches.
Speaker: Prof. Dr. Stephan Dahlke
Funded by: DFG (Priority Programmes)
Funding: from 2008 until 2015SPP 1094: Global Methods in Complex Geometry
Subproject: Positivity of divisors on algebraic manifolds
A divisor on an algebraic manifold is a subset that can be locally represented as the zero set of a regular function. Positive (or ample) divisors are of fundamental importance in algebraic geometry, such as in the study of projective embeddings. In recent years, there has been a growing interest in a quantitative understanding of positivity. Seshadri constants, real numbers naturally associated with a positive divisor, have proven to be extremely suitable measures of positivity. They often contain subtle information about the divisor and the surrounding manifold in surprising ways.The proposed project focuses on the investigation of the positivity of divisors on surfaces, Jacobians, and Prym varieties. While the applicant has achieved complete results for abelian surfaces, the situation for higher-dimensional varieties is largely unexplored. In particular, no explicit results are known. Therefore, the plan is to study Seshadri constants with two objectives: to provide as explicit numerical results as possible and to gain a deeper geometric understanding of these algebraically defined constants.
Applicant: Prof. Dr. Thomas Bauer
Funded by: DFG (Priority Programmes)
Funding: from 2000 until 2008SPP 1388: Representation Theory
Subproject: Homogeneous Einstein metrics and their geometric properties
The scientific focus of this project is on the relation between geometric structures on homogeneous Riemannian manifolds and special metrics that they may carry, in particular, Einstein metrics. Einstein metrics are vacuum solutions of the Einstein equation of general relativity with a cosmological constant. The geometric structures we have in mind are compact homogeneous manifolds with special holonomy properties (both Riemannian and for more general metric connections with torsion), contact structures, almost Hermitian and paracomplex structures, G2 and hyper-Kähler structures as well as their relatives, a by now well established field of differential geometry with many links to mathematical physics (in particular, superstring theory). These structures occur in a natural way for solutions of spinorial field equations or other, geometrically motivated differential equations. We plan a systematic construction of new homogeneous Einstein metrics and the investigation of their weak holonomy and spinorial properties like eigenvalues of the Dirac operator. Although the scientific setting is of general geometric interest, our methods are deeply rooted in representation theory.
Applicant: Professor Dr. Ilka Agricola
Funded by: DFG (Priority Programmes)
Funding: from 2012 until 2015German Federation for the Curation of Biological Data (GFBio)
The German Federation for Biological Data (GFBio) aims to set up a sustainable, service oriented, national data infrastructure facilitating data sharing and stimulating data intensive science in the fields of biological and environmental research. GFBio follows a holistic approach including technical, organizational, cultural, and policy aspects. The development of the infrastructure is essentially based on the collective experience and expertise of leading researchers from multiple disciplines as well as on a network of complementary and professional data facilities in the biological and environmental sciences communities, including PANGAEA, major German natural history collection data repositories, and selected facilities from the molecular biology research community. GFBio is projected for three phases setting out the way from development to management of services. The current, preparatory phase focusses on conceptualizing and prototyping GFBio components such as the archive backbone and the service platform. Phase II will concentrate on implementation and the last phase on consolidation of the infrastructure.
Applicant: Prof. Dr. Bernhard Seeger
Funded by: DFG (Research data and software (Scientific Library Services and Information Systems))
Funding: from 2013 until 2022SPP 1096: String Theory in the Context of Particle Physics, Quantum Field Theory, Quantum Gravity, Cosmology and Mathematics
Subproject: The holonomy of the B-field in string theory
Non-integrable special Riemannian geometries in low dimensions n<8 were studied in differential geometry in the 1970s by A. Gray et al. and have played a significant role in the study of small eigenvalues of the Dirac operator on a Riemannian manifold since the second half of the 1980s (Friedrich et al.). A renewed interest in non-integrable geometries emerged in recent years due to developments in string theory. Initially, the integrable geometries (Calabi-Yau manifolds, Joyce manifolds, etc.) were solutions to the Strominger equations (1986) of string theory, albeit with a vanishing B-field. By deforming these vacuum solutions and seeking models with non-trivial B-fields, an approach developed by Friedrich/Ivanov (2001-2003) suggests that solutions from special non-integrable geometries can be obtained by uniquely associating them with non-torsion-free connections. In the case of homogeneous models, Agricola uncovered a relationship with Kostant's cubic differential operator and representation theory in 2002. In several works starting in 2003, Agricola/Friedrich began studying the holonomy theory of linear connections with skew-symmetric torsion and their parallel spinors (supersymmetries). The goal of the project is to further develop this program, particularly through intensive collaboration with colleagues in theoretical physics represented in the focus area, to contribute modern differential geometry to current developments in string theory.
Applicant: Professor Dr. Ilka Agricola
Funded by: DFG (Priority Programmes)
Funding: from 2004 until 2007SPP 1388: Representation Theory
Subproject: Spherical subalgebras of quantized enveloping algebras - structure theory and classification problems
Spherical subgroups of Lie or algebraic groups have been investigated since the 1970ies because of their interesting geometric, algebraic, combinatorial and representation theoretical properties. Nowadays generalizations like spherical varieties are in the focus of interest. For another generalization towards quantum groups one first has to find the proper setting: an obvious description via Hopf subalgebras of Hopf algebras fails due to the lack of sufficiently many Hopf subalgebras. Based on the case-by-case construction of quantum symmetric spaces in the 1990ies and on recent developments on right coideal subalgebras of quantized enveloping algebras, now we are in the position to develop a substantial structure theory of spherical subalgebras of quantized enveloping algebras using right coideal subalgebras and to initiate classification projects. (In the classical, cocommutative setting right coideal subalgebras are automatically Hopf subalgebras.) It is a very interesting question, to which extent the classical and the quantum theories and examples are analogous and whether one can observe significant new aspects.
Applicant: Prof. Dr. István Heckenberger
Funded by: DFG (Priority Programmes)
Funding: from 2012 until 2015SPP 1962: Non-smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization
Subproject: Generalized Nash Equilibrium Problems with Partial Differential Operators: Theory, Algorithms, and Risk Aversion
The subject of this proposal is generalized Nash equilibrium problems (GNEPs) with partial differential equation (PDE) constraints under uncertainty and their extension to new classes of equilibrium problems in function space. The latter includes so-called equilibrium problems with equilibrium constraints (EPECs) and multiple optimization problems with equilibrium constraints (MOPECs) in infinite dimensions. The new classes of PDE-constrained problems under consideration offer a wide range of mathematical novelty. From a theoretical perspective, the derivation of existence and stationarity results requires techniques from non-smooth optimization and set-valued analysis, which includes fixed point theorems and generalized differentiation for set-valued mappings. On the other hand, the variational form of these problems typically lack the necessary monotonicity properties that would allow the direct application of known function-space based numerical methods from the study of non-smooth variational problems and standard PDE-constrained optimization. The proposed framework extends the classical mathematical programming paradigm beyond a single-objective optimization problem and thus, allows one to consider a broader array of equilibrium problems in the sciences and economics. In particular, problems with hierarchical solution concepts such as Nash equilibria or Nash-Stackelberg equilibria (multi-leader-follower equilibria) can be considered. The existence proofs and derivation of stationarity conditions are to be carried out in conjunction with the derivation of fast numerical algorithms, which take into account the subtleties of partial differential operators and the distributed parameter setting. In order to model risk-aversion in a competitive setting with a complex system subject to uncertainties, coherent risk measures are employed. A four part research program is proposed for the rigorous development of an existence and stationarity theory, algorithms and numerical analysis, and handling uncertainties via risk measures.
Applicant: Prof. Dr. Michael Hintermüller, Prof. Dr. Thomas Surowiec
Funded by: DFG (Priority Programmes)
Funding: from 2016 until 2021SPP 1593: Design for Future - Managed Software Evolution
Subproject: Specifying and Recognizing Model Changes in Networks of Models
Model-based software development (MBSD) has become a widespread paradigm for developing software in various application domains. Models are a good means to abstract from details, hence they have the potential to carry important knowledge about different aspects of software systems. Hence, models are subject to version management, notably comparison, patching and updating of models.The first funding phase of this project has been dedicated to the lifting of version management services to a higher level of abstraction. Instead of reporting model changes elementwise and in their internal representations, they are reported on the basis of domain-specific edit operations as known from domain-specific model editors. They cluster atomic changes in a meaningful way and abstract from internal representations.A system under development is often modeled by several related models, i.e., a network of models, which represents different parts or perspectives of the system representing viewpoints of different stakeholders. Although developers often require to revise single models of such a network independently, this requirement is not met by current approaches to model versioning. The whole network of models is considered as one monolithic unit of versioning.The main goal of the second funding phase of the project is to remove this limitation, i.e., to allow single models and moreover, any subset of models, being independent units of versioning. This is a challenge if model relations are implemented by additional correspondence (or trace) structures which have to be subject of versioning as well. Our solution shall lead to an effective version management system for co-evolving models being implemented on top of the Eclipse Model Project. To lift version management for co-evolving models to domain-specific edit operations as well, solutions of the first funding phase are extended to co-evolving models. To increase the usability of our tool support, it is further enriched yielding a comprehensive configuration support for domain experts. The implemented tool environment will be evaluated in a variety of case studies considering long-living systems in the fields of automation engineering and information systems.
Applicant: Prof. Dr. Udo Kelter, Prof. Dr. Gabriele Taentzer
Funded by: DFG (Priority Programmes)
Funding: from 2012 until 2021SPP 1140: Middleware for Self-organizing Infrastructures in Networked Mobile Systems
Subproject: Scalable context-dependent routing algorithms for self-organizing cellular networks
Routing methods are essential for establishing connections between communication partners within a computer network and are therefore of significant importance for its functionality. In self-organizing mobile networks, the development of effective routing algorithms is challenging because there is no fixed infrastructure of base stations to rely on, individual devices can move extensively, and communication reliability is significantly lower than in fixed networks. The proposed project aims to design, implement, simulate, and test new efficient routing algorithms for self-organizing mobile networks. Building on experiences from alternative approaches and extensive prior work, the project will develop methods that (a) adapt flexibly to changing communication scenarios ("context-dependent adaptation"), (b) tolerate potentially large increases in the number of mobile devices ("scalability"), and (c) can be integrated into existing fixed networks, especially the Internet ("Internet operability").
Applicant: Prof. Dr.-Ing. Bernd Freisleben
Funded by: DFG (Priority Programmes)
Funding: from 2002 until 2008SPP 1063: Informatics methods for analysing and interpreting large amounts of genomic data
Subproject: Modeling of metabolic networks based on in vivo, in vitro and in silico data
Applicant: Prof. Dr.-Ing. Bernd Freisleben
Funded by: DFG (Priority Programmes)
Funding: from 2003 until 2006FKO 615: Media Upheavals. Media Cultures and Media Aesthetics at the Beginning of the 20th century and in the crossover to the 21st century
Subproject: Methods and Tools for Computer-Based Media Analysis (MT)
The subproject "MT" addresses the following tasks: Firstly, the existing grid infrastructure is expanded into an e-Service Media Grid to make the developed analysis algorithms, data sets, and results of the SFB/FK 615 available beyond its boundaries. Secondly, a new analysis tool for multimedia social web content to support media and social science research activities is implemented; new methods for the semantic analysis of videos are developed. Thirdly, a software solution for archiving the data sets of the research center is designed in cooperation with the University Library, the Center for Information and Media Technology, and the Institute for Media Research at the University of Siegen.
Subproject Manager: Prof. Dr.-Ing. Bernd Freisleben, Prof. Dr. Manfred Grauer
Funded by: DFG (CRC/Cultural Studies Research Centres)
Funding: from 2002 until 2010SPP 1962: Non-smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization
Subproject: Constrained Mean Field Games: Analysis and Algorithms
The purpose of this proposal is to develop new analytical approaches and solution algorithms for mean-field games arising from differential Nash equilibrium problems with control and state constraints. The incorporation of control and state constraints into mean field games leads to new classes of dynamic infinite-dimensional mixed complementarity problems with nonsmooth operators and nonlinear couplings. Due to the inclusion of control and state constraints, novel analytical and numerical solution paradigms will be developed for this rapidly growing area of applied mathematics. Mean field games arise in a natural way by letting the number of agents grow to infinity in N-player non-cooperative differential Nash equilibrium problems. After deriving appropriate first-order optimality conditions for the non-cooperative game, the effective equations appearing in the limit constitute a mean field game. One important aspect is the assumption that the N strategic agents are statistically homogeneous in their objectives, constraints, and dynamics. This makes mean field games ideal for investigating complex dynamical systems of competing entities, who appear more or less homogeneous as the size of the population grows, e.g. in macroeconomics, biology, and large networks. From a mathematical perspective, mean field games can be viewed as a fixed point iteration on a space of flows of probability measures that represent the evolution of the density of the states in time. Starting from an initial population distribution, this flow is determined by the solution of a continuity equation, whose driving field is linked to a family of optimal control problems of a representative agent, who in turn is reacting to this flow of measures. In a broader sense, there are four main issues to be addressed for any given mean field game (MFG). Approximate Equilibria: Does the solution of the MFG relate to the original problem? Existence, Uniqueness: Does the MFG possess a (unique) solution? Convergence Problem: Does the Nash game actually converge to the MFG? Computation: Can we solve constrained MFGs for practical applications? Within the context of these categories, we will consider several general classes of constrained MFGs with general quadratic objective functionals important for many applications, functionals with robust misfit terms to represent the agents' sensitivity to outliers to the mean field interaction, and sparse control actions. We allow several categories of both control and state constraints in the form of conic, time-dependent bilateral constraints, and general polyhedral constraints. For the individual dynamics, we will consider both deterministic and stochastic linear dynamics and deterministic nonlinear dynamics arising in applications.
Ehemaliger: Prof. Dr. Thomas Michael Surowiec, until 9/2022
Funded by: DFG (Priority Programmes)
Funding since: 2019KONDA - Continuous quality management of dynamic research dataresearch data on objects of material culture using the LIDO standard
The aim of the project is to develop a systematic quality assurance of structured research data on objects of material culture, a desideratum for research in the humanities and cultural sciences.
Project homepage SUB Göttingen
Participating: Prof. Dr. Gabriele Taentzer