Schriftzug: Fachbereich Mathematik 
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Angenommene Minisymposien / Accepted Minisymposia

  1. Abiturstandards — Möglichkeiten, Chancen und Grenzen ihrer Umsetzung (Three hours; organizer: Gabriele Kaiser, Hamburg)

    In dem Minisymposium sollen die 2012 von der Kultusministerkonferenz erlassenen Bildungsstandards im Fach Mathematik für die Allgemeine Hochschulreife (sogenannte Abiturstandards) aus verschiedenen Perspektiven beleuchtet werden. So sollen die Abiturstandards diskutiert werden unter der Frage, welche Möglichkeiten zur Veränderung des herkömmlichen Mathematikunterrichts diese Standards bieten, wie sich Mathematikunterricht durch diese neuen Bildungsstandards innovativ weiterentwickeln kann, z.B. durch eine Verbesserung des begrifflichen Verständnisses zentraler Konzepte und Stärkung von Grundvorstellungen, der Stärkung des Rechnereinsatzes, der Erhöhung der Bedeutung von Modellierung und Anwendung. Es soll aber auch intensiv reflektiert werden, welche Gefahren diese neuen Standards beinhalten bzgl. eines möglichen Verlusts der Bedeutung innermathematischer Fragestellungen oder allgemeiner Aspekte wie Beweisen. Die Beteiligten an dem Mini-Symposium waren bzw. sind an zentraler Stelle mit der Entwicklung der Abiturstandards beteiligt bzw. an ihrer Realisierung in Hamburg.

  2. Algebraic Aspects of Cryptology (Six hours; organizers: Benjamin Fine, Fairfield CT; Anja Moldenhauer, Hamburg; Gerhard Rosenberger, Hamburg)

    In the minisymposium Algebraic Aspects of Cryptology we aim to discuss various aspects, methods and theories of mathematical cryptology. In addition to number-theoretic cryptosystems and protocols, we plan to focus on algebraic cryptology using methods of group theory and noncommutative Gröbner bases as well as cryptanalysis.

  3. Algebraic Quantum Field Theory on Lorentzian Manifolds (Six hours; organizers: Christian Bär, Potsdam; Klaus Fredenhagen, Hamburg; Rainer Verch, Leipzig)

    After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. This approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes.

    Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and hyperbolic partial differential equations, as well as more recently the insights from suitable concepts such as microlocal analysis.

  4. Applied and Computational Harmonic Analysis (Six hours; organizers: Gitta Kutyniok, Berlin; Jakob Lemvig, Kungens Lyngby)

    Recent advances in modern technology have created a new world of enormous, multivariate data structures. In biomedical imaging, seismic imaging, astronomical imaging, computer vision, and video processing, the capabilities of modern computers and highprecision measuring devices have generated 2D, 3D, and even higher dimensional data sets of sizes that were infeasible just a few years ago. We need to efficiently handle such data has initiated an intense study in developing efficient multivariate (directional) representation systems in the applied harmonic analysis research community.

    From a computational point of view one searches for transforms which, in particular, provide compressible approximations, resolve wavefront sets, possess fast decomposition algorithms, and allow for a unified treatment of continuum and discrete data. From an abstract point of view one seeks to understand the underlining principles of such "successful" transforms; where "successful" is measured in terms of the above listed desirable properties. Which classes of transforms will have the desirable properties? From a representation-theoretic viewpoint one can ask for a characterization of groups which through their associated transforms lead to desirable properties.

    This workshop will explore diverse topics within this area with presentations from both Danish and German researchers.

  5. Computer Algebra and Applications (Six hours; organizers: Mohamed Barakat, Kaiserslautern; Janko Böhm, Kaiserslautern; Claus Fieker, Kaiserslautern)

    Increasingly complex structures arise in various areas of pure mathematics. Exploring and understanding such structures is often indispensable for theoretical progress. This elevates the interest in constructive aspects and their algorithmic treatment. Computer algebra provides a framework for such algorithmic explorations. It profits from the rapid development of hard and software technology. This mini-symposium will highlight recent achievements in and supported by computer algebra.

  6. DGVFM-Minisymposium in Financial and Insurance Mathematics (4 hours; organizer: Alexander Szimayer, Hamburg; Christian Hilpert, Hamburg)

    The DGVFM-Minisymposium will bring together leading researchers in the field of financial and insurance mathematics and will be organized in corporation with the Deutsche Gesellschaft für Versicherungs- und Finanzmathematik (DGVFM, German Association for Financial and Insurance Mathematics). Topics include derivative pricing, quantitative risk management, risk measures and issues related to regulation of the financial sector (Basel III and Solvency II).

  7. Didactical aspects and functions of graphical representations (Three hours; organizer: Eva Müller-Hill, Köln)

    The symposium focuses on aspects and functions of graphical representations relevant to mathematics education. It combines different perspectives on the issue of graphical representations in teaching and learning of mathematics that are developed and discussed rather separately in existing literature.

    Well-investigated and already quite strongly related core areas regarding the didactics of graphical representations are "ideas, Grundvorstellungen, cognition", "concept formation", "problem solving" and "dynamical representations (CAS, DGS)". In addition, there are research perspectives in mathematics education focussing more specifically on one of the following issues:

    1. the role of graphical representations for mathematical proof and explanation in classroom;
    2. the special importance of graphical, esp. geometrical, interpretations for the teaching and learning of algebra;
    3. semiotic and discursive aspects of graphical representations in mathematics classroom;
    4. the historical development of the role of graphical representations and its relevance for mathematics education;
    5. the relation between usage of graphical representations in classroom, teachers (esp. epistemological) beliefs and overarching conceptions of mathematics, and the development of learners' mathematical beliefs and conceptions of mathematics.

    Questions regarding the conditions and potential of multi-perspective considerations will connect individual contributions from these different perspectives.

  8. Discontinuous Galerkin methods for the unsteady compressible Navier-Stokes equations (Three hours; organizers: Jochen Schütz, Aachen; Andrea Beck, Stuttgart)

    The fundamental physical behavior of compressible fluid flows can be described by what are called the "compressible" Navier-Stokes equations. Due to their importance in, e.g., engineering applications, but also due to their complicated, yet fascinating mathematical structure, these equations have attracted much research in the past centuries.

    The minisymposium will deal with the approximation of solutions to the time-dependent compressible Navier-Stokes equations using (variants of) the discontinuous Galerkin (DG) method. This method has been developed independently for elliptic and hyperbolic equations in the 70s, and has since received lots of attention in both mathematical and engineering communities. At the root of the method lies the approximation of unknown quantities (e.g., density, momentum...) using cell-wise polynomial approximations. Evolving methods differ, for example, in the choice of supported element types, basis and flux functions and temporal integration. All ingredients have been recognized to be extremely sensitive to the quality of an approximate solution and the stability and efficiency of an algorithm.

    Using the DG method for solutions to the Navier-Stokes equations is a highly active field of research. Therefore, in the minisymposium, we aim at bringing together researchers from both mathematics and engineering to discuss new concepts, such as hybrid DG, nodal DG, non-standard temporal integrators, efficient implementation, e.g., with respect to parallelization and many more.

  9. Dynamics of Patterns (Four hours; organizers: Christian Kuehn, Vienna; Jens Rademacher, Bremen).

    The analysis of patterns as emergent phenomena in evolutionary equations is a topic undergoing rapid development. This minisymposium aims to capture recent trends in the analytical and numerical study of nonlinear waves and other coherent structures. Key themes are existence, stability, dynamics and numerical computation: Does a wave exist? If so, is it stable? How does it interact with other patterns? Can we efficiently compute it and/or its properties? These questions apply to any other form of pattern and it is the aim of this minisymposium to communicate current challenges in the broad area of pattern formation.

  10. Experimental mathematics (Four hours; organizers: Søren Eilers, Copenhagen; Frank Lutz, Berlin)

    The modus operandi of using computer experiments to generate conjectures or even (hints for) proofs in pure mathematics is rapidly gaining ground these years, and German and Danish experimental mathematics has intersected nontrivially over the last years due in part to targeted funding at Copenhagen and Odense. The strong German presence at the recent conference "Discrete, Computational and Algebraic Topology" in Copenhagen bears witness to this.

    Our aim is to further the interaction between mathematicians working systematically with experimentation in the two countries, and to offer inspiration to all mathematicians interested in expanding their experimental repertoire. We intend to focus on topics arising in operator algebras, number theory, and topology, and combinatorial methods are ubiquitous in the area.

  11. Geometric Variational Problems (Three hours; organizers: Bernd Kawohl, Köln; Carlo Nitsch, Naples).

    This minisymposium will deal with quantitative forms of isoperimetric inequalities and best constants in various geometric estimates. In recent years there has been a surge of investigations surrounding isoperimetric conjectures. To give examples, [1] answered a long standing conjecture of Polya and [2] deals with Faber-Krahn-type inequalities for nonlinear eigenvalue problems under Neumann boundary conditions. Entire conferences in Oberwolfach, Banff and Luminy have been dedicated to such subjects.

    1. L. Esposito, V. Ferone, B. Kawohl, C. Nitsch and C. Trombetti: The longest shortest fence and sharp Poincaré Sobolev inequalities, Arch. Ration. Mech. Anal. 206 (2012), p. 821-851.
    2. L. Esposito, C. Nitsch, B. Kawohl and C. Trombetti: The Neumann eigenvalue problem for the ∞-Laplacian, arXiv: 1405.3535

  12. Heteroclinic Dynamics: Theory and Applications (Four hours; organizers: Alexander Lohse, Hamburg, Porto; Sofia Castro, Porto)

    Heteroclinic cycles and networks are a useful tool for modelling stop-and-go dynamics in various applications, ranging from geophysics to neuroscience. They display complex forms of non-asymptotic stability, possibly attracting and repelling sets of positive measure at the same time. Recently, different approaches have been taken to improve our understanding of heteroclinic dynamics and stability of networks and of cycles in networks. In this minisymposium we aim to discuss current ideas and developments on aspects of both purely theoretical and more application-oriented nature.

  13. History of Stochastics (Three hours; Wolfgang K. Härdle, Berlin; Annette Vogt, Berlin)

    Recent developments in modern science and technology have created an enormous set of data and data structures (big data as a synonym for this advancement). Looking back to history some problems and issues could be described as an evolution of certain methods and theories which were developed already in the 19th and 20th centuries. In the history the development of computer technology and of programming languages played an important role. In the minisymposium we will discuss some theories, methods and aspects of the history of stochastics and history of statistics from this perspective with the aim of understanding modern developments and their problems deeper and better. We will focus on the history of various stochastic theories, the introduction of certain statistical methods and their effects, the specific role computer technology and programming languages have played, the didactic uses of a bio-bibliographical database on leading mathematicians, statisticians and scholars in social sciences like economy or insurance science.

  14. Homotopy Type Theory and Univalent Foundations (Six hours; organizers: Benedikt Ahrens, Toulouse; Bas Spitters, Aarhus; Thomas Streicher, Darmstadt).

    Homotopy Type Theory refers to a new interpretation of Martin-Löf's system of intensional, constructive type theory into abstract homotopy theory. Propositional equality is interpreted as homotopy and type isomorphism as homotopy equivalence. Logical constructions in type theory then correspond to homotopy-invariant constructions on spaces, while theorems and even proofs in the logical system inherit a homotopical meaning. As the natural logic of homotopy, constructive type theory is also related to higher category theory as it is used e.g. in the notion of a higher topos. Voevodsky's Univalent Foundations program aims to provide a comprehensive, computational foundation for mathematics based on the homotopical interpretation of type theory. The subtle Univalence Axiom, introduced by Voevodsky, relates propositional equality on the universe with homotopy equivalence of small types. The program is currently being implemented with the help of the interactive proof assistant Coq. The Univalent Foundations program is closely tied to homotopy type theory and is being pursued in parallel by many of the same researchers.

    Research on Homotopy Type Theory (HoTT) takes place at the intersection of three domains: type theory and proof assistants, category theory and homotopy theory. Indeed, in the course of the development of HoTT, exciting connections have been discovered between these fields of research. Through these connections, the ideas, languages and methods of either of those fields are available for understanding HoTT. The goal of the mini-symposium is to present the underlying ideas of HoTT to researchers in these fields from the perspectives of logic, category theory and homotopy theory, thus enabling mathematicians from a wide variety of research areas to understand the problems HoTT tries to solve and the difficulties that need to be overcome in this undertaking.

    For more information see: Mini-Symposium Webpage:

  15. Jump processes and related topics (Six hours; organizers: Alexander Lindner, Ulm; Steen Thorbjørnsen, Aarhus)

    Lévy processes and more generally jump processes have constituted an active field of research during the last years. They have various applications in finance, insurance mathematics, engineering or physics, and are also interesting from a purely mathematical point of view. They have various connections to other disciplines such as Partial Differential Equations or Stochastic Analysis.

    The aim of this minisymposium is to bring together various people working in this area, with an emphasis on young researchers. Topics of the minisymposium include distributional properties of processes derived from Lévy processes, fluctuation theory of jump processes, connections with analysis, and applications of Lévy processes.

  16. Mathematical and Computational methods for Earth System Sciences (Six hours; organizers: Jörn Behrens, Hamburg; Thomas Slawig, Kiel)

    Complex multi-scale phenomena on earth and the more and more demanding societal pressure on resources and security call for simulation-based mathematical descriptions of natural systems. This is particularly visible in the earth system sciences, which have a great impact on societal decision making. Mathematical models play an important role in knowledge gaining in earth system sciences. However, transferring the insights in mathematical developments to complex real-life settings is often a hard task. The opposite transfer of problems in applied sciences like the geosciences into challenging mathematical research questions has traditionally generated fruitful developments in applied mathematics.

    This minisymposium aims at presenting current work and achievements in this field by demonstrating interesting problem settings in earth system sciences and their mathematical and computational solution in an interdisciplinary work environment.

  17. Mathematical General Relativity (Six hours; organizers: Oliver Rinne, Potsdam; Lars Andersson, Potsdam)

    Mathematical general relativity is a broad research field spanning differential geometry, partial differential equations, dynamical systems and scientific computing, among others. Much progress has been made in recent years. The problems of black hole stability and cosmic censorship have led to important advances in nonlinear hyperbolic PDEs. The study of initial data for the Einstein equations has motivated important problems in Riemannian geometry such as the Penrose inequality. Cosmological models provide rich dynamical systems and have led to insights into the structure of singularities. Numerical simulations have become a reliable tool both to model astrophysical processes and to investigate more fundamental aspects of the theory.

    The mini-symposium is intended to present a broad overview of current research directions and to attract a general mathematical audience to this fascinating subject. With the 100th anniversary of the genesis of general relativity, 2015 is a fitting time for such a mini-symposium.

  18. Mathematical Methods for Magnetic Particle Imaging (Four hours; organizers: Wolfgang Erb, Lübeck; Andreas Weinmann, München)

    Magnetic particle imaging (MPI) is a novel imaging modality that determines the spatial distribution of magnetic nanoparticles by measuring the non-linear magnetization response of the particles to an applied magnetic field. Due to its high spatial and temporal resolution as well as the fact that, in contrast to other tomographic methods such as PET or SPECT, no radioactive substances are needed, MPI is a very promising imaging modality for biomedical diagnostics such as blood flow imaging and cancer detection.

    The mathematical problem of MPI is to reconstruct the particle density function from the measured voltage signal induced in the receive coils. The intrinsic relation between particle distribution and measured signal is described by the so-called system function. The mathematical modelling and analysis of the system function is one of the major challenges in MPI. Since the reconstruction is ill-posed, appropriate regularization techniques which are also suitable for clinical purposes have to be included. Further, to improve the reconstruction quality, stable and efficient numerical algorithms have to be developed.

    In this Minisymposium, we bring together researchers working in MPI shedding light on both theoretic and practical aspects. There will be talks that give introductions as well as talks focusing on different mathematical aspects of MPI. Further, we want to address open problems and challenges related to this novel imaging modality.

  19. Mathematical Methods in Image and Signal Processing (Five hours; organizers: Ole Christensen, Kungens Lyngby; Armin Iske, Hamburg)

    This minisymposium brings together experts within mathematical methods in image and signal processing. The aim is to exchange recent advances in sampling theory, computational harmonic analysis and their relevant applications. Topics include wavelets and frames, compressed sensing, sparse representations and coding, dimensionality reduction, kernel-based approximation, medical image reconstruction, and other related topics.

  20. Mathematics of Fluid Interfaces (Six hours; organizers: Helmut Abels, Regensburg; Harald Garcke, Regensburg)

    In many fluid dynamic problems either free surfaces or interfaces between different fluids or phases occur. Hence, the governing equations of fluid dynamics (e.g., the Navier-Stokes equations or the Euler equations) have to be solved on a domain which has to be determined as part of the problem. The arising mathematical equations are highly nonlinear and notoriously difficult to solve.

    Recently several new ideas with respect to modelling and analysis of these phenomena were developed and need to be explored further. The aim of the mini-symposium is to present the state of the art of the field and focus on recent new developments. These include stability of fluid interfaces, diffuse interface models and their sharp interface limits, singularities for water waves, well-posedness results based on maximal regularity or new weak formulations, new models for complex phenomena at fluid interfaces (examples are transport phenomena and fluid-membrane interactions).

  21. Mathematics of Geophysical Flows (Four hours; organizers: Valerio Lucarini, Hamburg; Tobias Kuna, Reading)

    The fluid Earth is an excellent example of a forced, dissipative non-equilibrium system dominated by nonlinear processes and featuring multi-scale interactions, so that its understanding can be approached using the tools of dynamical systems theory, stochastic processes, and non-equilibrium statistical mechanics. The understanding of the statistical properties of a system under consideration is crucial per se and in a variety of applications, especially when considering large fluctuations, which may result into extreme events of relevant impact.

    There is a close connection between core questions and problems of pure and applied mathematics and core questions of geophysical fluid dynamics relevant for the investigation of the climate system and of its component. These are closely linked to defining rigorously what is a good model for such a complex system like the Navier-Stokes equations and their many variants and reductions, multi-scale properties and the selection of appropriate random terms. The response to external forcing and the characterization of large deviations and extreme events are essential challenges. The differential equations that describe mathematically the fluid components, in particular the Navier-Stokes equations and their many variants and reductions, are at the core of the work of any analyst working in nonlinear PDEs. Many of the still open fundamental questions are at the heart of the link between analysts and geophysicists.

    This minisymposium stems from the stimulation of the very successful international initiative Mathematics for Planet Earth 2013 supported by mathematical societies and institutes around the world. The minisymposium gives an overview of four macro-themes of interest where the progress has been impressive on the mathematical side and its impact in terms of theoretical, model-assisted, and observational investigations of the planet Earth: a) Dynamical Systems and Statistical Mechanics; b) Extreme Events; c) Partial Differential Equations d) Stochastic Processes.

  22. Mathematics on the Web and Mathematical Knowledge Management (Six hours; organizers: Wolfram Sperber, Karlsruhe; Michael Kohlhase, Bremen)

    The subject is the presentation and processing of mathematical knowledge on the Web. New approaches and methods allow not only an adequate presentation but also automatic processing of mathematical knowledge. There are a lot of projects and developments regarding different aspects of mathematical information and communication:

    • presentation of mathematical knowledge, e.g., TeX, MathML, OpenMATH, and OMDOC;
    • creation and further development of information services, e.g., digital mathematics libraries, information services as the bibliographic database zbMATH and the software database swMATH, or of mathematical glossaries;
    • application of mathematics in industry and services.

    Moreover, the communication and workaday life is under permanent transformation by the digitization and the emergence of the Web.

    Some recent trends and initiatives where German institutions are involved will be presented at the minisymposium.

  23. Moment Problems and Applications in Memoriam Murray Angus Marshall 24.3.1940 - 1.5.2015 (Six hours; organizers: Maria Infusino, Konstanz; Salma Kuhlmann, Konstanz; Tobias Kuna, Reading)

    The moment problem is a multi-facet theory with connections not only to several branches of mathematics but also to numerous applied fields. Despite of the huge literature about the moment problem and its applications, this is far to be a static theory. Indeed, there are many unknown aspects of the problem and also many related questions arising from applied fields. These are interesting to be explored both for their contribution to the moment problem and for their impact on other kind of problems. The aim of this minisymposium is to present this two-way interaction existing between the moment problem and other areas such as probability theory, operator theory, statistical mechanics and polynomial optimization. Specifically the intention is to highlight some questions arising in applications which are naturally connected to the moment problem, to present how these questions can shed some light on the unsolved points in moment theory and, at the same time, to explain how the moment problem can serve the progress in such areas. In particular, many instances of the moment problem appearing in applications are posed in an infinite dimensional setting. Therefore, this minisymposium would represent also a first encounter between the scientific community working on moment problems in finite dimensions and the one working in the infinite dimensional case. A deep interest for the interaction between the two communities has already been shown during the Oberwolfach workshop in April 2014 (ID 1415). This minisymposium could be a kickoff meeting in preparation for the next Oberwolfach workshop about this topic.

    For more information see the minisymposium webpage:

  24. Motivic Homotopy Theory and its application to problems in Algebra and Algebraic Geometry (Five hours; Marc Levine, Essen; Philip Herrmann, Hamburg)

    The initial breakthrough leading to the creation of the subject of motivic homotopy theory was the construction by Morel-Voevodsky of new versions of a stable homotopy category, which brought the "classical" versions from homotopy theory together with inputs from algebraic geometry and enabled one for the first time to work with the basic material of algebraic geometry, solutions of polynomial equations, with the flexibility and power previously only available in homotopy theory.

    Voevodsky used these homotopical methods in his proof of the celebrated Milnor conjecture, and motivic homotopy theory played an even more central role in his contribution to the proof of the Bloch-Kato conjecture, the successful culmination of thirty years of intensive research.

    Besides these quite spectacular applications, the fact that one could now use the ideas and methods of homotopy theory to solve problems in algebraic geometry has drawn in mathematicians from both fields and has led to a wealth of new constructions and applications. This mini-symposium intends to bring together experts working in current problems in motivic homotopy theory and its application to problems in algebra and algebraic geometry to promote the interaction and exchange of expertise between the different research directions and to profit from and contribute to these interactions.

  25. Numerical Methods in Dynamical Systems (Six hours; organizers: Peter Giesl, Brighton; Sigurdur Hafstein, Reykjavik)

    Dynamical systems, given by differential equations or iteration of maps, are a central modeling tool in physics, biology, chemistry, economics, weather forecast, cancer research and many more. Dynamical systems are interested in qualitative statements about solutions. In particular, the long-time behavior of solutions with different initial values is of fundamental importance. They can be characterized by the stability of invariant sets, the basin of attraction of (local) attractors or chaos. Depending on parameters, fundamental changes in their behavior can be studied by bifurcation. A further area of interest is non-autonomous systems, which can exhibit even more complicated dynamics and require new definitions and methods for their analysis.

    Many analytical tools have been developed for the study and analysis of dynamical systems. However, since the first studies of chaos by Lorenz, numerical methods have played a prominent role within Dynamical Systems. They have been used to study and describe dynamical systems and their use ranges from simulations of specific systems to their rigorous analysis. For example, the construction of Lyapunov functions to study basins of attraction has been an active area of research over the last decades [2]. Set-valued methods have been used to study invariant sets and dynamics [1] and have been incorporated into the computer package GAIO.

    The type of numerical methods employed includes as different methods as collocation to solve linear PDEs, approximation of functions in Reproducing Kernel Hilbert Spaces, set-valued methods, graph theoretical methods, and methods that use linear programs, linear matrix inequalities and convex optimization techniques. The minisymposium will present a range of these numerical methods and will facilitate the exchange between the different methods. This will lead to fruitful collaborations to combine various methods, or to generalize existing methods to new problems in dynamical systems.

    1. M. Dellnitz and O. Junge. Set oriented numerical methods for dynamical systems. In: Handbook of dynamical systems, Vol. 2, North-Holland, Amsterdam, 221-264, 2002.
    2. P. Giesl and S. Hafstein. Review on Computational methods for Lyapunov functions. submitted to Discrete Contin. Dyn. Syst. Ser. B.

  26. Octonion algebras, their norms and subspaces (Six hours; organizers: Markus Stroppel, Stuttgart; Norbert Knarr, Stuttgart)

    Isometry types of subspaces in octonion algebras play their role in areas such as

    • classical groups generated by suitable sets of multiplications by octonions,
    • homomorphisms between such classical groups (which may belong to different series of algebraic groups),
    • anisotropic forms of algebraic groups,
    • related Tits buildings,
    • subalgebras and related geometries (e.g. Clifford parallelisms),
    • isomorphisms and automorphisms of octonion algebras.

  27. Optimal Control of Nonlinear PDEs (Six hours; organizers: Eduardo Casas, Santander; Fredi Tröltzsch, Berlin)

    The focus of this minisymposium is analysis and numerics of optimal control problems with partial differential equations as state equation. Special emphasis will be laid on nonlinear equations, but also new results on problems with linear equations are welcome. Contributions are expected that extend the theory in the following directions: Error analysis for numerical approximations of optimal control problems, convergence of numerical optimization methods for solving PDE constrained control problems, numerical analysis for new applications in this field, extensions of the theory of necessary and sufficient optimality conditions, sparse optimal control and measure control.

  28. Polytopes, Algebra & Statistics (Three hours; organizers: Christian Haase, Berlin; Thomas Kahle, Magdeburg).

    This minisymposium is concerned with applications of polyhedral geometry and (commutative) algebra to statistics. The connection between these fields builds on foundational work of Diaconis and Sturmfels as well as Pistone, Riccomagno, and Wynn. In the last 15 years related work has been gathered under the name "algebraic statistics". The minisymposium will be a forum to connect researchers working in algebraic statistics and also allow interested mathematicians to get involved.

  29. Qualitative Aspects of Nonlinear Partial Differential Equations (Four hours; organizers: Christoph Walker, Hannover; Joachim Escher, Hannover).

    This minisymposium offers the possibility to present new developments and recent research on qualitative aspects of nonlinear partial differential equations. It particularly addresses young scientists in this field. Topics include bifurcation phenomena and stability investigations for parabolic equations, regularity of solutions to free boundary problems, and geometrical evolutions equations.

  30. Random Discrete Structures and Processes (Three hours; organizers: Konstantinos Panagiotou, München; Yury Person, Frankfurt)

    Random discrete structures and processes have been investigated systematically since the 60's, when Erdős and Rényi published their seminal paper about random graphs. From today's viewpoint, random structures have remained an influential area of studies not only in Mathematics, but also in Theoretical Computer Science and in Statistical Physics. This session will focus on recent advances in the study of various properties of random discrete structures and modern developments.

    This meeting aims at bringing together researchers in German speaking countries and neighbouring countries as well. We will also invite younger researchers to present their results.

  31. Recent Trends in the Arithmetic of Automorphic Forms (Four hours; organizers: Jens Funke, Durham; Ian Kiming, Copenhagen)

    The symposium will review the latest developments in the arithmetic of automorphic forms, in particular modular forms.

  32. Set Theory (organizers: Yurii Khomskii, Hamburg; Alexander C. Block, Hamburg; Hugo Nobrega, Amsterdam)

    Set theory is the study of the foundations of mathematics, and lies at the intersection of logic, philosophy, topology, analysis and other fields of pure mathematics. The field has undergone dramatic changes in the latter half of the 20th century, with new developments in forcing, large cardinals and descriptive set theory that led to unexpected progress, the resolution of long-standing open problems such as the Continuum Hypothesis, and the motivation of a search for new axioms of infinity. Moreover, in recent years set theory has seen a rise in applications and interactions with other fields of mathematics, ranging from algebraic topology to graph theory.

    This mini-symposium will bring together a small group of researchers in set theory from Germany and abroad, covering a wide variety of topics including forcing, large cardinals, inner model theory, descriptive set theory and applications to topology.

    This mini-symposium is supported by the Deutsche Vereinigung für Mathematische Logik und für Grundlagenforschung der exakten Wissenschaften (DVMLG).

  33. Statistics on complex structures (Four hours; organizers: Gilles Blanchard, Potsdam; Natalie Neumeyer, Hamburg; Angelika Rohde, Bochum)

    Statistics is a science of information: a central question is to analyze and quantify as precisely as possible how much information about a partially unknown mathematical structure of a given type can (or cannot) be conveyed through observed random data. Recent developments in the mathematical analysis of complex data have been particularly successful and pathbreaking when they were able to bring together traditional notions and questions of mathematical statistics (such as various notions of statistical convergence) with tools and points of views from other areas of mathematics, in order to have a better grasp of complex mathematical structures arising in modern data.

    The goal of this minisymposium is to focus on some specific topics where such interactions are currently particularly active and to open new perspectives for further developments. The intent is to foster interaction between the mathematical statistics community and other communities, and to raise the interest of mathematicians with an open eye towards interaction of their own field with that of statistics and data analysis.

    Topics covered will include:

    • Statistics of functional data and on general metric measure spaces. While functional analysis has been interacting for a long time with nonparametric statistics, a relatively young area opened by modern massive data collection possibilities is to model the observed data themselves as random functions. In parallel, going beyond standard spaces, there is a growing interest in statistics for using the tools and ideas of analysis on metric measure spaces. This interaction is still in its infancy and there is much untapped potential.
    • High-dimensional structured matrix models and graphical models. There have been enormous efforts in developing new methodologies and theory for the analysis of high-dimensional covariance and precision matrices and graphical models in the past decade, based on a small sample of high-dimensional measurements and incorporating complexity reducing structural assumptions. Nevertheless, there is still a big gap between theoretical developments and real data analysis. For instance, theoretically optimal estimators, with optimality defined typically in a minimax sense, may not be computationally feasible. On the other hand, recent advances in optimization theory allow meanwhile the development of implementable and fast algorithms to fit complicated models. Such estimators, however, may not be minimax optimal, or may even not have basic properties, such as consistency at a reasonable rate. Optimal adaptive estimation that is at the same time computationally feasible is very challenging, especially when the complexity of the data sets, and associated models, grows with the amount of data.
    • Statistics on graphs. A growing zoology of models for random graphs have been introduced, motivated by new sources of data taking such a form (such as social networks, communication networks, omics-data, brain modeling). Similarly to the previous topic, with which it overlaps partly, the question of statistical versus computational efficiency is a central one. Additionally, addressing the issue of adequation of these various models to observed data, as well as considering appropriate statistical limits of random graphs of growing size, are intensely being explored. Finally, the use of more sophisticated tools well-established in graph theory is only beginning to find its way towards addressing statistical questions.

    We intend to have for each subtopic a speaker giving an overview talk aimed at a general mathematical audience, followed by one or two speakers exposing recent developments.

    The minisymposium is associated with the DFG Research Unit 1735 "Structural Inference in Statistics".

  34. Structural and algorithmic aspects in graph theory (Three hours; organizers: Henning Bruhn-Fujimoto, Ulm; Matthias Kriesell, Ilmenau)

    Graphs are a fundamental modelling tool with applications in a large number of different domains. One of their main feature is their apparent simplicity that often allows to reduce a problem to its essential core. Yet despite this simplicity many algorithmic or structural problems involving graphs are wide open. Often, there is a fruitful interplay between algorithmic and structural aspects: advances on one of the two sides provides insights into the other, and vice versa.

    In this mini-symposium we will focus in particular on the interaction between structural and algorithmic questions in graph theory. Suggested topics include digraphs, graph colouring, connectivity, width parameters, and polyhedral questions.

  35. Symplectic Structures in Geometric Analysis (Six hours; organizers: Nils Waterstraat, Berlin; Bernhelm Booss-Bavnbek, Roskilde).

    The aim of this Minisymposium is to bring together specialists from symplectic geometry, global analysis, nonlinear differential equations, and mathematical physics. The emphasis is on recent applications of symplectic invariants to problems in geometric analysis. The topics covered will include spectral invariants of operators of Dirac- and Laplace-type and other geometrically defined differential operators, (weak) symplectic structures in Banach spaces, Conley-Zehnder and Maslov indices, as well as applications to bifurcation theory, Hamiltonian systems, the N-body problem, boundary value problems, (closed) geodesics, and minimal varieties.

  36. Topics in Delay Differential Equations (Six hours; organizers: Hans-Otto Walther, Giessen; Eugen Stumpf, Hamburg)

    The minisymposium shall pick up the discussion of the survey article [1] about delay differential equations. In particular, it is intended to provide an insight into both some recent developments of the general theory as well as into some applications of delay differential equations in other sciences as Biology, Physics etc.. The participation of young researchers, especially, of those who would like to present own results concerning delay differential equations and their applications, is welcome and encouraged.

    1. Walther, H.-O: Topics in Delay Differential Equations. Jahresbericht der DMV, vol. 116 (2), pp.87-114 (2014).

  37. Topology and geometry of Lie group actions (Six hours; organizers: Manuel Amann, Karlsruhe; Oliver Goertsches, München)

    The concept of symmetry has always played a crucial role in understanding geometric objects. A classical way of modeling symmetry of spaces is to impose the action of a group. This approach still proves to be very successful in modern mathematics yielding beautiful results in a multitude of fields, such as algebraic and geometric topology, or Riemannian and symplectic geometry.

    In this mini-symposium we will discuss recent results in this area; on the one hand concerning the theory of Lie transformation groups itself, and on the other hand using the existence of Lie group actions as a means to understand various geometric structures.

  38. Well-quasi orders: from theory to applications (Six hours; organizers: Peter Schuster, Verona; Monika Seisenberger, Swansea; Andreas Weiermann, Gent)

    This minisymposium is devoted to multiple and deep interactions between the theory of well quasi-orders (known as wqo-theory) and several fields of mathematics and logic (commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics, subrecursive hierarchies, and proof theory). Wqo-theory is currently a highly developed part of combinatorics with surprising applications in logic, mathematics and computer science. Well-quasi orders provide a unifying tool for elegant finiteness proofs and to some extent they even have frequently been rediscovered in various contexts.

    With the minisymposium we want to communicate recent developments in the field via talks by speakers from different areas, thereby facilitating knowledge transfer between different subjects in mathematics.

  39. Zum Einsatz von Mathematik-Brückenhilfen in den Schulen (Two hours; organizers: Ingenuin Gasser, Hamburg; Thomas Schramm, Hamburg)

    In diesem Minsymposium soll auf die Frage eingegangen werden, ob und wie sogenannte Mathematik-Brückenhilfen an der Schnittstelle Schule-Hochschule, wie z.B. der OMB+ (Online Mathe Brückenkurs +), auch teilweise in der Schule genutzt und eingesetzt werden könnten. Das primäre Ziel solcher Hilfen ist die kontinuierliche Auseinandersetzung mit Standardschulthemen der Mittel- und Oberstufenmathematik, um einen sicheren und schnellen Umgang mit diesen Grundlagen zu fördern. Der Verlust des sicheren und schnellen Umgangs mit den schulmathematischen Grundlagen wird häufig als eine der wichtigsten Ursachen beim Scheitern an Hochschulen in wirtschaftswissenschaftlich, mathematisch, informatisch und naturwissenschaftlichen Studiengängen gesehen.

    Das Minisymposium richtet sich u.a. auch an Lehrer.

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