Title: AIMS-TU Chemnitz Minisymposium on Applied Mathematics
Organisers: Mouhamed Moustapha Fall (AIMS Senegal), Franck Kalala Mutombo (AIMS South Africa) and Vladimir Shikhman (Chemnitz)
Abstract: The AIMS-TU Chemnitz Minisymposium is devoted to the current research in the area of Applied Mathematics conducted by members and partners of the AIMS network. The participants, mainly Phds and Post-Docs, will have an opprtunity for international networking and visibility while presenting their research results.
Title: Algorithms for stochastic optimization models beyond convexity
Organisers: Caroline Geiersbach (Wien) and Rüdiger Schultz (Duisburg-Essen)
Abstract: In it's early years, the algorithmic development in stochastic programming essentially dwelled on the convexity that is present for broad model classes, predominantly, but not restricted to, linear recourse models. In the minisymposium, recent progress in solving stochastic programs beyond the mentioned will , be discussed. This includes mixed-integer constrained and bilevel models as well as problems in infinite dimension amenable to stochastic gradient minimization.
Title: Applied shape and design optimization
Organisers: Martin Siebenborn (Universität Hamburg), Kevin Sturm (TU Wien) and Kathrin Welker (Helmut Schmidt Universität)
Abstract: The focus of this session is on computational aspects and algorithmic advances in the field of mathematical shape and topology optimization. While covering a large class of applications ranging from interface identification over shapes in aerodynamics to image segmentation, carefully selected experts report on recent developments and present practical approaches.
Title: Differential and Hodge Theoretic Methods in Algebraic Geometry
Organisers: Thomas Krämer (HU Berlin) and Thomas Reichelt (Heidelberg)
Abstract: Methods from the theory of algebraic differential equations and from topology play an increasing role in algebraic geometry, for instance in the study of singularities, moduli spaces, Hodge theory, mirror symmetry etc. The aim of the minisymposion is to give an overview of some recent developments in the area and to build new bridges between D-modules, algebraic and arithmetic geometry.
Title: Discrete Optimization
Organisers: Georg Loho (London School of Economics) and Matthias Schymura (EPF Lausanne)
Abstract: Discrete Optimization is a versatile theoretical framework with applications in mathematical sciences, technology, decision making, and other fields. The theory often draws its most fundamental insights from the structure of polytopes, graphs, and lattices. The goal of this mini symposium is to bring together young researchers in this field to exchange ideas, explore new trends, and foster new collaborations.
Title: Discretization aspects in PDE-constrained optimization
Organiser: Winnifried Wollner (Darmstadt)
Abstract: Over the last decades tremendous progress in the discretization analysis of PDE-constrained optimization problems has been made. While the discretization analysis for simple situations is now well understood recent focus has moved to the analysis of complex problems. These feature non-smooth or non-monotone equations, PDEs posed on graphs, uncertainty and many more. In addition, specialized discretiztion techniques are beeing developed. Some of these utilize reformulations of hard to tackle problems such as those with pointwise state constraints. Others techiques utilize specialized meshes or finite elements designed to utilize local regularity properties of the solution. This minisymposium will provide an overview of recent developments in the discretization analysis of PDE-constrained optimization problems.
Title: Extremal and Probabilistic Combinatorics
Organisers: Julia Böttcher (London School of Economics) , Yury Person (Ilmenau) and Anusch Taraz (TU Hamburg)
Abstract: This minisymposium will focus on recent advances in probabilistic and extremal combinatorics. We look forward to lectures on topics such as random graphs, Ramsey theory and density problems, and expect fruitful discussions concerning various approaches based on the probabilistic method, regularity techniques and analytic combinatorics.
Title: Geometric Analysis and Applications
Organisers: Simon Blatt (Salzburg), Philipp Reiter (Halle) and Armin Schikorra (Pittsburgh)
Abstract: The aim of this workshop is to discuss recent trends in Geometric Analysis in a broad sense. The general idea is to treat geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals involving pseudodifferential operators, discrete differential geometry, and numerical simulation.
Title: Locally convex methods in analysis
Organisers: Thomas Kalmes (Chemnitz) and Jochen Wengenroth (Trier)
Abstract: Modern aspects of the theory of locally convex spaces provide powerful tools to treat various problems from different fields of analysis such as Complex Analysis, Analysis of Partial Differential Operators, Spaces of (generalized) Functions, (Systems of) Partial Differential Equations, and Harmonic Analysis. The aim of the minisymposium is to present recent results based on abstract functional analytic methods as well as to discuss new trends and topics in locally convex spaces.
Title: Mathematics and Arts
Organisers: Milena Damrau (Bielefeld) and Martin Skrodzki (Wako)
Abstract: This minisymposium aims to bring together researchers interested in the connection of mathematics and arts. The talks cover a variety of topics, including mathematics in different art forms like painting, sculpture, architecture, textiles, and music, as well as teaching or communicating mathematics to the public through arts and artistic projects.
Title: Mathematics for Energy Systems with a focus on networks
Organisers: Martin Schmidt (Trier) and Sara Grundel (MPI Magdeburg)
Abstract: Simulation, Optimization and Control of Energy Networks is becoming more complex with the introduction of renewable, decentralized energy generation. This Minisymposium will present many different mathematical challenges in this context.
Title: Mixed-Integer Optimization
Organiser: Frauke Liers (Erlangen)
Abstract: The focus of this minisymposium is on new insights in the development of global solution approaches for hard mixed-integer optimization problems and its applications.
Title: Model order reduction
Organisers: Jochen Merker (HTWK Leipzig) and Patrick Kürschner (KU Leuven)
Abstract: In this minisymposium, model order reduction is discussed in a broad sense, including, e.g., sparse solutions of optimization problems, low-rank methods, and data-driven approaches. Thus, the minisymposium aims to provide an overview of state-of-the-art techniques for model order reduction from analysis as well as numerical mathematics and will also showcase new application scenarios of model reduction.
Title: Nonlinear Analysis - from Theory to Applications
Organisers: Rainer Mandel (Karlsruhe) and Nils Waterstraat (Halle)
Abstract: The aim of this minisymposium is to bring together young researchers working in Nonlinear Analysis. The talks cover a variety of topics including bifurcation theory, nonlinear PDEs, Hamiltonian systems as well as ramifications to Floer homology and Riemannian geometry.
Title: Nonlinear PDEs & Probability
Organisers: Tobias Ried (MPI MiS Leipzig) and Jonas Sauer (MPI MiS Leipzig)
Abstract: The aim of this mini-symposium (jointly organized with the Max Planck Institute for Mathematics in the Sciences Leipzig) is to present recent results in analysis and probability with applications to the study of nonlinear PDEs relating to mathematical physics and fluid mechanics. This includes questions of regularity (and irregularity), singular SPDEs and renormalization techniques, as well as convergence of large interacting particle systems towards nonlinear effective equations. We want to bring together young researchers and specialists of both PDE and probability to foster scientific exchange and explore new exciting developments in the fields.
Title: Non-smooth optimal control problems with partial differential
Organisers: Constantin Christof (München) and Daniel Wachsmuth (Würzburg)
Abstract: This minisymposium focuses on non-smooth aspects of optimization and optimal control problems that involve partial differential equations. Applications of these models include optimal control of variational inequalities and sparse control problems. The aim of the minisymposium is to present recent results on optimality conditions and solution algorithms.
Title: Nonlocal phenomena and regularity for stochastic evolution equations
Organisers: Michael Hinz (Bielefeld) and Jonas M. Tölle (Helsinki)
Abstract: We would like to gather experts from the field of stochastic evolution equations in order to discuss nonlocal phenomena and regularity for stochastic (partial) differential equations, where we focus on methods from harmonic analysis, fractional calculus and regularity theory. We are very interested in connections to variational analysis, rough path theory and fractional Gaussian processes as well as topics touching regularization by noise.
Title: Numerical Methods for port-Hamiltonian Systems
Organisers: Robert Altmann (Augsburg) and Benjamin Unger (TU Berlin)
Abstract: The port-Hamiltonian (pH) framework constitutes a new energy-based model paradigm that offers a systematic approach for the interactions of (physical) systems with each other and the environment via the underlying Stokes-Dirac structure. In this minisymposium, we focus on numerical methods for pH systems, including space and time discretization, model order reduction, and numerical linear algebra.
Title: Online Optimization
Organiser: Yann Disser (Darmstadt)
Abstract: Online optimization is concerned with discrete optimization problems over time, where input data only becomes available after some decisions have irrevocably been fixed, and the goal is to guarantee a good solution quality relative to an all-knowing optimum solution. This workshop highlights recent advances in this field.
Title: Optimal control and design with nonlinear PDE systems
Organisers: Michael Hintermüller and Axel Kröner (HU Berlin)
Abstract: This minisymposium addresses recent advances in optimal control and design with nonlinear PDE systems in a wide range. Topics include theoretical and numerical aspects as well as applications.
Title: Optimization on manifolds: theory and numerics
Organisers: Roland Herzog (Chemnitz) and Andre Uschmajew (MPI Leipzig)
Abstract: Classical optimization theory and algorithms are designed for optimization problems vector spaces. In recent years however there has been a growing interest in problems which are naturally formulated in nonlinear spaces, notably Riemannian manifolds. Examples include problems in shape analysis, image processing, nonlinear mechanics, matrix and tensor approximation, and data analysis. This minisymposiums presents recent developments regarding theory, numerical methods and applications for optimization problems on manifolds.
Title: PDE-constrained optimization
Organiser: Günter Leugering (Erlangen)
Abstract: PDE-constrained optimization has by now become a classical field in application oriented mathematics. While there is an intrinsic mathematical development in this field, modern applications provide challenges in the area of fluid or gas dynamics as well as elasticity on the macroscopic and microscopic scale. The mathematical challenge is related to shape- and topological sensitivities, non-smoothness and heterogeneity and intrinsic geometrical descriptions via manifolds in the context of partial differential equations. In this mini-symposium, we invite established and also young scientists to present their recent results ranging from shape sensitivity analysis of the Stokes-flow problem, over topological sensitivities of homogenized tensors in elasticity and manifold-based descriptions and optimal control of thin elastic rods to model predictive control for gas flow in pipe systems under model-switching. Driven by the applications, new mathematical concepts emerge.
Title: PDEs in Fluid Dynamics
Organisers: Gabriele Brüll (Karlsruhe) and Christina Lienstromberg (Bonn)
Abstract: The focus of this minisymposium is on mathematical modelling, existence and qualitative properties of solutions in the context of fluid dynamics.
Title: Proof and computation in mathematics
Organisers: Sam Sanders and Andrei Sipoș (Darmstadt)
Abstract: Proof theory is one of the four main pillars of mathematical logic, pioneered by David Hilbert around 1900. The subject of proof theory is the abstract study of proofs as mathematical objects with applications in computer science, linguistics, and philosophy. We survey recent developments in sub-fields of proof theory, including proof mining, proof assistants, and program extraction.
Title: Recent advances on evolutionary phase-transition problems
Organisers: Elisa Davoli (Wien) and Jan-Frederik Pietschmann (Chemnitz)
Abstract: The Cahn-Hilliard equation is a classical model for phase separation and by now many of its analytical aspects are well-understood. This includes the cases of degenerate mobility functions or different choices of the double-well potential. More recently, different Cahn-Hilliard models have been proposed and analyzed, also in connection with innovative applications, e.g in tumor growth modeling. An example is provided by non-local versions of the classical Cahn-Hilliard equations, introduced as gradient flows in suitable topologies of diffuse interface models for phase transitions where the classical Dirichlet energy is replaced by a convolution functional with a possibly degenerate kernel. This class of models is of particular relevance as they can be derived as a rigorous hydrodynamic limits. Further research directions are systems of (non-local) Cahn-Hilliard equations and Cahn-Hilliard-Navier-Stokes problems. The aim of this symposium is to present some recents advances and new trends in the modeling of evolutionary phase-transition problems.
Title: Spectral theory of operators and matrices and partial differential equations
Organisers: Matthias Täufer (London) and Martin Tautenhahn (Chemnitz)
Abstract: This Minisymposium brings together scientists working in spectral theory of operators and matrices, as well as their application to the analysis of PDE's. Emphasis will be put on general operators and spectral theory, structured operators and matrices, elliptic PDE's including Schrödinger operators, and Evolution equations, semigroups, as well as control theory.
Title: The impact of randomness on computation
Organisers: Rupert Hölzl (München) and Sam Sanders (Darmstadt)
Abstract: The notion of randomness has been formalised in mathematical logic via various definitions that capture intuitive properties of infinite random sequences (typicality, no compression, resistance to effective betting strategies). The topic of our minisymposium is the effect of random sources on computation, that is, whether such sources allow us to compute more or faster. The talks will deal with this question in the various existing frameworks, namely computability and randomness, Weihrauch degrees, and reverse mathematics.
Title: The many faces of mathematical systems theory
Organisers: Thomas Berger (Paderborn) and Felix Schwenninger (Twente)
Abstract: Systems theory arose in the mid-twentieth century as the mathematical foundation of control engineering. It has ever since connected various fields in mathematics, ranging from differential equations and numerical mathematics through (functional) analysis to algebra. Not only because of this multi-disciplinary appearance, the field offers many challenging mathematical problems. Likewise, viewpoints and techniques inspired by applications can be "fed back" to rather pure mathematics. The aim of this minisymposium is to present several important facets of modern mathematical systems theory.
Title: Theory and applications of mixed-integer and polynomial optimization
Organisers: Gennadiy Averkov and Armin Fügenschuh (Cottbus)
Abstract: This minisymposium deals with optimization problems that include differential equation constraints and nonlinear constraints, being quadratic or general polynomial. Further complications occur due to integrality restrictions on some or all of the variables. The spectrum of talks ranges from theoretically oriented ones, focusing on polytopes and spectrahedra, to applications in transport, production, scheduling, and set covering.
Title: Vector- and tensor-valued surface PDEs
Organisers: Arnold Reusken (RWTH Aachen) and Oliver Sander (TU Dresden)
Abstract: Most of the work on numerical methods for partial differential equations (PDEs) defined on curved surfaces is concerned with scalar-valued equations. In this case the coupling between surface geometry and PDE is relatively weak and many numerical approaches available for PDEs in Euclidean space have been extended to surface PDEs. For vector- and tensor-valued surface PDEs the situation is quite different. The surface vector- and tensor-fields need to be considered as elements of the tangent bundle. This makes the coupling between surface geometry and PDE much stronger and brings more topology into play. Significant progress on the development of modeling and simulation methods in the field of vector- and tensor-valued surface PDEs is currently made in different communities and in the course of studying specific problems from different application areas, including fluid dynamics, materials science, mechanics and biophysics. The minisymposium contains presentations treating different aspects of vector- and tensor-valued surface PDES, with particular focus on mathematical modeling, numerical analysis, and simulations.
Titel: Digitale Unterstützung für die mathematische Hochschullehre
Organisatoren: Ingo Dahn (Koblenz) und Daniel Potts (Chemnitz)
Zusammenfassung: Hochschullehre mit einem hohen Mathematik-Anteil stellt besondere Anforderungen an die Unterstützung durch digitale Medien. Konventionelle Lernmanagementsysteme werden dafür durch spezielle Mathematik-Systeme ergänzt und erweitert. Dabei gibt es sowohl freie als auch kommerzielle Angebote. Im Minisymposium werden aktuelle Beispiele dafür vorgestellt, die in der Lehre in den WiMINT-Fächern eingesetzt werden. Anhand von Entwicklungen der letzten Jahre wird dabei die Wirksamkeit hochschulübergreifender Zusammenarbeit, z.B. in Sachsen und Rheinland-Pfalz, sichtbar. Das Minisymposium bietet eine Orientierung in den vielfältigen Möglichkeiten der digitalen Unterstützung mathematischer Hochschullehre und einen Einblick in die Arbeit unterstützender offener Netzwerke.
Titel: Zur Geschichte der modernen Mathematik - Kooperationen, Netzwerke, Konfrontationen
Organisatoren: Peter Ullrich (Koblenz-Landau) und Hans Fischer (Eichstätt)
Zusammenfassung: Obwohl noch der einflussreiche Berliner Mathematiker Leopold Kronecker gemeint hatte, gemeinsame Arbeit würde den Fortschritt behindern, wurden nach der Mitte des 19. Jahrhunderts die verschiedenen Formen wissenschaftlicher Zusammenarbeit und ihrer Anwendungsgebiete in der Mathematik zunehmend wichtig. Dies führte zur Entstehung institutioneller wie auch informeller Strukturen (Fachgesellschaften, Forschungseinrichtungen, „Schulen“, „Netzwerke“) mit vielfältigen Arten der Kooperation, aber auch der Konfrontation. In besonderer, vielleicht sogar verstärkter Weise bestimmten weiterhin führende Persönlichkeiten die wissenschaftliche Entwicklung, indem sie die ständig erweiterten Formen wissenschaftlicher Zusammenarbeit intensiv nutzten. Im geplanten Minisymposium werden Fallbeispiele aus verschiedenen Bereichen der Mathematik für die Zeit von ca. 1850 bis in das letzte Drittel des 20. Jahrhunderts hinein erläutert; auch der Bereich der angewandten Mathematik einschließlich der Stochastik wird dabei wesentlich berücksichtigt.