http://publications.mfo.de/handle/mfo/3700 Oberwolfach Reports Volume 17 (2020) Tue, 28 Apr 2026 15:21:02 GMT 2026-04-28T15:21:02Z http://publications.mfo.de/handle/mfo/3855 New Directions in Rough Path Theory (online meeting) Rough path theory emerged as novel approach for dealing with interactions in complex random systems. It settled significant questions and provided an effective deterministic alternative to Itô calculus, itself a major contribution to 20$^{\mathrm{th}}$ century mathematics. Its impact has grown substantially in recent years: most prominently, rough paths ideas are at the core of Martin Hairer's Fields Medal-winning work on regularity structures, but there are also original and successful applications in other areas. The workshop focused on three areas that have been strongly influenced by the core ideas in rough path theory and which have witnessed considerable activity over the past few years: applications to data science, algebraic aspects and connections with stochastic analysis. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3855 2020-01-01T00:00:00Z Rough path theory emerged as novel approach for dealing with interactions in complex random systems. It settled significant questions and provided an effective deterministic alternative to Itô calculus, itself a major contribution to 20$^{\mathrm{th}}$ century mathematics. Its impact has grown substantially in recent years: most prominently, rough paths ideas are at the core of Martin Hairer's Fields Medal-winning work on regularity structures, but there are also original and successful applications in other areas. The workshop focused on three areas that have been strongly influenced by the core ideas in rough path theory and which have witnessed considerable activity over the past few years: applications to data science, algebraic aspects and connections with stochastic analysis. http://publications.mfo.de/handle/mfo/3843 Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (hybrid meeting) Both self-avoidance and self-contact of geometric objects can be modeled using repulsive energies that separate isotopy classes. Giving rise to nonlocal operators, they are interesting objects in their own right. Moreover, their analytical structure allows for devising numerical schemes enjoying robust features such as energy stability. This workshop aimed at discussing recent trends in this matter, including potential applications to modeling. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3843 2020-01-01T00:00:00Z Both self-avoidance and self-contact of geometric objects can be modeled using repulsive energies that separate isotopy classes. Giving rise to nonlocal operators, they are interesting objects in their own right. Moreover, their analytical structure allows for devising numerical schemes enjoying robust features such as energy stability. This workshop aimed at discussing recent trends in this matter, including potential applications to modeling. http://publications.mfo.de/handle/mfo/3842 History of Mathematics: A Global Cultural Approach (online meeting) The primary purpose of this workshop was to take account of progress on an ongoing six-volume cultural history of mathematics from antiquity to the present. This project is led by nine editors working with a large team of authors. Since the workshop had to be held remotely, it took the form of various group meetings held throughout the week. The final session involved assessments by editors of the six volumes with an eye toward completing the project by the end of 2021. The abstracts below summarize the contents of the individual chapters in the entire project, which will be published in Bloomsbury's cultural history series. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3842 2020-01-01T00:00:00Z The primary purpose of this workshop was to take account of progress on an ongoing six-volume cultural history of mathematics from antiquity to the present. This project is led by nine editors working with a large team of authors. Since the workshop had to be held remotely, it took the form of various group meetings held throughout the week. The final session involved assessments by editors of the six volumes with an eye toward completing the project by the end of 2021. The abstracts below summarize the contents of the individual chapters in the entire project, which will be published in Bloomsbury's cultural history series. http://publications.mfo.de/handle/mfo/3839 Structure-Preserving Discretizations for Nonlinear Systems of Because of the pandemia, the workshop on "Structure-Preserving Discretizations for Nonlinear Systems of Hyperbolic, Involution-Constrained Partial Differential Equations on Manifolds" could not be realized in the usual format or in the new hybrid format. Only one participant (P. Helluy) was able to physically come the MFO. He worked remotely with C. Klingenberg on a structure preserving time integration for kinetic models. This allows to building efficient schemes for solving conservation laws. A preprint describing this work, with applications to MHD, can be found here: https://hal.archives-ouvertes.fr/hal-02965967. Meanwhile, C. Klingenberg organized a remote seminar on the topics of the workshop. From September 2020 to December 2020, 13 talks were given online by participants to the workshop and other personalities. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3839 2020-01-01T00:00:00Z Because of the pandemia, the workshop on "Structure-Preserving Discretizations for Nonlinear Systems of Hyperbolic, Involution-Constrained Partial Differential Equations on Manifolds" could not be realized in the usual format or in the new hybrid format. Only one participant (P. Helluy) was able to physically come the MFO. He worked remotely with C. Klingenberg on a structure preserving time integration for kinetic models. This allows to building efficient schemes for solving conservation laws. A preprint describing this work, with applications to MHD, can be found here: https://hal.archives-ouvertes.fr/hal-02965967. Meanwhile, C. Klingenberg organized a remote seminar on the topics of the workshop. From September 2020 to December 2020, 13 talks were given online by participants to the workshop and other personalities. http://publications.mfo.de/handle/mfo/3836 Classical and Quantum Mechanical Models of Many-Particle Systems (online meeting) The collective behaviour of many-particle systems is a common denominator in the challenges of a highly diverse range of applications: from classical problems in Physics (gas dynamics e.g. Boltzmann's equation, plas\-ma dynamics e.g. various Vlasov equations, semiconductors, quantum mechanics) to current models in biology (kinetic models for collective interaction e.g. swarming, evolution of trait-structured species) to rising topics in social sciences (opinion formation, crowding phenomena) and economics (wealth distribution, mean-field games).\\ Key mathematical questions concern the analysis (global-in-time wellposedness, regularity), rigorous scaling resp. macroscospic limits (model reduction from many-particle models to mean-field/mesoscopic descriptions to macroscopic evolutions), efficient and asymptotic preserving numerical methods and qualitative results (e.g. large-time equilibration). Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3836 2020-01-01T00:00:00Z The collective behaviour of many-particle systems is a common denominator in the challenges of a highly diverse range of applications: from classical problems in Physics (gas dynamics e.g. Boltzmann's equation, plas\-ma dynamics e.g. various Vlasov equations, semiconductors, quantum mechanics) to current models in biology (kinetic models for collective interaction e.g. swarming, evolution of trait-structured species) to rising topics in social sciences (opinion formation, crowding phenomena) and economics (wealth distribution, mean-field games).\\ Key mathematical questions concern the analysis (global-in-time wellposedness, regularity), rigorous scaling resp. macroscospic limits (model reduction from many-particle models to mean-field/mesoscopic descriptions to macroscopic evolutions), efficient and asymptotic preserving numerical methods and qualitative results (e.g. large-time equilibration). http://publications.mfo.de/handle/mfo/3829 Computational Inverse Problems for Partial Differential Equations (hybrid meeting) Inverse problems in partial differential equations (PDEs) consist in reconstructing some part of a PDE such as a coefficient, a boundary condition, an initial condition, the shape of a domain, or a singularity from partial knowledge of solutions to the PDE. This has numerous applications in nondestructive testing, medical imaging, seismology, and optical imaging. Whereas classically mostly boundary or far field data of solutions to deterministic PDEs were considered, more recently also statistical properties of solutions to random PDEs have been studied. The study of numerical reconstruction methods of inverse problems in PDEs is at the interface of numerical analysis, PDE theory, functional analysis, statistics, optimization, and differential geometry. This workshop has mainly addressed five related topics of current interest: model reduction, control-based techniques in inverse problems, imaging with correlation data of waves, fractional diffusion, and model-based approaches using machine learning. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3829 2020-01-01T00:00:00Z Inverse problems in partial differential equations (PDEs) consist in reconstructing some part of a PDE such as a coefficient, a boundary condition, an initial condition, the shape of a domain, or a singularity from partial knowledge of solutions to the PDE. This has numerous applications in nondestructive testing, medical imaging, seismology, and optical imaging. Whereas classically mostly boundary or far field data of solutions to deterministic PDEs were considered, more recently also statistical properties of solutions to random PDEs have been studied. The study of numerical reconstruction methods of inverse problems in PDEs is at the interface of numerical analysis, PDE theory, functional analysis, statistics, optimization, and differential geometry. This workshop has mainly addressed five related topics of current interest: model reduction, control-based techniques in inverse problems, imaging with correlation data of waves, fractional diffusion, and model-based approaches using machine learning. http://publications.mfo.de/handle/mfo/3828 Mini-Workshop: Relativistic Fluids at the Intersection of Mathematics and Physics (online meeting) Relativistic Hydrodynamics is the description of fluid motion in regimes where relativistic effects are important. This is the case for fluids moving at high velocities or interacting with very strong gravitational fields, such as in the physics of black hole accretion disks or neutron star mergers but also in the microscopic dynamics of high-energy heavy-ion collisions. Although the first formulation of hydrodynamic equations dates back to the beginning stages of relativity theory, many mathematical problems remain wide open. In particular, the development of the theory of relativistic "viscous" fluids was slow and mathematical progress only made recently. The purpose of this Mini-Workshop was to bring together a diverse group of researchers, including specialists in nonlinear PDEs and physicists, to jump-start the mathematical development of this field. This allowed for a vital exchange of ideas between mathematics and physics communities. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3828 2020-01-01T00:00:00Z Relativistic Hydrodynamics is the description of fluid motion in regimes where relativistic effects are important. This is the case for fluids moving at high velocities or interacting with very strong gravitational fields, such as in the physics of black hole accretion disks or neutron star mergers but also in the microscopic dynamics of high-energy heavy-ion collisions. Although the first formulation of hydrodynamic equations dates back to the beginning stages of relativity theory, many mathematical problems remain wide open. In particular, the development of the theory of relativistic "viscous" fluids was slow and mathematical progress only made recently. The purpose of this Mini-Workshop was to bring together a diverse group of researchers, including specialists in nonlinear PDEs and physicists, to jump-start the mathematical development of this field. This allowed for a vital exchange of ideas between mathematics and physics communities. http://publications.mfo.de/handle/mfo/3826 Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (online meeting) The goal of this mini-workshop is to gather specialists of the dimer, Ising and spanning tree models around recent and ongoing progress in two directions. One is understanding the connection to the spectral curve of these models in the cases when the curve has positive genus. The other is the introduction of universal embeddings associated to these models. We aim to use these new tools to progress in the study of scaling limits. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3826 2020-01-01T00:00:00Z The goal of this mini-workshop is to gather specialists of the dimer, Ising and spanning tree models around recent and ongoing progress in two directions. One is understanding the connection to the spectral curve of these models in the cases when the curve has positive genus. The other is the introduction of universal embeddings associated to these models. We aim to use these new tools to progress in the study of scaling limits. http://publications.mfo.de/handle/mfo/3825 Mini-Workshop: Computational Optimization on Manifolds (online meeting) The goal of the mini-workshop was to study the geometry, algorithms and applications of unconstrained and constrained optimization problems posed on Riemannian manifolds. Focus topics included the geometry of particular manifolds, the formulation and analysis of a number of application problems, as well as novel algorithms and their implementation. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3825 2020-01-01T00:00:00Z The goal of the mini-workshop was to study the geometry, algorithms and applications of unconstrained and constrained optimization problems posed on Riemannian manifolds. Focus topics included the geometry of particular manifolds, the formulation and analysis of a number of application problems, as well as novel algorithms and their implementation. http://publications.mfo.de/handle/mfo/3822 Stochastic Processes under Constraints (hybrid meeting) The analysis of random processes under various constraints and conditions has been a central theme in the theory of stochastic processes, which links together several mathematical subdisciplines. The connection between potential theory and a certain type of conditioning of Markov processes via Doob's h-transform can be seen as a classical highlight. The last decades have seen further exciting and highly interesting developments which are related to the title of the workshop such as the analysis of persistence exponents for various classes of processes and various types of penalization problems. Many of these problems are rooted in questions from statistical mechanics. The workshop aims to investigate the topic stochastic processes under constraints from all these different perspectives. Wed, 01 Jan 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3822 2020-01-01T00:00:00Z The analysis of random processes under various constraints and conditions has been a central theme in the theory of stochastic processes, which links together several mathematical subdisciplines. The connection between potential theory and a certain type of conditioning of Markov processes via Doob's h-transform can be seen as a classical highlight. The last decades have seen further exciting and highly interesting developments which are related to the title of the workshop such as the analysis of persistence exponents for various classes of processes and various types of penalization problems. Many of these problems are rooted in questions from statistical mechanics. The workshop aims to investigate the topic stochastic processes under constraints from all these different perspectives.