http://publications.mfo.de/handle/mfo/2819 Oberwolfach Reports Volume 15 (2018) Tue, 14 Apr 2026 08:34:57 GMT 2026-04-14T08:34:57Z http://publications.mfo.de/handle/mfo/3679 Mini-Workshop: Mathematical and Numerical Analysis of Maxwell's Equations In this mini-workshop 17 leading mathematicians from Europe and United States met at the MFO to discuss and present new developments in the mathematical and numerical analysis of Maxwell’s equations and related systems of partial differential equations. The report at hand offers the extended abstracts of their talks. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3679 2018-01-01T00:00:00Z In this mini-workshop 17 leading mathematicians from Europe and United States met at the MFO to discuss and present new developments in the mathematical and numerical analysis of Maxwell’s equations and related systems of partial differential equations. The report at hand offers the extended abstracts of their talks. http://publications.mfo.de/handle/mfo/3678 Mini-Workshop: Innovative Trends in the Numerical Analysis and Simulation of Kinetic Equations In multiscale modeling hierarchy, kinetic theory plays a vital role in connecting microscopic Newtonian mechanics and macroscopic continuum mechanics. As computing power grows, numerical simulation of kinetic equations has become possible and undergone rapid development over the past decade. Yet the unique challenges arising in these equations, such as highdimensionality, multiple scales, random inputs, positivity, entropy dissipation, etc., call for new advances of numerical methods. This mini-workshop brought together both senior and junior researchers working on various fastpaced growing numerical aspects of kinetic equations. The topics include, but were not limited to, uncertainty quantification, structure-preserving methods, phase transitions, asymptotic-preserving schemes, and fast methods for kinetic equations. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3678 2018-01-01T00:00:00Z In multiscale modeling hierarchy, kinetic theory plays a vital role in connecting microscopic Newtonian mechanics and macroscopic continuum mechanics. As computing power grows, numerical simulation of kinetic equations has become possible and undergone rapid development over the past decade. Yet the unique challenges arising in these equations, such as highdimensionality, multiple scales, random inputs, positivity, entropy dissipation, etc., call for new advances of numerical methods. This mini-workshop brought together both senior and junior researchers working on various fastpaced growing numerical aspects of kinetic equations. The topics include, but were not limited to, uncertainty quantification, structure-preserving methods, phase transitions, asymptotic-preserving schemes, and fast methods for kinetic equations. http://publications.mfo.de/handle/mfo/3677 Mini-Workshop: Numerical Analysis for Non-Smooth PDE-Constrained Optimal Control Problems This mini-workshop brought together leading experts working on various aspects of numerical analysis for optimal control problems with nonsmoothness. Fifteen extended abstracts summarize the presentations at this mini-workshop. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3677 2018-01-01T00:00:00Z This mini-workshop brought together leading experts working on various aspects of numerical analysis for optimal control problems with nonsmoothness. Fifteen extended abstracts summarize the presentations at this mini-workshop. http://publications.mfo.de/handle/mfo/3676 Convex Geometry and its Applications The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of algorithms in computer science. The purpose of this meeting was to bring together researchers from the analytic, geometric and probabilistic groups who have contributed to these developments. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3676 2018-01-01T00:00:00Z The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of algorithms in computer science. The purpose of this meeting was to bring together researchers from the analytic, geometric and probabilistic groups who have contributed to these developments. http://publications.mfo.de/handle/mfo/3675 Free Probability Theory The workhop brought together leading experts, as well as promising young researchers, in areas related to recent developments in free probability theory. Some particular emphasis was on the relation of free probability with random matrix theory. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3675 2018-01-01T00:00:00Z The workhop brought together leading experts, as well as promising young researchers, in areas related to recent developments in free probability theory. Some particular emphasis was on the relation of free probability with random matrix theory. http://publications.mfo.de/handle/mfo/3674 Enveloping Algebras and Geometric Representation Theory The workshop brought together experts investigating algebraic Lie theory from the geometric and categorical viewpoints. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3674 2018-01-01T00:00:00Z The workshop brought together experts investigating algebraic Lie theory from the geometric and categorical viewpoints. http://publications.mfo.de/handle/mfo/3673 Complexity Theory Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3673 2018-01-01T00:00:00Z Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes. http://publications.mfo.de/handle/mfo/3672 Combinatorial Optimization Combinatorial Optimization is an active research area that developed from the rich interaction among many mathematical areas, including combinatorics, graph theory, geometry, optimization, probability, theoretical computer science, and many others. It combines algorithmic and complexity analysis with a mature mathematical foundation and it yields both basic research and applications in manifold areas such as, for example, communications, economics, traffic, network design, VLSI, scheduling, production, computational biology, to name just a few. Through strong inner ties to other mathematical fields it has been contributing to and benefiting from areas such as, for example, discrete and convex geometry, convex and nonlinear optimization, algebraic and topological methods, geometry of numbers, matroids and combinatorics, and mathematical programming. Moreover, with respect to applications and algorithmic complexity, Combinatorial Optimization is an essential link between mathematics, computer science and modern applications in data science, economics, and industry. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3672 2018-01-01T00:00:00Z Combinatorial Optimization is an active research area that developed from the rich interaction among many mathematical areas, including combinatorics, graph theory, geometry, optimization, probability, theoretical computer science, and many others. It combines algorithmic and complexity analysis with a mature mathematical foundation and it yields both basic research and applications in manifold areas such as, for example, communications, economics, traffic, network design, VLSI, scheduling, production, computational biology, to name just a few. Through strong inner ties to other mathematical fields it has been contributing to and benefiting from areas such as, for example, discrete and convex geometry, convex and nonlinear optimization, algebraic and topological methods, geometry of numbers, matroids and combinatorics, and mathematical programming. Moreover, with respect to applications and algorithmic complexity, Combinatorial Optimization is an essential link between mathematics, computer science and modern applications in data science, economics, and industry. http://publications.mfo.de/handle/mfo/3671 Emergence of Structures in Particle Systems: Mechanics, Analysis and Computation The meeting focused on the last advances in particle systems. The talks covered a broad range of topics, ranging from questions in crystallization and atomistic systems to mesoscopic models of defects to machine learning approaches and computational aspects. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3671 2018-01-01T00:00:00Z The meeting focused on the last advances in particle systems. The talks covered a broad range of topics, ranging from questions in crystallization and atomistic systems to mesoscopic models of defects to machine learning approaches and computational aspects. http://publications.mfo.de/handle/mfo/3670 Computational Engineering This Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants were mathematicians and engineers with focus on mixed and nonstandard finite element schemes and their applications. Mon, 01 Jan 2018 00:00:00 GMT http://publications.mfo.de/handle/mfo/3670 2018-01-01T00:00:00Z This Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants were mathematicians and engineers with focus on mixed and nonstandard finite element schemes and their applications.