http://publications.mfo.de/handle/mfo/2812 Oberwolfach Reports Volume 8 (2011) Wed, 08 Apr 2026 12:02:10 GMT 2026-04-08T12:02:10Z http://publications.mfo.de/handle/mfo/3271 Stratified Spaces: Joining Analysis, Topology and Geometry For manifolds, topological properties such as Poincaré duality and invariants such as the signature and characteristic classes, results and techniques from complex algebraic geometry such as the Hirzebruch-Riemann-Roch theorem, and results from global analysis such as the Atiyah-Singer index theorem, worked hand in hand in the past to weave a tight web of knowledge. Individually, many of the above results are in the meantime available for singular stratified spaces as well. The 2011 Oberwolfach workshop “Stratified Spaces: Joining Analysis, Topology and Geometry” discussed these with the specific aim of cross-fertilization in the three contributing fields. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3271 2011-01-01T00:00:00Z For manifolds, topological properties such as Poincaré duality and invariants such as the signature and characteristic classes, results and techniques from complex algebraic geometry such as the Hirzebruch-Riemann-Roch theorem, and results from global analysis such as the Atiyah-Singer index theorem, worked hand in hand in the past to weave a tight web of knowledge. Individually, many of the above results are in the meantime available for singular stratified spaces as well. The 2011 Oberwolfach workshop “Stratified Spaces: Joining Analysis, Topology and Geometry” discussed these with the specific aim of cross-fertilization in the three contributing fields. http://publications.mfo.de/handle/mfo/3270 Variational Methods for Evolution The meeting focused on the last advances in the applications of variational methods to evolution problems governed by partial differential equations. The talks covered a broad range of topics, including large deviation and variational principles, rate-independent evolutions and gradient flows, heat flows in metric-measure spaces, propagation of fracture, applications of optimal transport and entropy-entropy dissipation methods, phase-transitions, viscous approximation, and singular-perturbation problems. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3270 2011-01-01T00:00:00Z The meeting focused on the last advances in the applications of variational methods to evolution problems governed by partial differential equations. The talks covered a broad range of topics, including large deviation and variational principles, rate-independent evolutions and gradient flows, heat flows in metric-measure spaces, propagation of fracture, applications of optimal transport and entropy-entropy dissipation methods, phase-transitions, viscous approximation, and singular-perturbation problems. http://publications.mfo.de/handle/mfo/3269 Geometric Partial Differential Equations: Theory, Numerics and Applications This workshop concentrated on partial differential equations involving stationary and evolving surfaces in which geometric quantities play a major role. Mutual interest in this emerging field stimulated the interaction between analysis, numerical solution, and applications. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3269 2011-01-01T00:00:00Z This workshop concentrated on partial differential equations involving stationary and evolving surfaces in which geometric quantities play a major role. Mutual interest in this emerging field stimulated the interaction between analysis, numerical solution, and applications. http://publications.mfo.de/handle/mfo/3268 Combinatorial Optimization Combinatorial Optimization is a very active field that benefits from bringing together ideas from different areas, e.g., graph theory and combinatorics, matroids and submodularity, connectivity and network flows, approximation algorithms and mathematical programming, discrete and computational geometry, discrete and continuous problems, algebraic and geometric methods, and applications. We continued the long tradition of triannual Oberwolfach workshops, bringing together the best researchers from the above areas, discovering new connections, and establishing new and deepening existing international collaborations. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3268 2011-01-01T00:00:00Z Combinatorial Optimization is a very active field that benefits from bringing together ideas from different areas, e.g., graph theory and combinatorics, matroids and submodularity, connectivity and network flows, approximation algorithms and mathematical programming, discrete and computational geometry, discrete and continuous problems, algebraic and geometric methods, and applications. We continued the long tradition of triannual Oberwolfach workshops, bringing together the best researchers from the above areas, discovering new connections, and establishing new and deepening existing international collaborations. http://publications.mfo.de/handle/mfo/3267 Mathematical Logic: Proof Theory, Constructive Mathematics The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexity. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3267 2011-01-01T00:00:00Z The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexity. http://publications.mfo.de/handle/mfo/3266 Emigration of Mathematicians and Transmission of Mathematics: Historical Lessons and Consequences of the Third Reich This conference provided a focused venue to explore the intellectual migration of mathematicians and mathematics spurred by the Nazis and still influential today. The week of talks and discussions (both formal and informal) created a rich opportunity for the cross-fertilization of ideas among almost 50 mathematicians, historians of mathematics, general historians, and curators. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3266 2011-01-01T00:00:00Z This conference provided a focused venue to explore the intellectual migration of mathematicians and mathematics spurred by the Nazis and still influential today. The week of talks and discussions (both formal and informal) created a rich opportunity for the cross-fertilization of ideas among almost 50 mathematicians, historians of mathematics, general historians, and curators. http://publications.mfo.de/handle/mfo/3265 Correlations and Interactions for Random Quantum Systems Random quantum systems cover a broad range of mathematical models from random Schrödinger operators to random matrices and quantum spin models with random parameters. Their understanding requires techniques which combine functional analysis and probability. The workshop brought together researchers from these various branches which discussed new results, methods and future challenges. This is a report on the meeting containing extended abstracts of the lectures. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3265 2011-01-01T00:00:00Z Random quantum systems cover a broad range of mathematical models from random Schrödinger operators to random matrices and quantum spin models with random parameters. Their understanding requires techniques which combine functional analysis and probability. The workshop brought together researchers from these various branches which discussed new results, methods and future challenges. This is a report on the meeting containing extended abstracts of the lectures. http://publications.mfo.de/handle/mfo/3264 Arbeitsgemeinschaft: Quantum Ergodicity Quantum Ergodicity aims at understanding the eigenstates of quantum mechanical systems admitting chaotic classical limiting dynamics. A paradigmatic system is the Laplace-Beltrami operator on a compact manifold of negative sectional curvature: its classical limit is the geodesic flow on the manifold, which is of Anosov type. Although no explicit expression is available for the eigenstates, one may use various tools from semiclassical analysis in order to gather some partial information on their structure. The central result (Quantum Ergodicity Theorem) states that almost all eigenstates are equidistributed over the energy shell, in the semiclassical limit, provided the classical system is ergodic. The lectures review the background techniques of semiclassical analysis and ergodic theory, give several versions of the QE theorem, and present several extensions of the result, which apply to specific systems, for instance chaotic systems enjoying arithmetic symmetries. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3264 2011-01-01T00:00:00Z Quantum Ergodicity aims at understanding the eigenstates of quantum mechanical systems admitting chaotic classical limiting dynamics. A paradigmatic system is the Laplace-Beltrami operator on a compact manifold of negative sectional curvature: its classical limit is the geodesic flow on the manifold, which is of Anosov type. Although no explicit expression is available for the eigenstates, one may use various tools from semiclassical analysis in order to gather some partial information on their structure. The central result (Quantum Ergodicity Theorem) states that almost all eigenstates are equidistributed over the energy shell, in the semiclassical limit, provided the classical system is ergodic. The lectures review the background techniques of semiclassical analysis and ergodic theory, give several versions of the QE theorem, and present several extensions of the result, which apply to specific systems, for instance chaotic systems enjoying arithmetic symmetries. http://publications.mfo.de/handle/mfo/3263 Very High Dimensional Semiparametric Models Very high dimensional semiparametric models play a major role in many areas, in particular in signal detection problems when sparse signals or sparse events are hidden among high dimensional noise. Concrete examples are genomic studies in biostatistics or imaging problems. In a broad context all kind of statistical inference and model selection problems were discussed for high dimensional data. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3263 2011-01-01T00:00:00Z Very high dimensional semiparametric models play a major role in many areas, in particular in signal detection problems when sparse signals or sparse events are hidden among high dimensional noise. Concrete examples are genomic studies in biostatistics or imaging problems. In a broad context all kind of statistical inference and model selection problems were discussed for high dimensional data. http://publications.mfo.de/handle/mfo/3262 Complex Algebraic Geometry The conference focused on several classical and modern topics in the realm of complex algebraic geometry, such as moduli spaces, birational geometry and the minimal model program, Mirror symmetry and Gromov–Witten invariants, Hodge theory, curvature flows, algebraic surfaces and curves. Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/3262 2011-01-01T00:00:00Z The conference focused on several classical and modern topics in the realm of complex algebraic geometry, such as moduli spaces, birational geometry and the minimal model program, Mirror symmetry and Gromov–Witten invariants, Hodge theory, curvature flows, algebraic surfaces and curves.