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- ItemMini-Workshop: Geometry of Quantum Entanglement(Zürich : EMS Publ. House, 2009) Szarek, Stanislaw; Werner, Elisabeth; Zyczkowski, KarolThe workshop aimed at developing interactions between researchers from quantum information theory and from asymptotic geometric analysis. A central notion discussed was the phenomenon of quantum entanglement, which naturally leads to geometric considerations in high-dimensional vector spaces. In these spaces, phenomena such as concentration of measure become prominent and may invalidate our low-dimensional intuition.
- ItemHeat Kernels, Stochastic Processes and Functional Inequalities(Zürich : EMS Publ. House, 2016) Kumagai, Takashi; Saloff-Coste, Laurent; Sturm, Karl-TheodorThe general topic of the 2016 workshop Heat kernels, stochastic processes and functional inequalities was the study of linear and non-linear diffusions in geometric environments including smooth manifolds, fractals and graphs, metric spaces and in random environments. The workshop brought together leading researchers from analysis, geometry and probability, and provided an excellent opportunity for interactions between scientists from these areas at different stages of their career. The unifying themes were heat kernel analysis, mass transportation problems and functional inequalities while the program straddled across a great variety of subjects and across the divide that exists between discrete and continuous mathematics. Other unifying concepts such as the notions of metric measure space, Otto Calculus and Lott-Sturm-Villani synthetic Ricci curvature bounds played an important part in the discussions. Novel directions including the study of Liouville quantum gravity were included. The workshop provided participants with an opportunity to discuss how these ideas and techniques can be used to approach problems regarding optimal transport, Riemannian and sub-Riemannian geometry, and analysis and stochastic processes in random media.
- ItemMini-Workshop: Efficient and Robust Approximation of the Helmholtz Equation(Zürich : EMS Publ. House, 2012) Monk, Peter; Wieners, ChristianThe accurate and efficient treatment of wave propogation phenomena is still a challenging problem. A prototypical equation is the Helmholtz equation at high wavenumbers. For this equation, Babuška & Sauter showed in 2000 in their seminal SIAM Review paper that standard discretizations must fail in the sense that the ratio of true error and best approximation error has to grow with the frequency. This has spurred the development of alternative, non-standard discretization techniques. This workshop focused on evaluating and comparing these different approaches also with a view to their applicability to more general wave propagation problems.
- ItemMini-Workshop: Product Systems and Independence in Quantum Dynamics(Zürich : EMS Publ. House, 2009) Franz, Uwe; Skeide, MichaelQuantum dynamics, both reversible (i.e., closed quantum systems) and irreversible (i.e., open quantum systems), gives rise to product systems of Hilbert spaces or, more generally, of Hilbert modules. When we consider reversible dynamics that dilates an irreversible dynamics, then the product system of the latter is equal to the product system of the former (or is contained in a unique way). Whenever the dynamics is on a proper subalgebra of the algebra of all bounded operators on a Hilbert space, in particular, when the open system is classical (commutative) it is indispensable that we use Hilbert modules. The product system of a reversible dynamics is intimately related to a filtration of subalgebras that are independent in a state or conditionally independent in a conditional expectation of the reversible system. This has been illustrated in many concrete dilations that have been obtained with the help of quantum stochastic calculus. Here the underlying Fock space or module determines the sort of quantum independence underlying the reversible system. The mini-workshop brought together experts from quantum dynamics, product systems and quantum independence who have contributed to the general theory or who have studied intriguing examples. As the implications of the tight relationship between product systems and independence had so far been largely neglected, we expect from our mini-workshop a strong innovative impulse to this field.
- ItemMini-Workshop: Attraction to Solitary Waves and Related Aspects of Physics(Zürich : EMS Publ. House, 2008) Comech, Andrew; Komech, Alexander; Vainberg, Boris[no abstract available]
- ItemLow-dimensional Topology(Zürich : EMS Publ. House, 2020) Moriah, Yoav; Purcell, Jessica; Schleimer, SaulThe workshop brought together experts from across all areas of low-dimensional topology, including knot theory, mapping class groups, three-manifolds and four-manifolds. In addition to the standard research talks we had five survey talks by Burton, Minsky, Powell, Reid, and Roberts leading to discussions of open problems. Furthermore we had three sessions of five-minute talks by a total of thirty-five participants.
- ItemTopological and Geometric Combinatorics(Zürich : EMS Publ. House, 2011) Kalai, Gil; Novik, Isabella; Ziegler, Günter M.The 2011 Oberwolfach meeting “Topological and Geometric Combinatorics” was organized by Anders Björner (Stockholm), Gil Kalai (Jerusalem), Isabella Novik (Seattle), and Günter M. Ziegler (Berlin). It covered a wide variety of aspects of Discrete Geometry, Topological Combinatorics, and Geometric Topology. Some of the highlights of the conference included (1) counterexamples to the Hirsch conjecture, (2) the latest results around the colored Tverberg theorem, and (3) recent developments on the complexity of the simplex algorithm.
- ItemNoncommutative Geometry and Loop Quantum Gravity: Loops, Algebras and Spectral Triples(Zürich : EMS Publ. House, 2010) Marcolli, Matilde; Nest, RyszardSpectral triples have recently turned out to be relevant for different approaches that aim at quantizing gravity and the other fundamental forces of nature in a mathematically rigorous way. The purpose of this workshop was to bring together researchers mainly from noncommutative geometry and loop quantum gravity –two major fields that have used spectraltriples independently so far– in order to share their results and open issues.
- ItemMini-Workshop: Chromatic Phenomena and Duality in Homotopy Theory and Representation Theory(Zürich : EMS Publ. House, 2018) Krause, Henning; Stojanoska, VesnaThis mini-workshop focused on chromatic phenomena and duality as unifying themes in algebra, geometry, and topology. The overarching goal was to establish a fruitful exchange of ideas between experts from various areas, fostering the study of the local and global structure of the fundamental categories appearing in algebraic geometry, homotopy theory, and representation theory. The workshop started with introductory talks to bring researches from different backgrounds to the same page, and later highlighted recent progress in these areas with an emphasis on the interdisciplinary nature of the results and structures found. Moreover, new directions were explored in focused group work throughout the week, as well as in an evening discussion identifying promising long-term goals in the subject. Topics included support theories and their applications to the classification of localizing ideals in triangulated categories, equivariant and homotopical enhancements of important structural results, descent and Galois theory, numerous notions of duality, Picard and Brauer groups, as well as computational techniques.
- ItemRepresentation Theory of Quivers and Finite Dimensional Algebras(Zürich : EMS Publ. House, 2014) Iyama, Osamu; Keller, Bernhard; Krause, HenningMethods and results from the representation theory of quivers and finite dimensional algebras have led to many interactions with other areas of mathematics. Such areas include the theory of Lie algebras and quantum groups, commutative algebra, algebraic geometry and topology, and in particular the new theory of cluster algebras. The aim of this workshop was to further develop such interactions and to stimulate progress in the representation theory of algebras.