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- ItemLanglands Correspondence and Constructive Galois Theory(Zürich : EMS Publ. House, 2014) Heinloth, Jochen; Yun, ZhiweiRecent progress in the Langlands programm provides a significant step towards the understanding of the arithmetic of global fields. The geometric Langlands program provides a systematic way to construct l-adic sheaves (resp. D-modules) on algebraic curves which subsumes the construction of classical sheaves, like rigid local systems, used in inverse Galois theory (by Belyi, Malle, Matzat, Thompson, Dettweiler, Reiter) for the construction of field extension of the rational function fields $\mathbb F_p(t)$ or $\mathbb Q(t)$ (recent work of Heinloth, Ngo, Yun and Yun). On the other hand, using Langlands correspondence for the field $\mathbb Q$, Khare, Larsen and Savin constructed many new automorphic representations which lead to new Galois realizations for classical and exceptional groups over $\mathbb Q$. It was the aim of the workshop, to bring together the experts working in the fields of Langlands correspondence and constructive Galois theory.
- ItemMini-Workshop: Differentiable Ergodic Theory, Dimension Theory and Stable Foliations(Zürich : EMS Publ. House, 2014) Stratmann, BerndThe mini-workshop Differentiable Ergodic Theory, Dimension Theory and Stable Foliations brought together experts in thermodynamical formalism, hyperbolic dynamics and dimension theory from several countries. The geographic representation was broad, from Europe, USA and Japan. All participants gave interesting 1-hour talks, and there was organized also an open problem session, where directions for future work and many open problems were discussed. Among the topics presented/discussed in the workshop, there were ones related to dimension theory and probability measures on fractals, various types of hyperbolicity, systems with overlaps, complex dynamics and iterated function systems.
- ItemRecent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws and their Use in Science and Engineering(Zürich : EMS Publ. House, 2012) Bijl, Hester; Meister, Andreas; Sonar, ThomasModern numerical methods for hyperbolic conservation laws rely on polynomials of high degree, mostly orthogonal polynomials, on triangular or quadrilateral meshes. Due to shocks stability is an issue and modern means of filtering like spectral viscosity is required. Additional TV-filters are needed in most cases as postprocessors and the choice of the solver for the differential equations to integrate in time is crucial. The workshop was organised to bring together researchers from different areas of mathematics in order to fuel the research on high-order efficient and robust numerical methods.
- ItemVariational Methods for the Modelling of Inelastic Solids(Zürich : EMS Publ. House, 2018) Garroni, Adriana; Hackl, Klaus; Ortiz, MichaelThis workshop brought together two communities working on the same topic from different perspectives. It strengthened the exchange of ideas between experts from both mathematics and mechanics working on a wide range of questions related to the understanding and the prediction of processes in solids. Common tools in the analysis include the development of models within the broad framework of continuum mechanics, calculus of variations, nonlinear partial differential equations, nonlinear functional analysis, Gamma convergence, dimension reduction, homogenization, discretization methods and numerical simulations. The applications of these theories include but are not limited to nonlinear models in plasticity, microscopic theories at different scales, the role of pattern forming processes, effective theories, and effects in singular structures like blisters or folding patterns in thin sheets, passage from atomistic or discrete models to continuum models, interaction of scales and passage from the consideration of one specific time step to the continuous evolution of the system, including the evolution of appropriate measures of the internal structure of the system.
- ItemIntegral Geometry and its Applications(Zürich : EMS Publ. House, 2013) Bernig, Andreas; Schuster, FranzIn recent years there has been a series of striking developments in modern integral geometry which has, in particular, lead to the discovery of new relations to several branches of pure and applied mathematics. A number of examples were presented at this meeting, e.g. the work of Bernig, Solanes, and Fu on kinematic formulas on complex projective and complex hyperbolic spaces, that of Schneider and Vedel Jensen on tensor valuations and a series of results on convex body valued valuations by Abardia, Ludwig, Parapatits, and Wannerer.
- ItemLattice Differential Equations(Zürich : EMS Publ. House, 2013) Pelinovsky, Dmitry; Rapti, Zoi; Schneider, GuidoThe workshop focused on recent advances in the analysis of lattice differential equations such as discrete Klein-Gordon and nonlinear Schrödinger equations as well as the Fermi-Pasta-Ulam lattice. Lattice differential equations play an important role in emergent directions of modern science. These equations are fascinating subjects for mathematicians because they exhibit phenomena, which are not encountered in classical partial differential equations, on one hand, but they may present toy problems for understanding more complicated Hamiltonian differential equations, on the other hand.
- ItemMini-Workshop: Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions(Zürich : EMS Publ. House, 2017) Lang, Annika; Szpruch, Lukasz; Yaroslavtseva, LarisaThis Mini-Workshop is devoted to regularity and numerical analysis of stochastic ordinary and partial differential equations (SDEs for both). The standard assumption in the literature on SDEs is global Lipschitz continuity of the coefficient functions. However, many SDEs arising from applications fail to have globally Lipschitz continuous coefficients. Recent years have seen a prosper growth of the literature on regularity and numerical approximations for SDEs with non-globally Lipschitz coefficients. Some surprising results have been obtained – e.g., the Euler–Maruyama method diverges for a large class of SDEs with super-linearly growing coefficients, and the limiting equation of a spatial discretization of the stochastic Burgers equation depends on whether the discretization is symmetric or not. Several positive results have been obtained. However the regularity of numerous important SDEs and the closely related question of convergence and convergence rates of numerical approximations remain open. The aim of this workshop is to bring together the main contributers in this direction and to foster significant progress.
- ItemMini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems(Zürich : EMS Publ. House, 2015) Carlini, Enrico; Guardo, Elena; Harbourne, BrianIt is a fundamental challenge for many problems of significant current interest in algebraic geometry and commutative algebra to understand symbolic powers $I^{(m)}$ of homogeneous ideals $I$ in polynomial rings, particularly ideals of linear varieties. Such problems include computing Waring ranks of polynomials, determining the occurrence of equality $I^{(m)} = I^m$ (or, more generally, of containments $I^{(m)} \subseteq I^r$), computing Waldschmidt constants (i.e., determining the limit of the ratios of the least degree of an element in $I^{(m)}$ to the least degree of an element of $I^m$), and studying major conjectures such as Nagata’s Conjecture and the uniform SHGH Conjecture (which respectively specify the Waldschmidt constant of ideals of generic points in the plane and the Hilbert functions of their symbolic powers).
- ItemMini-Workshop: The p-Laplacian Operator and Applications(Zürich : EMS Publ. House, 2013) Lindqvist, Peter; Kawohl, BerndThere has been a surge of interest in the $p$-Laplacian in many different contexts from game theory to mechanics and image processing. The workshop brought together experts from many different schools of thinking to exchange their knowledge and points of view.
- ItemMoist Processes in the Atmosphere(Zürich : EMS Publ. House, 2019) Klein, Rupert; Smith, LeslieProcesses related to water in the atmosphere lead to severe uncertainties in weather forecasting and climate research. Atmospheric water vapor and cloud water strongly influence the Earth's energy budget through, e.g., energy conversions associated with phase changes, fluid dynamical effects associated with buoyancy, and through their influence on radiative transfer properties of the atmosphere. Given the critical green-house effect of water vapor, it seems astounding that climate modellers cannot with certainty state whether the Earth's cloud system has a positive or negative influence on the global mean temperature. The formation of clouds involves small-scale processes currently unresolved by climate models, and thus cloud cover is one of the main sources of uncertainty. This large uncertainty has its roots in the extremely wide range of length and time scales associated with moist processes, which pose an equally wide range of challenges to mathematical and computational modelling. New and innovative methods, modeling frameworks, efficient computational techniques, and complex statistical data analysis procedures as well as their mathematical analysis are urgently needed in order to make progress in this new field -- from the mathematicians point of view. One of the main goals of this workshop is to show the path forward for current and future applied mathematical scientists, to work hand in hand across the disciplines of mathematics, physics, and atmospheric science, in order to tackle the complex problem of dynamical and thermodynamical processes associated with clouds and moisture, both from the theoretical and the applied view points.