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- ItemMini-Workshop: Women in Mathematics: Historical and Modern Perspectives(Zürich : EMS Publ. House, 2017) Oswald, Nicola; Tobies, RenateThe aim of the workshop is to build a bridge between research on the situation of women in mathematics at the beginning of coeducative studies and the current circumstances in academia. The issue of women in mathematics has been a recent political and social hot topic in the mathematical community. As thematic foci we place a double comparison: besides shedding light on differences and similarities in several European countries, we complete this investigation by comparing the developments of women studies from the beginnings. This shall lead to new results on tradition and suggest improvements on the present situation.
- ItemAlgebraic Statistics(Zürich : EMS Publ. House, 2017) Kahle, Thomas; Sturmfels, Bernd; Uhler, CarolineAlgebraic Statistics is concerned with the interplay of techniques from commutative algebra, combinatorics, (real) algebraic geometry, and related fields with problems arising in statistics and data science. This workshop was the first at Oberwolfach dedicated to this emerging subject area. The participants highlighted recent achievements in this field, explored exciting new applications, and mapped out future directions for research.
- ItemAlgebraische Zahlentheorie(Zürich : EMS Publ. House, 2018) Sujatha, Ramdorai; Urban, Eric; Venjakob, OtmarThe origins of Algebraic Number Theory can be traced to over two centuries ago, wherein algebraic techniques are used to glean information about integers and rational numbers. It continues to be at the forefront of
- ItemAlgebraic K-theory and Motivic Cohomology(Zürich : EMS Publ. House, 2016) Huber-Klawitter, Annette; Jannsen, Uwe; Levine, MarcAlgebraic $K$-theory and motivic cohomology have developed together over the last thirty years. Both of these theories rely on a mix of algebraic geometry and homotopy theory for their construction and development, and both have had particularly fruitful applications to problems of algebraic geometry, number theory and quadratic forms. The homotopy-theory aspect has been expanded significantly in recent years with the development of motivic homotopy theory and triangulated categories of motives, and $K$-theory has provided a guiding light for the development of non-homotopy invariant theories. 19 one-hour talks presented a wide range of latest results on many aspects of the theory and its applications.
- ItemMini-Workshop: Fast Solvers for Highly Oscillatory Problems(Zürich : EMS Publ. House, 2016) Börm, Steffen; Le Borne, Sabine; Martinsson, Per-GunnarThe efficient numerical solution of highly oscillatory problems is one of the grand challenges of Applied Mathematics with diverse applications across the natural sciences and engineering. This workshop brings together experts in domain based methods and integral equation methods to share novel ideas and to discuss challenges on the way to developing efficient solvers at high frequencies.
- ItemMini-Workshop: Asymptotic Invariants of Homogeneous Ideals(Zürich : EMS Publ. House, 2018) Cooper, Susan; Harbourne, Brian; Szpond, JustynaRecent decades have witnessed a shift in interest from isolated objects to families of objects and their limit behavior, both in algebraic geometry and in commutative algebra. A series of various invariants have been introduced in order to measure and capture asymptotic properties of various algebraic objects motivated by geometrical ideas. The major goals of this workshop were to refine these asymptotic ideas, to articulate unifying themes, and to identify the most promising new directions for study in the near future. We expect the ideas discussed and originated during this workshop to be poised to have a broad impact beyond the areas of algebraic geometry and commutative algebra.
- ItemMini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory(Zürich : EMS Publ. House, 2018) Manon, Christopher; Mixon, Dustin G.; Vinzant, CynthiaFrames are collections of vectors in a Hilbert space which have reconstruction properties similar to orthonormal bases and applications in areas such as signal and image processing, quantum information theory, quantization, compressed sensing, and phase retrieval. Further desirable properties of frames for robustness in these applications coincide with structures that have appeared independently in other areas of mathematics, such as special matroids, Gel’Fand-Zetlin polytopes, and combinatorial designs. Within the past few years, the desire to understand these structures has led to many new fruitful interactions between frame theory and fields in pure mathematics, such as algebraic and symplectic geometry, discrete geometry, algebraic combinatorics, combinatorial design theory, and algebraic number theory. These connections have led to the solutions of several open problems and are ripe for further exploration. The central goal of our mini-workshop was to attack open problems that were amenable to an interdisciplinary approach combining certain subfields of frame theory, geometry, and combinatorics.
- 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.
- ItemMini-Workshop: Gibbs Measures for Nonlinear Dispersive Equations(Zürich : EMS Publ. House, 2018) Schlein, Benjamin; Sohinger, VedranIn this mini-workshop we brought together leading experts working on the application of Gibbs measures to the study of nonlinear PDEs. This framework is a powerful tool in the probabilistic study of solutions to nonlinear dispersive PDEs, in many ways alternative or complementary to deterministic methods. Among the special topics discussed were the construction of the measures, applications to dynamics, as well as the microscopic derivation of Gibbs measures from many-body quantum mechanics.
- ItemMini-Workshop: Spaces and Moduli Spaces of Riemannian Metrics(Zürich : EMS Publ. House, 2017) Tuschmann, WilderichThe mini-workshop focused on central questions and new results concerning spaces and moduli spaces of Riemannian metrics with lower or upper curvature bounds on open and closed manifolds and, moreover, related themes from Anosov geometry. These are all described in detail below. The event brought together young and senior researchers working about (moduli) spaces of negative and nonnegative sectional, nonnegative Ricci and positive scalar curvature as well as Anosov metrics, and the talks and discussions brought about many new and inspiring research problems to pursue.