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- ItemImplications of possible interpretations of ‘greenhouse gas balance’ in the Paris Agreement(London : The Royal Society, 2018) Fuglestvedt, J.; Rogelj, J.; Millar, R. J.; Allen, M.; Boucher, O.; Cain, M.; Forster, P. M.; Kriegler, E.; Shindell, D.The main goal of the Paris Agreement as stated in Article 2 is ‘holding the increase in the global average temperature to well below 2°C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5°C’. Article 4 points to this long-term goal and the need to achieve ‘balance between anthropogenic emissions by sources and removals by sinks of greenhouse gases'. This statement on ‘greenhouse gas balance’ is subject to interpretation, and clarifications are needed to make it operational for national and international climate policies. We study possible interpretations from a scientific perspective and analyse their climatic implications. We clarify how the implications for individual gases depend on the metrics used to relate them. We show that the way in which balance is interpreted, achieved and maintained influences temperature outcomes. Achieving and maintaining net-zero CO2-equivalent emissions conventionally calculated using GWP100 (100-year global warming potential) and including substantial positive contributions from short-lived climate-forcing agents such as methane would result in a sustained decline in global temperature. A modified approach to the use of GWP100 (that equates constant emissions of short-lived climate forcers with zero sustained emission of CO2) results in global temperatures remaining approximately constant once net-zero CO2-equivalent emissions are achieved and maintained. Our paper provides policymakers with an overview of issues and choices that are important to determine which approach is most appropriate in the context of the Paris Agreement.
- ItemClimate extremes, land–climate feedbacks and land-use forcing at 1.5°C(London : The Royal Society, 2018) Seneviratne, Sonia I.; Wartenburger, Richard; Guillod, Benoit P.; Hirsch, Annette L.; Vogel, Martha M.; Brovkin, Victor; van Vuuren, Detlef P.; Schaller, Nathalie; Boysen, Lena; Calvin, Katherine V.; Doelman, Jonathan; Greve, Peter; Havlik, Petr; Humpenöder, Florian; Krisztin, Tamas; Mitchell, Daniel; Popp, Alexander; Riahi, Keywan; Rogelj, Joeri; Schleussner, Carl-Friedrich; Sillmann, Jana; Stehfest, ElkeThis article investigates projected changes in temperature and water cycle extremes at 1.5°C of global warming, and highlights the role of land processes and land-use changes (LUCs) for these projections. We provide new comparisons of changes in climate at 1.5°C versus 2°C based on empirical sampling analyses of transient simulations versus simulations from the ‘Half a degree Additional warming, Prognosis and Projected Impacts’ (HAPPI) multi-model experiment. The two approaches yield similar overall results regarding changes in climate extremes on land, and reveal a substantial difference in the occurrence of regional extremes at 1.5°C versus 2°C. Land processes mediated through soil moisture feedbacks and land-use forcing play a major role for projected changes in extremes at 1.5°C in most mid-latitude regions, including densely populated areas in North America, Europe and Asia. This has important implications for low-emissions scenarios derived from integrated assessment models (IAMs), which include major LUCs in ambitious mitigation pathways (e.g. associated with increased bioenergy use), but are also shown to differ in the simulated LUC patterns. Biogeophysical effects from LUCs are not considered in the development of IAM scenarios, but play an important role for projected regional changes in climate extremes, and are thus of high relevance for sustainable development pathways.
- ItemSpectral Theory of Infinite Quantum Graphs(Cham (ZG) : Springer International Publishing AG, 2018) Exner, Pavel; Kostenko, Aleksey; Malamud, Mark; Neidhardt, HagenWe investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection together with spectral theory of (unbounded) discrete Laplacians on infinite graphs, we prove a number of new results on spectral properties of quantum graphs. Namely, we prove several self-adjointness results including a Gaffney-type theorem. We investigate the problem of lower semiboundedness, prove several spectral estimates (bounds for the bottom of spectra and essential spectra of quantum graphs, CLR-type estimates) and study spectral types.
- 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
- 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.