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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
- ItemAlgebraische Zahlentheorie(Zürich : EMS Publ. House, 2014) Kings, Guido; Sujatha, Ramdorai; Venjakob, OtmarThe workshop brought together leading experts in Algebraic Number Theory. The talks presented new methods and results that intertwine a multitude of topics ranging from classical diophantine themes to modern arithmetic geometry, modular forms and p-adic aspects in number theory.
- ItemAlgebraic K-theory(Zürich : EMS Publ. House, 2019) Hesselholt, Lars; Huber-Klawitter, Annette; Kerz, MoritzAlgebraic $K$-theory has seen a fruitful development during the last three years. Part of this recent progress was driven by the use of $\infty$-categories and related techniques originally developed in algebraic topology. On the other hand we have seen continuing progress based on motivic homotopy theory which has been an important theme in relation to algebraic $K$-theory for twenty years.
- ItemAnalytic Number Theory(Zürich : EMS Publ. House, 2019) Matomäki, Kaisa; Vaughan, Robert C.; Wooley, Trevor D.Analytic number theory is a subject which is central to modern mathematics. There are many important unsolved problems which have stimulated a large amount of activity by many talented researchers. At least two of the Millennium Problems can be considered to be in this area. Moreover in recent years there has been very substantial progress on a number of these questions.
- ItemMini-Workshop: Singularities in G2-geometry(Zürich : EMS Publ. House, 2015) Haskins, Mark; Weiss, HartmutAll currently known construction methods of smooth compact $\mathrm G_2$-manifolds have been tied to certain singular $\mathrm G_2$-spaces, which in Joyce’s original construction are $\mathrm G_2$-orbifolds and in Kovalev’s twisted connected sum construction are complete G2-manifolds with cylindrical ends. By a slight abuse of terminology we also refer to the latter as singular $\mathrm G_2$-spaces, and in fact both construction methods may be viewed as desingularization procedures. In turn, singular $\mathrm G_2$-spaces comprise a (conjecturally large) part of the boundary of the moduli space of smooth compact $\mathrm G_2$-manifolds, and so their deformation theory is of considerable interest. Furthermore, singular $\mathrm G_2$-spaces are also important in theoretical physics. Namely, in order to have realistic low-energy physics in M-theory, one needs compact singular $\mathrm G_2$-spaces with both codimension 4 and 7 singularities according to Acharya and Witten. However, the existence of such singular $\mathrm G_2$-spaces is unknown at present. The aim of this workshop was to bring reserachers from special holonomy geometry, geometric analysis and theoretical physics together to exchange ideas on these questions.
- 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: Degeneration Techniques in Representation Theory(Zürich : EMS Publ. House, 2019) Fourier, Ghislain; Lanini, MartinaModern Representation Theory has numerous applications in many mathematical areas such as algebraic geometry, combinatorics, convex geometry, mathematical physics, probability. Many of the object and problems of interest show up in a family. Degeneration techniques allow to study the properties of the whole family instead of concentrating on a single member. This idea has many incarnations in modern mathematics, including Newton-Okounkov bodies, tropical geometry, PBW degenerations, Hessenberg varieties. During the mini-workshop Degeneration Techniques in Representation Theory various sides of the existing applications of the degenerations techniques were discussed and several new possible directions were reported.