449 results
Search Results
Now showing 1 - 10 of 449
- ItemzbMATH Open: API Solutions and Research Challenges(Aachen, Germany : RWTH Aachen, 2021) Petrera, Matteo; Trautwein, Dennis; Beckenbach, Isabel; Ehsani, Dariush; Müller, Fabian; Teschke, Olaf; Gipp, Bela; Schubotz, Moritz; Balke, Wolf-Tilo; de Waard, Anita; Fu, Yuanxi; Hua, Bolin; Schneider, Jodi; Song, Ningyuan; Wang, XiaoguangWe present zbMATH Open, the most comprehensive collection of reviews and bibliographic metadata of scholarly literature in mathematics. Besides our website zbMATH.org which is openly accessible since the beginning of this year, we provide API endpoints to offer our data. APIs improve interoperability with others, i.e., digital libraries, and allow using our data for research purposes. In this article, we (1) illustrate the current and future overview of the services offered by zbMATH; (2) present the initial version of the zbMATH links API; (3) analyze potentials and limitations of the links API based on the example of the NIST Digital Library of Mathematical Functions; (4) and finally, present thezbMATHOpen dataset as a research resource and discuss connected open research problems.
- ItemMathematics in Wikidata(Aachen, Germany : RWTH Aachen, 2021) Scharpf, Philipp; Schubotz, Moritz; Gipp, Bela; Kaffee, Lucie-Aimée; Razniewski, Simon; Hogan, AidanDocuments from Science, Technology, Engineering, and Mathematics (STEM) disciplines usually contain a signicant amount of mathematical formulae alongside text. Some Mathematical Information Retrieval (MathIR) systems, e.g., Mathematical Question Answering (MathQA), exploit knowledge from Wikidata. Therefore, the mathematical information needs to be stored in items. In the last years, there have been efforts to define several properties and seed formulae together with their constituting identifiers into Wikidata. This paper summarizes the current state, challenges, and discussions related to this endeavor. Furthermore, some data mining methods (supervised formula annotation and concept retrieval) and applications (question answering and classification explainability) of the mathematical information are outlined. Finally, we discuss community feedback and issues related to integrating Mathematical Entity Linking (MathEL) into Wikidata and Wikipedia, which was rejected in 33% and 12% of the test cases, for Wikidata and Wikipedia respectively. Our long-term goal is to populate Wikidata, such that it can serve a variety of automated math reasoning tasks and AI systems.
- 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.
- ItemMini-Workshop: Superpotentials in Algebra and Geometry(Zürich : EMS Publ. House, 2020) González, Eduardo; Rietsch, Konstanze; Williams, LaurenMirror symmetry has been at the epicenter of many mathematical discoveries in the past twenty years. It was discovered by physicists in the setting of super conformal field theories (SCFTs) associated to closed string theory, mathematically described by $\sigma$-models. These $\sigma$-models turn out in two different ways: the A-model and the B-model. Physical considerations predict that deformations of the SCFT of either $\sigma$-model should be isomorphic. Thus the mirror symmetry conjecture states that the A-model of a particular Calabi-Yau space $X$ must be isomorphic to the B-model of its mirror $\check{X}$. Mirror symmetry has been extended beyond the Calabi-Yau setting, in particular to Fano varieties, using the so called Landau-Ginzburg models. That is a non-compact manifold equipped with a complex valued function called the \emph{superpotential}. In general, there is no clear recipe to construct the mirror for a given variety which demonstrates the need of joining mathematical forces from a wide range. The main aim of this Mini-Workshop was to bring together experts from the different communities (such as symplectic geometry and topology, the theory of cluster varieties, Lie theory and algebraic combinatorics) and to share the state of the art on superpotentials and explore connections between different constructions.
- 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.