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, Xiaoguang

We 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.

2012, Carstensen, Carsten, Schröder, Jörg, Wriggers, Peter

The finite element method is the established simulation tool for the numerical solution of partial differential equations in many engineering problems with many mathematical developments such as mixed finite element methods (FEMs) and other nonstandard FEMs like least-squares, nonconforming, and discontinuous Galerkin (dG) FEMs. Various aspects on this plus related topics ranging from order-reduction methods to isogeometric analysis has been discussed amongst the pariticpants form mathematics and engineering for a large range of applications.

2008, Stephan, Ernst P.

[no abstract available]

2005, Derezinski, Jan, Solovej, Jan-Philip

The MFO-Workshop 0538 Analysis and Quantum Theory focussed on problems in mathematical physics, especially those connected to quantum field theory. Several theoretical physicists introduced a mostly mathematically oriented audience to topics in theoretical physics such as perturbative quantum field theory and fractional quantum Hall effect, thus bridging the gap between theoretical physics and mathematics. Apart from these reviews, a selection of research reports on recent results in mathematical physics was presented.

2021, Scharpf, Philipp, Schubotz, Moritz, Gipp, Bela, Kaffee, Lucie-Aimée, Razniewski, Simon, Hogan, Aidan

Documents 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.

2017, Kahle, Thomas, Sturmfels, Bernd, Uhler, Caroline

Algebraic 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.

2013, Huber-Klawitter, Annette, Jannsen, Uwe, Levine, Marc

Algebraic K-theory and motivic cohomology are strongly related tools providing a systematic way of producing invariants for algebraic or geometric structures. The definition and methods are taken from algebraic topology, but there have been particularly fruitful applications to problems of algebraic geometry, number theory or quadratic forms. 19 one-hour talks presented a wide range of latest results on the theory and its applications.

2017, Oswald, Nicola, Tobies, Renate

The 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.

2002, Jansen, Klaus, Schiermeyer, Ingo

[no abstract available]

2010, Gaboriau, Damien, Grunewald, Fritz

The workshop brought together experts in finite group theory, L2-cohomology, measured group theory, the theory of lattices in Lie groups, probability and topology. The common object of interest was residually finite groups, that each field investigates from a different angle.