UH

Electrons in a magnetic field experience a drift transverse to their velocity, which gives rise to intriguing effects such as the whole family of Hall Effects. Interestingly, this drift can also appear without a charged particle and without magnetic field, i.e. for ultra-cold quantum gases in optical lattices with non-trivial topology, described by a Berry curvature. This enables researchers to use the tunability of quantum gases and allow for studies beyond the possibilities of condensed matter systems. Furthermore, it allows to mimic and study in great detail fascinating effects such as topological insulators and edge-states. Especially, the interplay between topology and interactions is not well understood and the existence of many interesting states, such as topological insulators, fractional Chern insulators and topological superfluids, is predicted, but have not yet been observed. In recent years, great progress has been made in engineering topological band structures for quantum gases. Whereas theoretical proposals are well developed, so far there are only few experimental realizations of topological band structures, especially for fermionic quantum gases. In this action, we want to create non-trivial topological band structures and explore (many-body) phases that can emerge for fermions and mixtures of bosons and fermions. We will map out the Berry curvature and study the detection of edge states, which provides a clear signature of a non-trivial topology. For the first time, we will realize a new creation and detection method for topological band structures and study high spin Fermi systems in topological optical lattices.

SIHAFA explores the late Ottoman (1890s–1918) Arabic ideosphere of the Eastern Mediterranean through its periodical press. SIHAFA transcends the individual periodical for a systematic and computational study of the periodical press as a discursive field and at scale in order to better understand both the intellectual history of the Eastern Mediterranean at a crucial historical juncture and periodical production itself. As MSCA fellow, Dr. Grallert will receive crucial training at Universität Hamburg and will scrutinise a digital corpus of seven Arabic journals from Baghdad, Beirut, Cairo and Damascus with more than 7 million words (the result of his current research) through a combination of stylometric authorship attribution, social network analysis, and close reading of bio-bibliographical dictionaries. He will evaluate theoretical and methodological approaches, workflows, and tools developed in the Global North for their applicability to cultural heritage of the Global South. A secondment at Uniwersytet Jagielloński will provide methodological training in stylometry. The research objectives are to: (1) fill a gap in research by developing and evaluating methods for the study of Arabic periodicals; (2) challenge established narratives of the Arabic Renaissance (nahda) by re-introducing non-Syrian and Muslim authors and periodicals from beyond Cairo and Beirut commonly ignored by scholarly literature through the leading research question "What were the core nodes of authors and periodicals in this ideosphere and how did they change over time?"; (3) help establish the field of Arab Periodical Studies through community building across the postcolonial north-south divide. SIHAFA is committed to FAIR data and open access. Dr. Grallert will produce and publish: ground-breaking research to be published in English and Arabic; improved digital scholarly editions; authority files; an OCR model for Arabic periodicals; and a plain text corpus of authorship candidates.

This proposed research is in mathematical logic and foundations of mathematics, more specifically in set theory. It is motivated by the interplay between regularity properties and definability for subsets of real numbers. By "regularity properties" we are referring to certain desirable properties of sets, and by "definability" to the logical description of such sets, in the sense of Descriptive Set Theory. The study of such questions goes back to classical issues in topology, analysis and related fields of mathematics, raised by the great pioneers of abstract mathematics of the late 19th and early 20th century, such as Georg Cantor, Emile Borel, Henri Lebesgue and others. These mathematicians were faced with seemingly insurmountable challenges which could only be resolved later with the advent of logical and meta-mathematical methods, developed by Kurt Gödel in 1938 and by Paul Cohen in 1964. Since that time, the study of Regularity Properties has continued to hold a central position in the foundations of mathematics. Many mathematicians and logicians of high status and prestige have contributed to this area, among them W. Hugh Woodin (winner of the Hausdorff Medal 2013), Stevo Todorčević (winner of the CRM-Fields-PIMS prize 2012) and Saharon Shelah (winner of numerous awards, among them the Erdös Prize 1977 and the Karp Prize 1983). We propose to contribute to this line of research in a number of interrelated directions, such as: studying new regularity properties (relevant to other fields of mathematics), developing abstract frameworks for such properties, studying higher complexity classes, and generalising results to spaces other than the classical real numbers. Several technical results involving the method of "forcing" needed to construct models of set theory, will also be worked out along the way.