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Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Algebraic geometry is the field of mathematics which concerns the study of spaces cut out by polynomial equations. This workshop concern the interaction of two important objects in algebraic geometry - the K-groups and the Brauer group. In algebraic geometry, we study spaces via invariants - the procedure of attaching simpler, more "linear" objects to these spaces in the hope of extracting information about them. Both the K-groups and Brauer group are such examples which have had an excellent track record in being both powerful and accessible at the same time. Roughly speaking, the K-groups are built out from \emph{vector bundles} on such a space - a continuous assignment of vector spaces on each point of the space. On the other hand the Brauer groups are built from "twisted" vector bundles. Both invariants have had a history of interaction and cross-pollination and the goal of the workshop is to bring together researchers in both areas to share their research and pave the way for even more fruitful interaction in the future. We are particularly excited about the prospect of new, field-driving questions to come out from this workshop.

Algebra,    Kurse und Veranstaltungen für Studenten der Mathematik

Casa Matemática Oaxaca (CMO)

Recently, a lot of efforts have been for made the development of quantum technologies. Against this background, and partly motivated by it, the study of quantum channels and their continuous version, quantum Markov semigroups, has undergone an active development as a part of the mathematical framework of the theory. Because the new mathematical developments are being driven by problems arising in a wide variety of potential applications, it is especially timely to bring both seasoned researches, who are leading the various different aspects of the recent advances in the field, together with young recently graduated PhD in order to develop a general perspective of the current research advances, problems and opportunities. We welcome young researchers interested in these topics. The main topics of the workshop will include: Quantum Gaussian states and semigroups, Generalized quantum Gaussian semigroups, Weak-coupling, low density, digraph induced and G-circulant semigroups, Invariant states, attraction domains and decoherence-free subalgebras, applications to quantum transport and information theory.