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Beliaev, D; Smirnov, S (Ed.)
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Asok, Aravind; Fasel, Jean (, Proceedings of the International Congress of Mathematicians)Beliaev, D; Smirnov, S (Ed.)We survey recent developments related to the problem of classifying vector bundles on algebraic varieties. We focus on the striking analogies between topology and algebraic geometry, and the way in which the Morel–Voevodsky motivic homotopy category can be used to exploit those analogies.more » « less
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De_Lellis, Camillo (, European Mathematical Society Publishing House)Beliaev, D; Smirnov, S (Ed.)
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Dobrinen, Natasha (, EMS Press)Baliaev, D; Smirnov, S (Ed.)This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems. Exciting recent developments include new methods involving logic, topological Ramsey spaces, and category theory. The paper concentrates on big Ramsey degrees, presenting their essential structure where known and outlining areas for further development. Cognate areas, including infinite dimensional Ramsey theory of homogeneous structures and partition theory of uncountable structures are also discussed.more » « less
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