セミナー

談話会

タイトル Symmetries of quantum spaces
開催日時 2015年7月24日 17:00~18:00
主催者
講演者 Sven Raum 氏(Marie Curie International Outgoing Fellow/京都大学数理解析研究所)
場所 矢上キャンパス14棟631A/B
内容 In 1936, Murray and von Neumann introduced a class of complex algebras that they termed "rings of operators". They were motivated, as they say, by applications in quantum mechanics and unitary representation theory. Nowadays the algebras they introduced are called "von Neumann algebras" and constitute the birth of the subject of operator algebras in general. In this talk we introduce and motivate von Neumann algebras, which can be thought of as "noncommutative measure spaces". Our first aim is to make the audience acquainted with von Neumann algebras by describing several natural occurrences from group representations, ergodic theory and mathematical physics. Our second aim is to point out new and interesting phenomena arising in the "noncommutative setting" by considering possible symmetries of a von Neumann algebra. We mean to make the audience think about a non-classical point of view on how to interpret the word "symmetry" in mathematics.
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