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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Non-commutative homotopy theory SemesterWiSe 2026 / 27 Lecturer Ulrich Bunke Type of course (Veranstaltungsart) Vorlesung German title Nichtkommutative Homotopietheorie Contents Non-commutative homotopy theory in the sense of this lecture course is the study of C*-algebras via homological functors. We will start with an introduction to C*-Algebras from a categorical perspective. We will discuss Gelfand duality and properties of unitaries and projections. We further introduce concepts like multiplier algebras and tensor products. We then introduce homological functors and explain C*-algebra K-theory as a particular example. The central theme is the motivic perspective. We will study the universal examples of homological functors, known as KK and E-theory. We will construct them and study basic properties of their targets. We will discuss applications to index theory and algebraic topology. This course will be continued in the summer semester to capture equivariance and parametrization. This course is intended for master students and PhD-students. It does not require pre-knowledge on C*-algebras. Some experience in the usage of categorical language (limits, colimits, adjoint functors) is eligible. We will introduce infinity-categorical language on demand. Literature Besides the standard textbooks for the foundations of C*-algebra theory see also https://bunke.app.uni-regensburg.de/VorlesungCastcats-1.pdf. Later parts of this course are based on https://arxiv.org/abs/2304.12607. Time/Date Mo, Do 10-12 Location M102 Additional question session Time/Date: Mo 12-14 Location: Course homepage https://bunke.app.uni-regensburg.de (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
MV, MGAGeo ECTS 9 |