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Lectures and seminars on current research in noncommutative geometry.
Last update: Šmíd Dalibor, Mgr., Ph.D. (15.05.2022)
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The seminar is concerned with noncommutative geometry in a broad sense. As was realised over the course of the 20th century, many geometric and topological structures can be expressed in terms of the function algebra of a manifold, or algebraic variety. The general philosophy behind noncommutative geometry is to extend such structures to certain types of noncommutative algebras, which despite their noncommutativity, share many similarities with function algebras. The seminar has two distinct but related trends. First is the C*-algebra approach, stemming from the Gelfand theorem which states that the category of compact Hausdorff spaces and commutative C*-algebras are dual. The second is the quantum group approach, which looks at Hopf algebras as noncommutative generalisations of Lie groups, focusing in particular on q-deformations of the universal enveloping algebra of a complex semisimple Lie algebra.
Prerequisites for the seminar are a good understanding of the basics of either of these two trends. For the C*-algebraic approach, the student should have a good grasp of functional analysis, in particular Hilbert spaces and their bounded operators. They should also be comfortable with point set topology. For the quantum group approach the student should have a good algebraic background and some exposure to category theory. Moreover, they should should have taken a course in Lie groups and Lie algebras, and preferably be comfortable with the basics of differential geometry. Last update: Šmíd Dalibor, Mgr., Ph.D. (15.05.2022)
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Papers and books recommended by the lecturers. Last update: Šmíd Dalibor, Mgr., Ph.D. (15.05.2022)
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Programme of the seminar is specified by its members at the beginning of each semester. Last update: Šmíd Dalibor, Mgr., Ph.D. (15.05.2022)
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