Prof. Dr. Roland Speicher
Non-Commutative (Algebraic) Geometry(Winter Semester 2017/2018)
- The lecture on Monday, December 18, takes place in Zeichensaal (U.39) in (lecture hall-)building E2 5.
- The first exercise sheet is online.
- The lecture on Monday, December 11, takes place in SR9.
- The Thursday lectures start at 12:00 st.
LectureMonday, 10 -- 12, and Thursday, 12 -- 14
Lecture Hall IV, Building E2 4
Classical spaces (e.g., topological, measurable, geometric) can be encoded via functions on those spaces; and very often classical mathematical theories can be re-formulated in terms of the algebras of these functions. Clearly those function algebras are commutative. Non-commutative versions of these theories consist then in giving up the requirement of commutativity of the algebras, but keeping as much as possible of the remaining structures and ideas. Non-commutative geometry is such a non-commutative version of classical algebraic geometry.
Whereas classical algebraic geometry deals with solutions of systems of equations in commuting variables by looking on corresponding commutative algebras, non-commutative algebraic geometry is trying to deal with equations in non-commuting variables by looking on non-commutative algebras in a similar way.
At the moment there are many bits and pieces of such a theory, but the final picture has still to be found. We will address various pieces, like:
updated: 24 October 2017 Felix Leid