Methods of Noncommutative Geometry 1000-1S21MGN
The topics of the seminar will include the following tools used in the study of topological spaces and operator algebras:
- the Dirac operator and spectral triples,
- local index formula and K-homology,
- Hopf-cyclic homology and foliations,
- unbounded representatives in Kasparov KK-theory,
- quantum symmetries and equivariant spectral triples.
Type of course
Mode
Course coordinators
Learning outcomes
Knowledge and skills:
1. Understanding the classical relationships between spaces and algebras.
2. Understanding the subtle relationship between Dirac operators and the manifold structure.
3. Knowledge of the basic concepts of noncommutative geometry.
4. Knowledge of the basic methods of differential geometry, differential operators, homological algebra and functional analysis used in solving problems of geometry and representation theory, crowned by the first glimpse into the theory of operator algebras.
5. Ability to prepare and deliver lectures of varying degrees of difficulty on the basis of the assigned reading.
Social competence:
1. Ability to cooperate with representatives of the physical sciences in building mathematical models in physics (e.g., noncommutative versions of the Standard Model of elementary particles).
2. Ability to deliver mathematical lectures understandable for representatives of other sciences and lectures for mathematicians on mathematical models in physics.
3. Ability to popularize modern mathematics.
Assessment criteria
Delivering a talk at the seminar.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: