MBTDO Introduction to bundle theory and Dirac operators

Faculty of Science
Spring 2020
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Dr. Ioannis Chrysikos (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 16:00–18:50 MS1,01016
Prerequisites
the course is suitable for students interested in modern geometric analysis
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course aims at basic orientation in some essential geometric and analytic concepts appearing in differential geometry and mathematical physics
Learning outcomes
knowledge of the topics mentioned in the detailed syllabus
Syllabus
  • 1 Bundle theory 1 (basic aspects+topology) 2 Bundle theory 2 (connections+geometry) 3 Clifford algebras (basic aspects+classification) 4 Clifford algebras, spin group and spin representations 5 Spin structures, spinorial calculus and Dirac operator 6 Dirac operator and twistor operator (basic properties+applications) 7 Conformal invariance and twistor spinors 8 SL-formula, harmonic spinors, and Atiyah Singer Index Theorem 9 Special spinors, parallel spinors and Killing spinors (classification)
Teaching methods
standard lectures
Assessment methods
oral exam
Language of instruction
English
Further comments (probably available only in Czech)
Study Materials
The course is taught only once.
Teacher's information
The first lecture in the course will take place on Wednesday, February 19 and it will also include agreement on the schedule (3 hours lectures, but not every week).
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