Course Code : | 2001WETNGQ |

Study domain: | Mathematics |

Bi-anuall course: | Taught in academic years starting in an even year |

Academic year: | 2019-2020 |

Semester: | 2nd semester |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | English |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Boris Shoykhet |

At the start of this course the student should have acquired the following competences:

an active knowledge of

general notion of the basic concepts of

specific prerequisites for this course

an active knowledge of

- English

- general knowledge of the use of a PC and the Internet

general notion of the basic concepts of

General knowledge of Set theory and Linear algebra

specific prerequisites for this course

Algebra and Differential geometry on Bachelor level

- The students will know basic things about deformation theory of associative algebras and about Hochschild cohomology.
- The students will get acquainted with the contemporary approach to deformation theory via differential graded algebras, Lie algebras, etc. and their formalities.
- The students will get acquainted with the ``mathematical physics´´ approach to deformation quantisation problem, via the Kontsevich formality. As well, the students get some fluency in homological algebra computations.

We start with the problem of deformation quantization.

Then the Hochschild homology naturally appear, as well as their non-linear structure, the Gerstenhaber bracket.

We formulate the Kontsevich's formality theorem and show that its solution implies a solution of the deformation quantization problem.

We discuss the original proof by Kontsevich of his formality theorem.

The course has an international dimension.

Class contact teachingLectures Seminars/Tutorials Skills training

Personal workExercises Assignments Individually

Personal work

ExaminationOral with written preparation Closed book

Continuous assessmentExercises

Continuous assessment

Course notes will be uploading to the blackboard.

The main reference books are:

Ch. Weibel, Introduction to homological algebra.

J.-L. Loday, Cyclic homology

Prof. Boris Shoikhet

Boris.Shoikhet@uantwerpen.be