# Non-commutative geometry

Course Code : | 2001WETNGQ |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

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 |

### 1. Prerequisites *

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

### 2. Learning outcomes *

- 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.

### 3. Course contents *

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.

### 4 International dimension*

The course has an international dimension.

### 5. Teaching method and planned learning activities

Class contact teachingLectures Seminars/Tutorials Skills training

Personal workExercises Assignments Individually

Personal work

### 6. Assessment method and criteria

ExaminationOral with written preparation Closed book

Continuous assessmentExercises

Continuous assessment

### 7. Study material *

#### 7.1 Required reading

Course notes will be uploading to the blackboard.

**7.2 Optional reading**

The following study material can be studied voluntarily :The main reference books are:

Ch. Weibel, Introduction to homological algebra.

J.-L. Loday, Cyclic homology

### 8. Contact information *

Prof. Boris Shoikhet

Boris.Shoikhet@uantwerpen.be