Program
Topics in noncommutative geometry
Student No.:50
Time:Mon 10:00-11:50, 2017-02-20~ 2017-06-05 (except for public holidays)
Instructor:Si Li  [Tsinghua University]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-2-20
Ending Date:2017-6-5
 

 

Description:

 

 

Quantum world is noncommutative. This course aims to discuss certain aspects of homological methods in noncommutative geometry. We introduce basics on Hochschild, cyclic (co)homology and noncommutative Chern-Weil theory. As applications, we discuss several examples that arise from quantum field theories, including Kontsevich’s formality theorem, Ginzburg’s Calabi-Yau algebra, and Batalin-Vilkovisky’s quantization. At the end of the course, I will discuss my formalism with Costello on the B-twisted open-closed string field theory and its relation with homological mirror symmetry.

 
 

 

 

Prerequisite:

 

 

Basics on homological algebra, algebraic geometry and differential geometry. Some knowledge on quantum field theory will be helpful, but not required.

 

 

 

Reference:

 

 

JL Loday, Cyclic homology. Grundlehren Math.Wiss. 301, Springer (1998)

 

V Ginzburg, Lectures on Noncommutative Geometry. arXiv:math.AG/0506603

 

B Zwiebach, Oriented open-closed string theory revisited. arXiv:hep-th/9705241

 

M Kontsevich, Deformation quantization of Poisson manifolds. arXiv:math.QA/9709040

 

K Costello and S Li, Quantization of open-closed BCOV theory, I. arXiv:hep-th/1505.06703.

 

 

Other references used will be mentioned in the course.