Lecture (webinar) from a special course

of the Chinese-Russian Mathematical Center

«Homological Method in Quantum Field Theory»

Lecturer
	Si Li Professor, YMSC, Tsinghua University
Bio: Si Li (李思) got his Ph.D. in mathematics from Harvard University in 2011. He is currently a professor at Yau Mathematical Sciences Center (YMSC), Tsinghua University. He works on algebraic and geometric aspects of quantum field theory and string theory.

This course introduces basic ideas and various recent mathematical developments about quantization that arises from quantum field theory and string theory. The focus is on homological method and its applications in geometry and topology.

The course is addressed to senior and postgraduate students of Mathematics and Physics interested in studying the methods and ideas of modern Mathematical and Theoretical Physics and related topics in Mathematics. The prerequisits are Linear Algebra, Calculus, basic ideas from Differential Equations and Differential Geometry. Some acquaintance with Homological Algebra and Topology is advisable, but not necessary.

Tentative syllabus about the subjects to be covered in this course:

1. Perturbative theory and Feynman diagram
2. Homotopy algebras and transfer
3. Maurer-Cartan equation and moduli
4. BRST-BV formalism
5. Renormalization and effective field theory
6. Deformation quantization 7. Topological quantum mechanics and index theory
7. 2d chiral conformal field theory and BV quantization
8. Chiral homology and chiral index 10. Topological B-model on Calabi-Yau geometry
9. ^* Holomorphic Chern-Simons: Large N method
10. ^* Boundary-Bulk and boundary transfer
11. ^* Koszul duality and holography

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^* The last three topics are tentative, to be covered if time permits.

The lecture will be held in English in the form of a webinar on the Zoom platform.

20:00 - 21:30 Beijing time（15:00 - 16:30 Moscow time)

Join Zoom Meeting:

https://zoom.us/j/85422463838?pwd=ZmtCOEExMEFmT21jeWY1QUZ0Y3VFQT09

Meeting ID：854 2246 3838

Passcode：073743

(link may change closer to the event)

• lecture notes (PDF)

Lecture recording