Current Teaching


Fall 2022:  Classical Mechanics

Time: Sep 16 - Dec 26(Monday 9:50-11:25, Friday 8:00-9:35). Except for holiday.
Office hour: Tuesday 16:00-17:25 (JIngzhai 305)

Description:

This course discusses Lagrangian mechanics, Hamiltonian mechanics and their geometric aspects on symplectic geometry.


Spring 2022:  Homological Method in Quantum Field Theory

Time: March 16 - May 25(Wednesdays)20:00-21:30 Beijing time(15:00 - 16:30 Moscow time). Except for May 4 which is holiday.
Join Zoom Meeting:
Meeting ID:854 2246 3838
Passcode:073743
This is an invited course at Moscow and PKU

Description:

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.

Syllabus

The course note is updated here:
1. Introduction
2. Perturbative theory and Feynman Diagram
3. Homotopy Lie algebra and BRST
4. Effective BV Quantization
5. Quantization and Obstruction
6. Deformation Quantization and Algebraic Index
7. Topological Quantum Mechanics-I
8. Topological Quantum Mechanics-II
9. Two-dim Chiral QFT- I
10. Two-dim Chiral QFT- II

Spring 2022:  Math Reading Seminar

Time: Saturday 12:00-15:00
Location:  静斋
Communication: Wechat
Description: This is the continuation of the Student Reading seminar on "Differential forms in algebraic topology" (GTM 82) from Fall 2021.

Spring 2022:  Physics Reading Seminar

Time: Saturday 15:00-18:00
Location:  静斋
Communication: Wechat
Description: Student Reading seminar on Ising Model in statistical physics.


Fall 2021:  Reading Seminar

Time: Saturday 14:00-17:00
Location: 致远斋
Communication: Wechat

Description:

Reading seminar on "Differential forms in algebraic topology" (GTM 82). Details available upon request.


Spring 2021:  Algebraic Topology

Time: Mon & Wed 9:50-11:20
Starting Date: 2021-2-22
Ending Date: 2021-6-9

Description:

This course introduces homotopy and homology theory in algebraic topology.

Prerequisite:

Undergraduate algebra and topology.

References:

The course lecture is based on: Lectures in Algebraic Topology (2020 version) This is a version updated in 2020 spring, and will be further updated by the end of this semester.

Other main resources are:
Hatcher: Algebraic Topology
Bott and Tu: Differential forms in algebraic topology.
May: A Concise Course in Algebraic Topology
Spanier: Algebraic Topology.


Fall 2020:  Mathematical Analysis-I

Time: Mon 8:00-9:40 & Wed 9:50-12:25
Starting Date: 2020-9-14
Ending Date: 2020-12-30
Office hour: By appointment.

Description:

Functions of one variable.

Prerequisite:

Interest in mathematics, in understanding mathematics, in working with mathematics.

Spring 2020:  Algebraic Topology

Time: Tue & Fri 13:30-15:05
Place: The lectures will be taught online. Email to ask for course live stream link.
Starting Date: 2018-2-18
Ending Date: 2018-6-18

Description:

This course introduces homotopy and homology theory in algebraic topology.

Prerequisite:

Undergraduate algebra and topology.

References:

Our main resources are:
Hatcher: Algebraic Topology
Bott and Tu: Differential forms in algebraic topology.
May: A Concise Course in Algebraic Topology
Spanier: Algebraic Topology.

The course note is updated here: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24


Spring 2019:  Topics in noncommutative geometry

Time: Monday 9:50-11:25, Tuesday 13:30-3:05
Place: 6B306
Office hour: By appointment.
Distribution and Online discussion: WeChat group.

Prerequisite:

Algebraic Topology, Homological algebra, Lie algebras, differential manifold.

Fall 2018:  Geometry and Symmetry

Time: Wed 13:30-16:10
Office hour: Jingzhai 305. Friday 10:00-11:00. Other time by email appointment.
Grades: Weekly homework+ Midterm exam+ Final exam.
Distribution and Online discussion: WeChat group.
Course note: available upon request.

Description:

This is a freshman math course which explores the idea of group by geometric examples and applications.

Prerequisite:

interest in math.

Spring 2018:  Algebraic Topology

Time: Tue & Wed 15:20-16:55
Place: 6B303 Building 6
Starting Date: 2018-2-27
Ending Date: 2018-6-13
Office hour: Jingzhai 305. Wed 10:00-11:00. Other time by email appointment.
Grades: Weekly homework+ Midterm project+ Final project.
Distribution and Online discussion: WeChat group.

Description:

This course introduces homotopy and homology theory in algebraic topology.

Prerequisite:

Undergraduate topology.

References:

Our main resources are:
Hatcher: Algebraic Topology
Bott and Tu: Differential forms in algebraic topology.
May: A Concise Course in Algebraic Topology
Spanier: Algebraic Topology.

The course note is updated here: Note-AT


Fall 2017:  Topics in mathematical physics-supersymmetry

Time: Mon & Wed 09:50-11:25
Place: Conference Room 3, Floor 2, Jinchun Yuan West Building
Starting Date: 2017-10-9
Ending Date: 2018-1-3

Description:

This topic course aims at discussing various geometric structures underlying supersymmetric gauge theories and supergravities. After a general discussion on spinors and supersymmetry algebra in various dimensions, we will study supersymmetric theories with a Lagrangian description, mainly in four dimension and its lower dimensional reductions. The subject will be presented in geometric language in terms of G-structures, isometry groups, symmetric spaces and variation of Hodge structures. The course ends with a brief discussion on dualities and topological twistings, with an emphasis on Kapustin-Witten's theory on 4D N=4 Super Yang-Mills theory and Geometric Langlands.

Prerequisite:

Differential geometry, complex geometry, classical mechanics, Lie group and Lie algebra, Knowledge on quantum field theory would be very helpful.

References:

Our main resources are: S. Cecotti: Supersymmetric field theories.
D.Z. Freedman, A. van Proeyen: Supergravity
A. Kapustin, E. Witten: Electric-Magnetic duality and the geometric langlands program.
Other relevant references will be given in class.

Notes:

Typed note for this lecture will be updated every a couple of weeks. The lastest version is available here: SUSY


I teach topics in mathematical physics regularly at YMSC. Here are some previous lecture information.