Fall 2024: **Mathematical Methods in Quantum Mechanics
**

Time: Monday 13:30-15:05, Friday 9:50-11:25

Tentative topics:

1. Deformation Quantization

2. Geometric Quantization

3. Stochastic Quantization

4. Spectral Theory

Fall 2024: ** Linear Algebra
**

Time: Monday 8:00-9:35, Friday 13:30-15:05

Spring 2024: **Mathematics in Poker
**

Time: Mar 2 - Apr 27 (Saturday 9-11). Enrollment via invitation.

Spring 2024: **Geometry and Physics
**

Time: Informal

Fall 2023: **Quantum Mechanics
**

Time: Sep 19 - Jan 4（Tuesday 8:00-9:35, Thursday 9:50-11:25). Except for holiday.

Fall 2023: **Ordinary Differential Equation
**

Time: Sep 19 - Jan 4（Tuesday 9:50-11:25, Thursday 8:00-9:35). Except for holiday.

Spring 2023: **Electrodynamics
**

Time: Feb 22 - June 22（Wednesday, Friday 8:00-9:35). Except for holiday.

Office hour: Tuesday 16:00-17:25 (JIngzhai 305)

**Description:**

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:**

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:**

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:**

Spring 2021: **Algebraic Topology **

Time: Mon & Wed 9:50-11:20

Starting Date: 2021-2-22

Ending Date: 2021-6-9

**Description:**

**Prerequisite:**

**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:**

**Prerequisite:**

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:**

**Prerequisite:**

**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:**

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:**

**Prerequisite:**

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:**

**Prerequisite:**

**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:**

**Prerequisite:**

**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:**

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

*Spring 2015: Topics in quantum field theory and geometric applications.*- Typed note for the first part of the lecture is available here
- The second part of the lecture was written into the paper arXiv:1612.01292[math.QA]

*2013 Summer school at MSC, Tsinghua University*: [Topics in quantum field theory] (introduction to Costello's renormalization theory)