Picture language in mathematics
Student No.:50
Time:Wed/Fri 13:20-14:50, 2017-05-12~2017-05-31
Instructor:Zhengwei Liu  [Harvard University]
Place:Conference Room 4, floor 2, Jin Chun Yuan West Building
Starting Date:2017-5-12
Ending Date:2017-5-31



Mathematicians have used pictures since the evolution of Euclidean geometry in ancient Greece. More recently pictures played a central role in the formulation and understanding of various areas in mathematics. We will talk about the analytic, algebraic and topological aspects of pictures.


1.      From algebras to planar algebras

2.      The free product and quotients

3.      Schur-Weyl duality since 1901

4.      Fourier analysis on the plain

5.      Quon language in quantum information

6.      Fourier duality





I will try to give talks for general audiences major in mathematics.


Topological quantum field theory, M. Atiyah

Planar algebra I, V. F. R. Jones

Noncommutative uncertainty principles, C. Jiang, Z. Liu and J. Wu

Yang-Baxter relation planar algebras, Z. Liu

Quon 3D language for quantum information, Z. Liu, A. Wozniakowski and A. Jaffe.