Symmetry, Almost

Explore the concept of symmetry and its mathematical implications in this 31-minute lecture from the Fields Institute. Delve into various definitions of symmetry, examining natural and mathematical examples such as snowflakes, butterflies, even and odd functions, fractals, matrices, and modular forms. Investigate the relationship between symmetry and beauty, questioning whether altering symmetries diminishes or enhances innate beauty. Focus on modular forms and their variants to understand the potential benefits of perturbing modular symmetries. Learn about the j-function, group actions, fundamental domains, mock theta functions, and quantum modular forms. Gain insights from Professor Amanda Folsom, a number theory specialist from Amherst College, as she explores the intricate world of "almost" symmetry in mathematics.

Intro
What is symmetry...?
The j-function (1800s)
A group action
Fundamental domains
Perturbing symmetry?
Mock theta functions
Symmetry, almost
Ramanujan revisited
Quantum modular forms
Mock, modular, and quantum symmetries