Abstract:

Drinking coffee in daily life can help us to observe surprising and beautiful topological principles. Suppose we gently stir the coffee, when the coffee becomes still，there must be a coffee molecule that returns to the initial position. This phenomenon can be described by the classical Brouwer fixed point theorem, which can be proven using algebraic topology method. Gently swirl the pitcher, the latte art pattern becomes more and more complex, but the abstract pattern will remain the same. This reflects the dynamics of surface homeomorphisms, and can be proven using Teichmuller space theory and Brouwer fixed point theorem.