# Category Archives: Lecture

## Symplectic Maps and Flows

Consider a physical system consisting of $k$ massive particles at positions in $\mathbb{R}^3$ which we can assemble in a vector in $\mathbf{q}\in\mathbb{R}^m$ where $m=3k$. Likewise, the velocities of these particles at a given instant of time can be described by … Continue reading

## Plateau problem

Let $\Sigma = (V,E,F)$ be a triangulated surface (with boundary). A realization of the surface in $\mathbb{R}^3$ is given by a map $p:V \rightarrow \mathbb{R}^3$ such that $p_i,p_j,p_k$ form a non degenerated triangle in $\mathbb{R}^3$ for all $\{i,j,k\} \in \Sigma$, … Continue reading