Hi, my name is Fangfei. My project is 'Brownina Motion and the Heat Equation'.

Motivation:

Brownian motion is a diffusion process. PDEs of diffusion type(such as heat question) are useful tools of studying the diffusion process. Conversely, diffusion processes give insight into solutions of diffusion type PDE. The connection between the heat equation and brownian motion is remarkable. In my project, I will demonstrate the relationships between brownian motion and the heat equation and also introduce the heat equation from probabilistic view.

Also:

There is one sample presentation from last year called ‘Random walk and PDE’. The random walk in continuous time and space becomes brownian motion. If you are interested in this material, you may read that presentation first.

Hope you will enjoy it!