Abstract: The real numbers are a completion of the rationals with respect to the usual absolute value, with the complex numbers as their only field extension. However, other completions of the rationals exist, one for each prime number $p$ and the associated $p$-adic absolute value. Extensions of these are called $p$-adic fields. Like the real and complex numbers, these spaces are Pontryagin self-dual, and admit an analogue of the Laplace operator using Fourier analysis. This operator defines an analogue of the heat equation, from which we can obtain a diffusion process. Time permitting, we will discuss some similarities and differences between these processes and their classical counterparts.

 

Oragnizers: Harry Richman (NCTS) & Wille Liu (Academia Sinica)