中央研究院數學研究所

Taipei Postdoc Seminar

Diffusion Processes in p-adic Fields and Vector Spaces

2026/03/11 (Wed.) 14:00~15:00

Date : 2026/03/11 (Wed.) 14:00~15:00
Location : Room 515, Cosmology Building, NTU
Speaker : Rahul Rajkumar (Academia Sinica)
Organizer : Wille Liu (AS), Harry Richman (NCTS)
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.