Inspired by several other (significantly more popular) blogs out there, I was tempted to write short summaries of my articles and generally ramble about mathematics here. This is still very much an experimental page and may yet disappear again.
From 9–24 November 2024, I taught at the National Higher School of Mathematics (NHSM) in Algiers, Algeria as part of the International Mathematics Masters Programme (IMM)1. Over the course of two weeks, I taught part of the “Advanced Probability” module, focusing on martingales and branching processes.
My article Minkowski weak embedding theorem1 with Stathis Chrontsios-Garitsis just got accepted at HJM, so it’s high time that I write a short summary.
The two sentence version: The Assouad embedding theorem loosely states that any metric space with finite Assouad dimension can be embedded into $\mathbb{R}^n$ without too much distortion. The Minkowski (or box-counting) dimension is smaller than the Assouad dimension and we show that an analogue of the Assouad embedding theorem still holds if one replaces the assumption of finite Assouad dimension with the weaker assumption of finite Minkowski dimension.
