Mathematics Graduate Students Organization

Seminar:

Date: April 23

A metric space is a natural concept to use whenever we want to quantify how different objects in a collection are, so metric spaces show up everywhere both in pure mathematics and in applications. Unfortunately, the idea is so general and abstract that it is very difficult to detect any structure in a given metric space. For that reason it is useful to embed metric spaces into normed spaces, where we have lots and lots of tools from geometry, functional analysis and even algebra at our disposal. In this talk we will review the basic concepts, look at the limitations of this kind of embeddings, state a couple of the most important mathematical results in the area and show a few examples of the applications of this type of thinking. The talk will be quite elementary, and the mathematical background required practically nonexistent. Basic familiarity with R^n (endowed with the Euclidean distance) will be more than enough.