When:
Monday, February 24, 2025
4:00 PM - 5:00 PM CT
Where: Lunt Hall, 107, 2033 Sheridan Road, Evanston, IL 60208 map it
Audience: Faculty/Staff - Student - Public - Post Docs/Docs - Graduate Students
Contact:
Rachel Greenfeld
Group: Department of Mathematics: Analysis Seminar
Category: Lectures & Meetings
Title: Embeddings into Euclidean spaces without shrinking
Abstract: We study the problem which spaces $(X,\rho)$ can be embedded into ${\mathbb R}^d$ without decreasing any of the distances in $X$. That is, we ask the question whether there is an $f:\,X\to{\mathbb R}^d$ such that $\|x-y\|\ge\rho(x,y)$ for every $x,y\in X$. Our aim is to find necessary and sufficient conditions under which such a mapping exists, and to show how this can be used to generalize/disprove some classical results in real analysis.