• Speaker: Edem Boahen, MSU
• Title: On outer Bi-Lipschitz Extensions of Linear JL-map embeddings of low-dimensional submanifolds of R^n
• Date: 03/20/2023
• Time: 2:00 PM - 3:00 PM
• Place: C329 Wells Hall (Virtual Meeting Link)
• Contact: Craig Gross (grosscra@msu.edu)

Dimensionality reduction is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. A classical embedding result is the well-know “Johnson–Lindenstrauss”. The JL lemma shows how a $n$-set of points in $\mathbb{R}^N$ can be embedded into a smaller dimensional space. In this talk we present a result similar to the JL-embedding in the interesting case where instead of a discrete set we embed a compact $d$-dimensional submanifold $\mathcal{M}$ of $\mathbb{R}^N$ into $\mathbb{R}^m $ where $m$ depends on the volume, reach and dimension of $\mathcal{M}.$ $\\$ This will be a hybrid seminar and take place in C329 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .