## Applied Mathematics

•  Jelani Nelson, UC Berkeley
•  Optimal terminal dimensionality reduction in Euclidean space; zoom link @ https://sites.google.com/view/minds-seminar/home
•  06/11/2020
•  2:30 PM - 3:30 PM
•

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home)  The Johnson-Lindenstrauss lemma states that for any X a subset of R^d with |X| = n and for any epsilon, there exists a map f:X-->R^m for m = O(log n / epsilon^2) such that: for all x in X, for all y in X, (1-epsilon)|x - y|_2 <= |f(x) - f(y)|_2 <= (1+epsilon)|x - y|_2. We show that this statement can be strengthened. In particular, the above claim holds true even if "for all y in X" is replaced with "for all y in R^d". Joint work with Shyam Narayanan.

## Contact

Department of Mathematics
Michigan State University
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College of Natural Science