Department of Mathematics
Colloquium
by
Prof. Bill Johnson

After discussing some of the history of nonlinear Banach space theory, the speaker will discuss the nonlinear concepts of Lipschitz and uniform quotients of Banach spaces, introduced recently by S. Bates, J. Lindenstrauss, D. Preiss, G. Schechtman, and the speaker. The main problem studied is: For what Banach spaces X is every Lipschitz (or uniform) quotient of X also a linear quotient of X? The investigation leads to new ways of approximating Lipschitz maps by affine maps and also suggests a new direction in finite dimensional geometric analysis.

Additional References:

1. "Nonlinear quotients" can be downloaded from the Banach space bulletin board, http://www.math.okstate.edu/~alspach/banach/recent.html.
2. For background on nonlinear Banach space theory, get benyaminiunifrm.tex from the same bulletin board (basic URL is http://www.math.okstate.edu/~alspach/banach/index.html).
3. A recent published paper on nonlinear Banach space theory: W. B. Johnson, J. Lindenstrauss, and G. Schechtman, Banach spaces determined by their uniform structures, Geometric and Functional Analysis 6 (1996), 430-470.