The Alfred Brauer Lectures, April 28–30, 2008
Charles Fefferman, Princeton University
Interpolation and extension of functions I, II, III
Fix positive integers m and n. Let E be a given (arbitrary) subset of R^n, and let f:E→R be a given function. How can we decide whether f extends to a C^m function F on the whole R^n? If F exists, then how small can we make its C^m norm? What can we say about the derivatives of F at a given point? Can we make F depend linearly on f? What if F is required to agree with f only approximately on E?
Suppose E is finite. How can we compute an F as above, with close-to-minimal C^m norm. How many computer operations does it take? What if we are allowed to discard a few of the points of E?
These problems go back to work of Whitney in 1934. Many of the recent results are joint work with Bo'az Klartag.
No background will be assumed beyond the most elementary analysis. In particular, ideas from computer science will be introduced as needed. The first talk will give precise statements of the problems and of the main results for finite sets E. The second talk will sketch the proof of a main theorem. The third talk will deal with infinite sets E, and (time permitting) with open problems.
| Brauer Lecture 1 | Phillips 215 | April 28, 4:00–5:00 PM |
|---|---|---|
| Brauer Lecture 2 | Phillips 332 | April 29, 4:00–5:00 PM |
| Brauer Lecture 3 | Phillips 332 | April 30, 4:00–5:00 PM |
There will be a reception in the Mathematics Faculty/Student Lounge on the third floor of Phillips Hall, Room 330 starting at 5:15 P.M. on Monday, April 28. Refreshments will be available at 3:30 before the second and third lectures.
About the 2008 Brauer Lecturer
Professor Fefferman obtained his B.A. from the University of Maryland at age 17, his Ph.D. from Princeton at 20 under E. M. Stein and was named a full professor by the University of Chicago when he was 22. He returned to Princeton in 1974 and has been a full professor there ever since. Dr. Fefferman works in the areas of classical Fourier analysis, PDEs, several complex variables, conformal geometry, quantum mechanics, fluid mechanics and computational geometry.
Professor Fefferman's many honors include the Fields Medal in 1978, the Salem Prize, the Waterman Award, the Bergman Prize and several honorary doctorates. The latest of his awards is the 2008 Maxime Bôcher Memorial Prize, given by the AMS in January. He has served as chairman of the Princeton Mathematics Department and currently chairs the board of trustees of the Mathematical Sciences Research Institute in Berkeley. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the American Philosophical Society.
