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Mathematics in Science and Society

Department of Mathematics, University of Illinois at Urbana-Champaign

presenting two talks by

Professor Ingrid Daubechies
Department of Mathematics
Program in Applied and Computational Mathematics
Princeton University

See the poster!

HOW I BECAME A MATHEMATICIAN

An informal visit with the scientist where she will describe her journey from physics to mathematics and illustrate her approach to solving problems. Future scientists, engineers, and mathematicians welcome!

Friday, September 27, 1996 at 11:30 Room 143, Mechanical Engineering Building

SURFING WITH WAVELETS

Wavelets have emerged in the last decade as a synthesis from many disciplines, ranging from pure mathematics (where forerunners were used to study singular integral operators) to electrical engineering (quadrature mirror filters), borrowing in passing from quantum physics, from geophysics and from computer aided design.

We will present an overview of the ideas in wavelet theory, and show how it fits into the different disciplines in which it is rooted, and discuss some recent applications, ranging from lossless as well as lossy image compression or speech analysis to nonlinear approximation methods.

Friday, September 27, 1996 at 4:30 pm, Room 314, Altgeld Hall.

Refreshments at 3:15 pm in Room 321, Altgeld Hall.

Professor Daubechies was awarded a Steele Prize for mathematical exposition in 1994 by the American Mathematical Society for her book, "Ten Lectures on Wavelets". We quote from the citation for the award: The concept of wavelets has its origins in many fields, and part of the accomplishment of Daubechies is finding those places where the concept arose and showing how all the approaches relate to one another. The use of wavelets as an analytical tool is like Fourier analysis -- simple and yet very powerful. In fact, wavelets are an extension of Fourier analysis to the case of localization in both frequency and space. And like Fourier analysis, it has both a theoretical side and practical importance. ... Daubechies has, of course, made major contributions to the subject herself. Haar wavelets (where the "mother wavelet" is the characteristic function on [0,1/2] minus the characteristic function on [1/2,1]) have been known since 1910; they were thought to be a curiosity but not very useful. With Daubechies' work, Haar wavelets have been shown to be the first in a whole family of compactly supported nonsmooth wavelets: beautiful exmaples of functions with fractal higher derivatives. ... In 1992 Professor Dabuechies was awarded a five-year MacArthur fellowship.