Sponser lecture today has been cancelled! The Gergen lectures will still take place.
Monday, April 6, 2009, 4:00pm,
Ingrid Daubechies (Princeton's Program in Applied and Computational Mathematics and Mathematics Department)
"Applications woven into the mathematical fabric"
Abstract:- Traditionally, applied mathematicians have often been interested in problems stemming from physics or other natural sciences.
In this framework, the standard paradigm is to carry out,
and push as far as feasible, a detailed non-quantitative
mathematical analysis of the phenomena at hand, even in cases
where the computation of quantitative results is a goal from
the start of the study. Typically, the transition to
numerical computation happens only after the theoretical analysis.
The realization that this transition has to be done extremely
carefully in order to give meaningful results, gave rise to the
very rich mathematical field of numerical analysis.
Nonetheless, there is often a separation between the two stages:
the mathematical analysis of the problem at hand in a first step,
followed by numerical analysis to determine good algorithms for
numerical results in a second step.
The last few decades have seen the emergence of branches of
applied mathematics in which the requirements of the
implementation not only drive the numerical analysis at the
end, but also play an important role in much earlier stages, including
the mathematical framing of the problem, at the start of the study.
This has generated a different kind of mathematical challenge, stimulated by the requirements of engineering design rather than natural science problems, but equally interesting and possibly far-reaching.
The presentation will present several instances of this interplay
between algorithms and analysis, borrowed from work done by the speaker
herself as well as many others; examples are wavelets, analog-to-digital
conversion and sparse expansions.
Generated at 3:06pm Wednesday, April 24, 2024 by Mcal. Top
* Reload
* Login