Johannes Kepler Symposium für Mathematik
Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Prof. Ingrid Daubechies, Department of Mathematics, Princeton University, am Thu, April 10, 2008 um 17:15 Uhr im HS 9 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "The Application as Architect for the Mathematical Framework" halten, zu dem die Veranstalter des Symposiums,O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)
hiermit herzlich einladen.
Series A - General Colloquium:
The intention is to present general information not only to experts, but also to students and guests from outside the mathematical institutes.
The Application as Architect for the Mathematical Framework
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 lead to 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 requirements of an engineering application, or of solving other problems designed by man (rather than nature) generate mathematical challenges that are equally interesting, in which the implementation modalities can play a role at earlier stages, driving not only the numerical analysis at the end, but playing an important role as well in the mathematical framing of the problem, at the start of the study.
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.