Harmonic Analysis for the Natural Sciences
 
 
Description: 

In the Natural Sciences, researchers are often faced with three problems of significant mathematical complexity.

 

The first problem arises in every science where the observation process plays an important role: the need of restricting their measurements to a subregion of the ambient space. The reasons can be diverse. Either the values outside that region are not accessible or they are simply irrelevant to the problem. Call it "The Localization Problem".

 

Another fundamental need of the Natural Sciences is to understand the behavior of random phenomena in high dimensions. A big challenge is to understand the macroscopic laws of large-scale mathematical and physical systems from their interaction at the microscopic level. Call it "The Large Scale Problem".

 

Yet another fundamental problem is the one of understanding natural phenomena modeled by random models where periodic characteristics can be identified. Scientists often need to approximate the random laws of nature from a few deterministic observations. Call it "The Spectral Estimation Problem".

 

In this talk we will outline a new method based on Harmonic Analysis that has been developed with the aim of providing several Natural Sciences (in particular Acoustics, Chemistry, Earth Sciences and Physics) with a robust methodology to deal with the above problems. The method has recently been used to prove 1982 Thomson's conjecture that the spectral window of his multi-taper estimator approaches an ideal band-pass filter, a fact which so far had only been offered numerical evidence.

Date:  2015-04-22
Start Time:   16:30
Speaker:  Luís Daniel Abreu (ARI-Austrian Academy of Sciences)
Institution:  ARI-Austrian Academy of Sciences
Research Groups: -Numerical Analysis and Optimization
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