Kempner Colloquium Abstracts


Title:  Wavelets, Tiling and Spectral Sets
Speaker:  Yang Wang
Affiliation:  Georgia Tech.
Time:   3:00pm, Monday, February 17
Location:  MATH 350

Abstract:  
A function $ f(x)$ is a wavelet in the traditional sense if $ \{2^{\frac{n}{2}}f(2^n x-n): m,n\in {\bf Z}\}$ is an orthonormal basis for $ L^2({\bf R})$. In the more general setting, A function $ f(x)$ in $ L^2({\bf R}^d)$ is a wavelet if $ \{\vert\det(D)\vert^{\frac{1}{2}}f(Dx-\lambda)\}$ is an orthonormal basis of $ L^2({\bf R}^d)$ for some set of matrices $ \{D\}$ and vectors $ \{\lambda\}$. But what are the constraints on $ \{D\}$ and $ \{\lambda\}$? This question has surprising connection to the study of tiling and spectral sets.


Title:  Local Methods in General Algebra
Speaker:  Ágnes Szendrei
Affiliation:  University of Szeged
Time:  4:15pm, Monday, March 3
Location:  BESC 180

Abstract:  
During the past twenty years, a theory of localization has been developed for completely general algebraic systems. This theory has been instrumental in the solution of many problems that were previously unapproachable. For the strategy of localization to be effective, it is necessary to understand the possible minimal local structures. This requires the solution of a wide family of classification problems. In the talk I will outline the method of localization, summarize the degree to which the required classification problems have been solved, and discuss some applications.



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