| Date | Speaker | Topic |
|---|---|---|
| September 12 |
Organizational Meeting |
Organizational Meeting Abstract: TBA . |
| September 19 |
Danshyl Boodhoo, Tufts University |
The Inverse Linearization Scheme for sine-Gordon like PDEs Abstract: We develop a method to restore an unknown sine-Gordone like nonlinear partial differential equation (PDE) from its linearization around an unknown stationary solution. The main idea is to use the Goldstone theorem to establish a correspondence between eigenfunctions of the Schrodinger equation and the nonlinearity of the PDE. . |
| September 26 | Ilya Krishtal, Northern Illinois University |
Kadec-type theorems for unit-norm frames and atomic decompositions Abstract: In 1964 Kadec established the exact value of the Paley-Wiener constant which bounds the perturbation of harmonics in the orthonormal basis of exponential functions for the system to remain a Riesz basis. The result has many extensions such as the theorems by Katznelson, Avdonin, and Balan. All of these extensions, however, apply to systems of exponential functions on an interval. In this talk I will show how to extend Kadec’s proof to systems of vectors generated by sampling an orbit of a vector under an isometric group representation. The talk is based on joint work with B. Miller. |
| October 3 |
TBA |
TBA Abstract: TBA . |
| October 10 |
Martin Buck, Tufts University |
A Short-time Fourier Transform on the Sierpinski Gasket Abstract: We present a definition of a short-time Fourier transform in terms of the eigenfunctions of the Neumann Laplacian and the corresponding heat kernel on the Sierpinski Gasket. We show that that for |
| October 17 |
TBA
|
TBA Abstract: TBA . |
| October 24 |
No Meeting – Fall Fourier Talks |
No Talk Abstract: No Talk . |
| October 31 | Dorsa Ghoreishi, Saint Louis University |
Frame theory and the study of vector recovery by phase retrieval and saturation recovery Abstract: Frames, like orthonormal bases, provide a continuous, linear, and stable reconstruction formula for vectors in a Hilbert space. Unlike orthonormal bases, frames allow for redundancy, which makes them more flexible for both theoretical work and practical applications. One such application is phase retrieval, which is used in fields like X-ray crystallography and coherent diffraction imaging, where only the intensity of each linear measurement is available, and the phase information is lost. In this talk, I will introduce the concepts of frames and phase retrieval, then discuss a real-world scenario where sensors are set up to clip any measurement that exceeds a threshold due to saturation. This problem, known as declipping or saturation recovery, focuses on reconstructing a vector from such clipped measurements. This talk will focus on methods for recovering vectors using phase retrieval and saturation recovery techniques.. . |
| November 7 |
TBA |
TBA Abstract: TBA . |
| November 14 |
TBA |
TBA Abstract: TBA . |
| November 21 |
TBA |
TBA Abstract: TBA . |
| November 28 |
Thanksgiving |
No Talk Abstract: No Talk . |
| December 5 |
TBA |
TBA Abstract: TBA . |
this is well-defined and leads to properties akin to that of the classical short-time Fourier transform. Furthermore, this leads to an inversion formula that allows one to express