Anticipating a math REU
I’m anticipating that this summer I’ll be participating in the Texas A&M REU in Wavelets and Matrix Theory. From the program description, if I get in, I’ll have a blast, learning about wavelets and matrices; here’s a clip from the webpage:
Focus of this Program. There is a fascinating interplay between wavelets, frames, and operator theory (i.e. the theory of linear maps between vector spaces). This interplay will be the key topic of investigation during this summer program. We shall investigate the role of wandering vectors for unitary systems, both in finite and infinite dimensions. Related topics include introductory ideas in frame theory, sampling theory, and operator algebras, again both in finite and infinite dimensions. Additional topics include wavelet sets and minimally supported frequency wavelets. This special class of wavelets has an interesting internal structure, but also provides concrete examples of important ideas that will be discussed. Finally, we will investigate several interesting intrinsic problems dealing with wavelet sets.
Proposed Research Problems:
- Open problems regarding wandering vectors for unitary systems acting on Rn or Cn.
- Open problems concerning finite frames and their relationships with matrix analysis and operator theory.
- An open problem on the reflexivity of finite dimensional operator algebras which is purely algebraic in nature.
- Characterize interpolation pairs of minimally supported frequency wavelets.
- How can a wavelet set be perturbed to give rise to an interpolation pair?
- Does there exist a wavelet set in the support of the Fourier transform of any wavelet?
- An open problem in sampling theory.
In an amazing happenstance, it turns out that one of the profs I asked to write me a recommendation is friends with one of the head researchers in the wavelets and matrix theory REU, and wrote me a strong recommendation. So I think I have a very good chance of getting in.
Lovely!
Possibly relevant posts:
- And now for something completely different… (6/8/2004)
- Readings (10/13/2008)
- Bracketing Problem, and a useful summation identity. (1/29/2004)