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Colloquium, Winter 2006

Day: Monday January 23rd Time: 4:00pm Place: BH 428 Title: Multivariable Wavelets: at the boundary with number theory, geometry, and probability. Speaker: Eva Curry Abstract: In this talk, I will present the idea of radix representations of R^n. I will then describe the connections between radix representations, multivariable wavelets, and self-affine tiling sets in R^n. I will conclude with some questions for further research. The field of wavelet theory is a new and still fast-growing research area, and the basic idea of combining dilation by a factor of two with integer translations has been generalized in many different ways in recent years. In one such generalization, dilation by two is replaced with dilation by an expanding matrix that maps the integer lattice into itself, and integer translations are replaced by translation by vectors with integer entries. All main results carry over into the multidimensional setting, however their proofs become more complicated and require a deeper understanding of the geometry involved. Specifically, one needs to study self-affine tiling sets in R^n, which are best approached by considering a radix or digital representation of vectors in R^n. Refreshments: BH 300 at 3:30pm.