Analysis Seminar

The analysis seminar will be meeting this semester on Thursdays at 3:10pm in room Carver 204.

Date	Speaker	Abstract.
Oct. 18	Eric Weber, ISU The Kadison-Singer Problem, Part I	We introduce the Kadison-Singer problem, from C^* algebras and nearly 50 years old, and discuss its history.
Oct. 25	Eric Weber, ISU The Kadison-Singer Problem, Part II	We shall continue to discuss the history of the Kadison-Singer problem, highlighting connections to harmonic analysis and Banach space theory.
Nov. 1	Eric Weber, ISU The Kadison-Singer Problem, Part III	We shall discuss recent events concerning the Kadison-Singer problem, highlighting connections to frames, Riesz bases, and the uncertainty principle.
Nov. 8	Brody Johnson, Saint Louis University Characterizations of finite-dimensional tight frames	This talk will give an overview of a recent line of research in which finite-dimensional tight frames are characterized as the minimizers of a natural potential function, the frame potential. It turns out that such characterizations hold in many cases when the frame potential is restricted to collections that possess additional structure, e.g., group symmetries. The talk will also include a brief introduction to frame theory and some discussion of open areas of research.
Nov. 15	Karen Shuman, Grinnell College Iterated function systems and a result of Erd\H{o}s	Joint work with Palle Jorgensen, University of Iowa, and Keri Kornelson, Grinnell College In this talk we examine a result of Erd\H{o}s and some of its applications to invariant measures for certain contractive affine iterated function systems on $\mathbb{R}^d$. In particular we use the Fourier transform to study measures which are singular with respect to Lebesgue measure. We then describe a gradation of the class of singular measures associated with iterated function systems; measures at one end of the gradation are Cantor measures, and measures at the other end exhibit chaos.