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  • Thursday, September 21, 2017
  • 3:40 PM–4:30 PM
  • North Hall 276

I will address linear fractional transformations in the complex plane as they act on the bidisc.  A linear fractional transformation (LFT) is a holomorphic function from the complex plane to the complex plane defined by f(z1, z2)=(Az+B)/(C^*z+d) where A is a 2 by 2 complex matrix, B and C are vectors, and d is a complex number.  Linear fractional transformations are self-maps  of the open unit ball in multiple complex dimensions have been recently studied  by Cowen and MacCluer. Through our investigation, we prove a necessary condition for an LFT to be a self-map of the bidisc. We also show forms of LFT's where the image of the bidisc is a  disc cross a disc. In further exploration, we study the amount of fixed points LFTs have and determine a method for finding these fixed points. Finally, we use these ideas to construct LFT's with prescribed fixed points.

Refreshments precede the talk at 3:30 p.m. in NH 282.

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