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PRODID:-//Microsoft Corporation//Outlook 9.0 MIMEDIR//EN
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DTSTART:20170921T154000
DTEND:20170921T163000
LOCATION:North Hall 276
UID:51CF089D-2053-4E89-96FA-934CCD46BF22@cms.calvin.edu
DESCRIPTION;ENCODING=QUOTED-PRINTABLE: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.=0D=0ARefreshments precede the talk at 3:30 p.m. in NH 282.
SUMMARY;ENCODING=QUOTED-PRINTABLE:Mathematics and Statistics Colloquium
PRIORITY:1
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