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# Jameson Cahill : Geometry of unit norm tight frames

In this talk, we settle a long-standing problem on the connectivity of spaces of finite unit norm tight frames (FUNTFs), essentially affirming a conjecture first appearing in Dykema and Strawn (2003). Our central technique involves continuous liftings of paths from the polytope of eigensteps (see Cahill et al. (2012)) to spaces of FUNTFs. After demonstrating this connectivity result, we refine our analysis to show that the set of nonsingular points on these spaces is also connected, and we use this result to show that spaces of FUNTFs are irreducible in the algebro-geometric sense, and that generic FUNTFs are full spark.

**Category**: Applied Math and Analysis**Duration**: 01:34:51**Date**: February 10, 2014 at 4:25 PM**Views**: 123-
**Tags:**seminar, Applied Math And Analysis Seminar

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