NYGT Spring Seminar MAR 16: Ilya Kapovich, University of Illinois

posted Mar 12, 2012, 9:29 AM by Office Manager
Professor Ilya Kapovich of the University of Illinois will speak at the New York Group Theory Spring Seminar on March 16, 2012.  His talk will begin at 4pm in Room 5417.  Join us for tea and cookies at 3:30pm in the the Mathematics Lounge on the 4th floor.

On spectrally rigid subsets of free groups

It is well known that any tree $T$ in the (unprojectivized) Culler-Vogtmann Outer space $cv_N$ is uniquely determined by the translation length function (also known as the marked length spectrum) of $T$, $||.||_T: F_N\to [0,\infty)$. Here for $g\in F_N$, $||g||_T=\inf_{x\\in T} d_T(x,gx)$.

We say that a subset $S\subseteq F_N$ is spectrally rigid in $F_N$ if whenever $T,T'\in cv_N$ are such that $||g||_T=||g||_{T'}$ for every $g\in S$ then $T=T'$ in $cv_N$. By contrast to similar questions for the Teichmuller space, it is known that for $N\ge 2$ there does not exist a finite spectrally rigid subset of $F_N$.

We will discuss known results and open problems about spectral rigidity and non-spectral rigidity of various "natural" infinite subsets of $F_N$.

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