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# The (asymptotic) location of eigenvalues of a representation in the Hitchin component

## Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015

April 13, 2015 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Andrés Sambarino (Université de Paris VII (Denis Diderot) et Université de Paris VI (Pierre et Marie Curie))
Location: MSRI: Simons Auditorium
Tags/Keywords
• Riemann surfaces

• mapping class groups

• co-compact group action

• discrete group of isometries

• Hausdorff dimension

• entropy

• quasi-Fuchsian group

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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Abstract

The Hitchin component is a (special) connected component of the space of homomorphisms of a surface group into $\textrm{PSL}(d,\mathbb{R}).$  This component is a higher rank analogue of the Teichmuller space of the surface.  The purpose of the talk is to show that the critical exponent of a Hitchin representation has a rigid upper bound. This is a joint work with Rafael Potrie.

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