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SUMMARY:The Real Spectrum Compactification of Character Varieties and its 
 relationship with other compactifications - Victor Jaeck (ETH Zürich)
DTSTART:20241120T160000Z
DTEND:20241120T170000Z
UID:TALK220867@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:We study the moduli space of marked hyperbolic surfaces and re
 lated objects. Thurston shows that this space can be identified with the s
 pace of faithful and discrete representations of a finitely generated grou
 p in $\\mathrm{PSL}_2(\\mathbb{R})$\, up to post-conjugation by $\\mathrm{
 PSL}_2(\\mathbb{R})$. This space is a key connected component of the chara
 cter variety.\nIn this seminar we examine degenerations of these represent
 ations by studying compactifications of the character variety. In particul
 ar\, we present the real spectrum compactification\, its topological prope
 rties\, and show that it projects continuously onto the oriented compactif
 ication of the character variety\, defined by Maxime Wolff. To this end\, 
 we interpret its boundary points geometrically and associate oriented real
  trees with them.
LOCATION:MR13
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