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SUMMARY:On the real spectrum compactification of character varieties - Mar
 c Burger (ETH Zürich)
DTSTART:20250709T081500Z
DTEND:20250709T091500Z
UID:TALK232834@talks.cam.ac.uk
DESCRIPTION:In this talk I will describe various aspects of our work on th
 e real spectrum compactification of the\nG-character variety X(F\,G) of a 
 finitely generated group F. This compactification is mindful of the algebr
 aic topology of X(F\,G) and contains a lot of information: for instance\, 
 points in its boundary lead canonically to F-actions on lambda buildings\;
  these objects generalize lambda trees and affine Bruhat-Tits buildings.\n
 &nbsp\;\nWhen F is a compact surface group and G admits a theta positive s
 tructure\, X(F\,G) has connected components consisting entirely of faithfu
 l representations with discrete image\, these components are the higher Te
 ichmueller spaces. For such a component T\, the mapping class group Out(F)
  acts with virtually abelian stabilizers on the real spectrum compactifica
 tion Rspec(T) of T. This is based on a relation between Rspec(T) and the c
 ompactification of T by geodesic currents. I will explain how this relatio
 n leads to a new proof of a recent result of Charlie Reid establishing res
 trictions on boundary currents when G=PSL(n\,R) and T is the Hitchin compo
 nent. Joint work with A.Iozzi\, A.Parreau\, B.Pozzetti
LOCATION:Seminar Room 1\, Newton Institute
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