Geometry & Topology Seminar: Concave foliated flag structures and Hitchin representations in SL(3,R)

Abstract: In 1992 Hitchin discovered distinguished components of the PSL(d,R) character variety for closed surface groups π₁S and asked for an interpretation of those components in terms of geometric structures. Soon after, Choi-Goldman identified the SL(3,R)-Hitchin component with the space of convex projective structures on S. In 2008, Guichard-Wienhard identified the PSL(4,R)-Hitchin component with foliated projective structures on the unit tangent bundle T¹S. The case d ≥ 5 remains open, and compels one to move beyond projective geometry to flag geometry. In joint work with Alex Nolte, we obtain a new description of the SL(3,R)-Hitchin component in terms of concave foliated flag structures on T¹S. 

Host: Parker Evans