Events for 12/08/2016 from all calendars
Student/Postdoc Working Geometry Seminar
Time: 09:30AM - 10:30AM
Location: BLOC601AX
Speaker: JM Landsberg, TAMU
Title: The Chow variety II
Groups and Dynamics Seminar
Time: 3:30PM - 4:30PM
Location: BLOC 220
Speaker: Tian Yang, Stanford University
Title: On type-preserving representations of the four-punctured sphere group
Abstract: We give counterexamples to a conjecture of Bowditch that if a non-elementary type-preserving representation ρ : π1(Σg,n) → PSL(2; R) of a punctured surface group sends every non-peripheral simple closed curve to a hyperbolic element, then ρ must be Fuchsian. The counterexamples come from relative Euler class ±1 representations of the four-punctured sphere group. As a related result, we show that the mapping class group action on each non-extremal component of the character space of type-preserving representations of the four-punctured sphere group is ergodic. The main tool we use is Penner’s lengths coordinates of the decorated character spaces defined by Kashaev.