RTG Study Seminar -- Winter 2009

Thursdays 4:10-6:00 -- East Hall 3088

PAST SEMINARS: Winter09 Fall 08   Winter 08 Fall 07  Winter 07 Fall 06  Winter 06 

To schedule a talk, or for more information, please contact Pekka Pankka (pankka 'at' umich.edu) or Lars Louder (llouder 'at' umich.edu).

Thursday, February 19.

Speaker: Jon Handy (UM)
Title: The Painlev\'e Problem and Its Solution.

Abstract: The Painlev\'e problem, proposed by Ahlfors in 1947, was concerned with finding a geometric characterization of those sets in the complex plane which are removable for bounded analytic functions. In the first part of the talk, we will discuss the basic methods for determining such sets, and show how to reduce the problem to the case of sets of Hausdorff dimension one. In the second half of the talk, we will provide an historical overview of the developments which led to a solution to the Painlev\'e problem, culminating in the work of X. Tolsa in 2004.

Thursday, February 12.

Speaker: Mario Bonk (UM)
Title: Isometric actions on trees and degenerations of hyperbolic structures, Part II.

Abstract: Let H^n(G) be the space of conjugacy classes of discrete and faithful representations of a discrete group G in the isometry group of hyperbolic n-space. According to a theorem due to Culler, Morgan and Shalen H^n(G) admits a natural compactification arising from isometric actions of G on real trees. I will present a proof of this fact due to M. Bestvina. (cont.)

Thursday, January 29.

Speaker: Mario Bonk (UM)
Title: Isometric actions on trees and degenerations of hyperbolic structures.

Abstract: Let H^n(G) be the space of conjugacy classes of discrete and faithful representations of a discrete group G in the isometry group of hyperbolic n-space. According to a theorem due to Culler, Morgan and Shalen H^n(G) admits a natural compactification arising from isometric actions of G on real trees. I will present a proof of this fact due to M. Bestvina.