The Study Seminar -- Winter 2008

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

PAST SEMINARS: Fall 07  Winter 07 Fall 06  Winter 06 

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

Thursday, April 10.

Speaker: Anna Lenzhen, UM.
Title: Thurston's Classification Theorem

Abstract: I will talk about Bers' proof of the theorem.

Thursday, April 3.

Speaker: Mario Bonk, UM.
Title: L^p-cohomolgy

Abstract: Gromov introduced the notion of L^p-cohomology in geometric group theory. I will give an introduction to the subject and discuss open problems.

Thursday, March 27.

No seminar.

Thursday, March 20.

Speaker: Juan Souto, UM.
Title: McShane's identity

Abstract: McShane proved that a certain function, a series whose coefficients are determined by the lengths of the simple closed geodesics, is constant over Teichmueller space of the punctured torus. This remarkable identity, and its many generalizations, has recently obtained much attention because of its crucial role in Mirzakhani's computation of the volume of Moduli space. In this talk I will explain the proof of McShane's identity.

Thursday, March 13.

No seminar

Thursday, March 6.

No seminar

Thursday, February 28.

No seminar (Spring break)

Thursday, February 21.

No seminar

Thursday, February 14.

Speaker: Marshall Williams, UM.
Title: Rectifiable sets in metric and Banach spaces (after Ambrosio and Kirchheim) part 2.

Abstract: We will discuss a paper by Luigi Ambrosio and Bernd Kirchheim analyzing rectifiable subsets of metric spaces (a set is k-rectifiable if it is, up to an H^k null set, a countable union of Lipschitz images of subsets of R^k). Using isometric embeddings into dual Banach spaces, the authors define a weak* differential, which is shown to be intrinsic in a suitable sense. Weak* differentiation is closely related to “metric differentiation”, introduced in an earlier paper of Kirchheim. We will discuss these differentiation theorems and their applications, including a Rectifiability criterion as well as area and coarea formulas. (continued)

Thursday, February 7.

Speaker: Marshall Williams, UM.
Title: Rectifiable sets in metric and Banach spaces (after Ambrosio and Kirchheim).

Abstract: We will discuss a paper by Luigi Ambrosio and Bernd Kirchheim analyzing rectifiable subsets of metric spaces (a set is k-rectifiable if it is, up to an H^k null set, a countable union of Lipschitz images of subsets of R^k). Using isometric embeddings into dual Banach spaces, the authors define a weak* differential, which is shown to be intrinsic in a suitable sense. Weak* differentiation is closely related to “metric differentiation”, introduced in an earlier paper of Kirchheim. We will discuss these differentiation theorems and their applications, including a Rectifiability criterion as well as area and coarea formulas.

Thursday, January 31.

Speaker: Pekka Pankka, UM.
Title: Harmonic functions on polynomially growing groups (after Kleiner) part 2.

Abstract: A recent paper of Bruce Kleiner gives a new proof of Gromov's theorem on virtual nipotency of finitely generated groups of polynomial growth. The proof is based on finite dimensionality of the space of harmonic functions (of a small polynomial growth) on a Cayley graph of the group. I will focus on this part of the paper. (continued)

Thursday, January 24.

No seminar.

Speaker: Pekka Pankka, UM.
Title: Harmonic functions on polynomially growing groups (after Kleiner).

Abstract: A recent paper of Bruce Kleiner gives a new proof of Gromov's theorem on virtual nipotency of finitely generated groups of polynomial growth. The proof is based on finite dimensionality of the space of harmonic functions (of a small polynomial growth) on a Cayley graph of the group. I will focus on this part of the paper.