Workshop on infinite dimensional Teichm¨ uller space and moduli space
Organizer: Ege Fujikawa (Chiba University)
Time: November 19, 2007 – November 22, 2007
Place: Room 202, Research Institute for Mathematical Sciences, Kyoto University
Program November 19
10:00 – 11:00 Ege Fujikawa (Chiba University)
Intermediate Teichm¨uller space and complex analytic structure of moduli space
11:15 – 12:15 Frederick Gardiner (City University of New York) Teichm¨uller theory and the associahedron
14:00 – 15:00 Hideki Miyachi (Osaka University)
On the Gardiner-Masur boundary of Teichm¨uller space 15:15 – 16:15 Hiroshige Shiga (Tokyo Institute of Technology)
On conformal mappings and Kleinian groups 16:30 – 17:30 Katsuhiko Matsuzaki (Okayama University)
Symmetric structures on a Riemann surface
November 20
10:00 – 11:00 Katsuhiko Matsuzaki (Okayama University)
Quasiconformal mapping class groups having common fixed points on the asymptotic Teichm¨uller spaces
11:15 – 12:15 Frederick Gardiner (City University of New York) Circle expanding maps
14:00 – 15:00 Frederick Gardiner (City University of New York) Rohlin’s formula for UAA mappings
15:15 – 16:15 Hideki Miyachi (Osaka University) On the image of asymptotic Bers map 16:30 – 17:30 Yoichi Imayoshi (Osaka City University)
On the holomorphic sections of a holomorphic family of Riemann surfaces induced by a Kodaira surface
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November 21
10:00 – 11:00 Masahiko Taniguchi (Nara Women’s University)
Structure theorem for non-injective self-covers and some applications 11:15 – 12:15 Kunio Obitsu (Kagoshima University)
Asymptotics of the Weil-Petersson metric and the Takhtajan-Zograf metric 13:45 – 14:45 Zongliang Sun (Zhongshan University, Tokyo Institute of Technology)
On metrics in Teichm¨uller space and a description of thick parts of Teichm¨uller space
15:00 – 16:00 Kentaro Ito (Nagoya University)
Topology of quasifuchsian space of once-punctured torus
November 22
10:00 – 11:00 Mitsuhiro Shishikura (Kyoto University)
Renormalization in Complex Dynamics and Teichm¨uller space 11:15 – 12:15 Frederick Gardiner (City University of New York)
Thompson’s group in Teichm¨uller theory
14:00 – 15:00 Frederick Gardiner (City University of New York)
Infinite dimensional hyperelliptic Riemann surfaces generated by horseshoe maps
15:15 – 16:15 Toshihiro Nakanishi (Shimane University)
Trace identites and the mapping class group acting onSL(2,C)-representation spaces of punctured surface groups
16:30 – 17:30 free discussion
Abstracts of Gardiner’s lectures
• Title: Teichmuller theory and the associahedron
Abstract: The finite earthquake theorem is used to introduce Teichmuller geometry on the asso- ciahedron.
• Title: Circle expanding maps
Abstract: The Teichmuller space of uniformly asymptotically conformal circle expanding maps is constructed. The matching condition for solenoid functions and compatibility condition for scaling functions is described on dual Riemann surfaces.
• Title: Rohlin’s formula for UAA mappings
Abstract: A version of Rohlin’s formula for uniformly asymptotically affine circle expanding maps with integration of the scaling function over the dual Cantor circle is described.
• Title: Thompson’s group in Teichm¨uller theory
Abstract: There is a natural representation of Thompson’s F group in the group of isometries of the Teichmuller space of a Cantor set of bounded geometric type and of the Teichmuller space of degree 2 circle expanding maps. This action is shown to be discrete.
• Title: Infinite dimensional hyperelliptic Riemann surfaces generated by horseshoe maps
Abstract: A natural Teichmuller space with a pseudo-Anosov full horseshoe map is constructed and an unsolved type problem suggested by this construction is discussed.
