Report on Geometry, Topology and Dynamics of Character Varieties Program

The program took place at Institute for Mathematical Sciences of the National University of Singapore over the period 18 Jun – 15 Aug 2010. The main theme of the program was the character varieties of representations in a Lie group G of a discrete group π, for example, the fundamental group of a surface. These varieties have rich geometry and are related to interesting topological objects such as locally homogeneous geometric structures on manifolds, and moduli spaces arising in gauge theory. When π is the fundamental group of a surface group S, the mapping class group acts with a complicated and mysterious dynamics. Experts from all over the world studying various aspects of character varieties attended the program. In particular, we had experts in hyperbolic geometry and low dimensional topology, Teichmueller theory, higher Teichmueller theory, representation and character varieties and dynamical systems give talks in the program. The participants came from Asia (China, Taiwan, Japan, Korea, India), Australia and New Zealand, Europe (France, UK, Germany, Switzerland, Spain, Italy) and the US and Canada, among others.

The NSF grant was used to support (or partially support) the participants coming from US institutions.

There were three main periods of activities, a three week summer school, a two week workshop and a one week conference, the last two of which were ICM satellite conferences. The response for the program was overwhelming, with over 160 participants for the program, of which about 140 were from overseas and with over 20 local participants including some from NTU. The summer school featured series of lectures by 9 lecturers on topics related to the program, and attracted about 30-40 overseas students as well as several local graduate students and had excellent feedback from the participants. The workshop featured 10 survey talks by some of the leading experts on various related topics, and also allowed many of the overseas participants to give short talks on their recent research on topics connected to the main theme of the program. The spectrum of participants was impressive, including graduate students, young post- docs and junior and senior researchers across various disciplines, and there was considerable interaction among the participants. It attracted over 80 participants. The conference in the final week featured talks by some of the leading researchers in the world on the main topics of the program. They were very well received too and attracted about 50 participants. There was also a poster session for younger researchers to showcase their work during the workshop and the conference.

Both the workshop and the conference were satellite conferences of the ICM in Hyderabad, many of the speakers were either former invited speakers to the ICM (Steve Kerckhoff, Francois Labourie, Caroline Series, Scott Wolpert and Shicheng Wang), or were invited to speak at the ICM in Hyderabad (Gaven Martin and Bill Goldman).

The lectures from the Summer School are currently being edited for publication by the publishing company World Scientific.

By all accounts the program was a spectacular success. The IMS staff was indispensible in supporting this huge activity. Students at all levels, senior researchers and mathematicians from all over the world benefitted from the summer's activities. 

Last Modified: 05/01/2011
Modified by: William M Goldman