Program:

Geometry, Topology and Dynamics of Moduli Spaces

Location:

Institute for Mathematical Sciences, National University of Singapore, Singapore

Dates:

1 - 19 August, 2016

Website for information and registration:

http://www2.ims.nus.edu.sg/Programs/016wgeo/index.php

Organizers:

Co-Chairs

Ser Peow Tan (National University of Singapore)

Graeme Wilkin (National University of Singapore)

Members

Javier Aramayona (Université Paul Sabatier)

Vikraman Balaji (Chennai Mathematical Institute)

Martin Bridgeman (Boston College)

Francois Labourie (Université Paris-Sud, Orsay)

Richard A. Wentworth (University of Maryland)

Activities

Workshop on New Perspectives on Moduli Spaces in Gauge Theory: 1 - 5 August 2016

Informal discussions, research collaborations and mini-courses: 8 - 12 August 2016

Workshop on Moduli spaces of geometric structures: 15 - 19 August 2016

Overview

The subject of this program is the topic of moduli spaces and their connections with different areas of mathematics and physics. Moduli spaces arise naturally from the study of one of the most fundamental problems in mathematics: parametrising mathematical objects up to equivalence. Understanding the moduli space and its local and global structure can often give new information about the underlying geometric problem; for example Donaldson’s work on the moduli space of solutions to the Yang-Mills equations over four manifolds produced new information about smooth structures on these manifolds.

In this program we plan to focus on moduli spaces of geometric structures on Riemann surfaces and moduli spaces of Higgs bundles, for which the geometry, topology and dynamics gives new information about geometric and topological problems in low dimensions. The program will consist of two one-week workshops, each with a different focus but with interactions between the two. During the week between the two workshops we will have time for research discussions and collaborative work. One or two mini-courses are also planned for the second week.

Motivated by physics, one example of such a moduli problem is that of classifying solutions to equations from gauge theory; for example, solutions to the Yang-Mills equations and Yang-Mills-Higgs equations. In the first week (1-5 August) we will start with a workshop "New perspectives on moduli spaces in gauge theory" which will focus on these moduli spaces and their connections to different areas of mathematics and physics.

The second week will be mostly devoted to research discussions and collaborative work. One or two mini-courses will also be scheduled.

For the third week from 15-19 August, there will be a second workshop “Moduli spaces of geometric structures” devoted to the more geometric aspects of moduli spaces. In particular, talks will focus on the moduli spaces of various geometric structures including (real and complex) hyperbolic structures, (real and complex) projective structures, affine structures and the character varieties of a surface group into various Lie groups (focusing on the components corresponding to geometric structures), and the underlying geometry, topology and dynamics under the mapping class group and other group actions.

The main goals of the program are:

Bring together experts who study the geometry, topology and dynamics of moduli spaces.

Invite leading researchers to give talks on recent results and the latest developments in the field. 

Follow-up on collaborative work from previous IMS programs.

Introduce graduate students and young researchers to the latest research and open problems in the field.