Overview of the Thematic Area
Differential geometry has its origins in the monumental work of Gauss and Riemann in the 19th century. Its relevance for science has no better illustration than its use by Einstein as the mathematical foundation for his general theory of relativity. Over the course of the last 150 years, the subject has been invigorated by the adoption of global topological and analytical tools, and by its many applications in science and engineering, with general relativity, gauge field theory, and string theory deserving special mention. The pace of research activity and progress on fundamental problems in the field during the last decade continues to be breathtaking. The resolution of the Poincaré Conjecture and Thurston’s Geometrization Conjecture in low-dimensional topology was achieved by Perelman using Hamilton’s Ricci flow. In Kaehler geometry, the Fano case of Calabi’s problem about the existence of Kaehler-Einstein metrics was given a definitive answer by Chen-Donaldson-Sun and Tian. Recently in the area of global submanifold geometry, the Lawson conjecture was proved by Simon Brendle, and the Willmore conjecture was resolved jointly by F. Marques and A. Neves. These are only a few of a long list of deep results that were achieved in just the past decade.
The overall goal of the Program is to provide a forum for consolidating and extending these achievements and a platform for launching new directions of investigation, posing new problems, and developing new tools.
Although the program will include participation from researchers and graduate students working in many different areas within geometric analysis, there will be a focus on three main subthemes, to which we will denote individual workshops. These main subthemes are:
1. G2 manifolds and related topics,
2. General relativity and the AdS/CFT correspondence, and
3. Geometric flows.
Immediately preceding workshops for subthemes 1 and 3 there will be a two-day "minischool" during which guest lecturers will give short courses for postdocs, students, and non-expert researchers who are interested in the workshop subtheme, to provide them with the background they need to get the most out of the workshop talks.
Many other activities are planned for the program, such as:
Graduate Courses. There will be two graduate courses at the Fields Institute during the 2017 Fall academic term. One course will be "Introduction to geometric flows" by Robert Haslhofer; the other course will be announced soon.
Colloquia and Seminars. During the period of the thematic program, we will integrate the "Fields Institute Geometric Analysis Colloquium" with the activities of the program and have one speaker at least every two weeks during the September to December period. Moreover, graduate students and postdoctoral fellows associated with the thematic program will be encouraged to organize weekly working/learning seminars on topics related to the themes of the program. Finally, energetic visitors to the Institute during the program can also participate in the regular differential geometry seminars at the Universities of Toronto, McMaster, and Waterloo.
Postdoctoral Fellowships. Several postdoctoral fellowships associated with the program will be offered. Some will be for a two-year duration with the 18 months that do not coincide with the program being spent at one of the Fields Institute Principal Sponsoring Universities. Other postdoctoral fellowships will be only for the duration of the thematic program. These are expected to be offered to researchers who take a leave of absence from an existing postdoctoral position.
Long-term Visitors. Funding is available to support selected long-term visitors. The length of visit must be between two continuous weeks and six continuous months. For more details and to apply, please click on the link on the upper right of this page.
Short-term Visitors. Funding is also available to support selected long-term visitors. The length of visit should be less than two continuous weeks. For more details and to apply, please click on the link on the upper right of this page.
Public Outreach. Several public outreach activities are being planned.