Ailsa Keating

© Dr. Parwana Fayyaz

Symplectic topology is a central part of modern geometry, with historical roots in classical mechanics. Symplectic structures also arise naturally in low-dimensional topology, in representation theory, in the study of moduli spaces of algebraic varieties, and in quantum mechanics. A fundamental question is to understand the automorphisms of a symplectic manifold. The most natural ones are symplectomorphisms, i.e., diffeomorphisms preserving the symplectic structure. Ailsa Keating proposes to study structural properties of their group of isotopy classes, called the symplectic mapping class group.