In 2020–21, Allen Yuan, Visitor in the School of Mathematics and a recent graduate from MIT, is studying problems in homotopy theory and algebraic topology.

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Symplectic and contact structures first arose in the study of classical mechanical systems, allowing one to describe the time evolution of both simple and complex systems such as springs, planetary motion, and wave propagation. Understanding the evolution and distinguishing transformations of these systems led to the development of global invariants of symplectic and contact manifolds.