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Geometric Analysis and Partial Differential Equations Seminar
March 12, 2019 @ 11:30 am - 12:30 pm
Lachlan MacDonald (UOW)
Dynamical invariants of foliated manifolds
A foliation of a manifold M specifies the set of integral submanifolds (referred to in foliation theory as “leaves”) to some nonsingular system of differential equations on M. The “holonomy” of integral curves in a foliated manifold gives rise to an intrinsic dynamical system, whose topology has implications for the global behaviour of solutions to the corresponding system of DEs. In this talk, I will give a primer on foliations and their associated dynamical invariants, as well as discuss how this information can be accessed in the spirit of the Atiyah-Singer index theorem.