Abstract: The concept of soliton provides a useful way to discover elements in a given class of geometric structures that are somehow distinguished. Solitons sometimes play the role of "best" structures in the case when the most natural ones are not available. We aim in this talk to show that this is being very fruitful in the study of Riemannian, Hermitian, almost-Kähler and G2 structures on manifolds, with a particular strength on Lie groups. We will start discussing and finding solitons in some different contexts, including matrices, polynomials, plane curves, Lie group representations (moment maps) and the variety of Lie algebras.
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