Finding Solitons in Differential Geometry

Explore the concept of solitons in differential geometry through this comprehensive lecture by Jorge Lauret from FaMAF - Universidad Nacional de Cordoba CIEM - CONICET Cordoba, Argentina. Delve into the role of solitons as distinguished elements in geometric structures and their importance when natural structures are unavailable. Examine various contexts where solitons appear, including matrices, polynomials, plane curves, Lie group representations, and the variety of Lie algebras. Investigate the application of solitons in Riemannian, Hermitian, almost-Kähler, and G2 structures on manifolds, with a particular focus on Lie groups. Learn about heuristic preliminaries, shrinking CSF-solitons, soliton equations and flows, algebraic solitons in homogeneous cases, algebraic Ricci solitons, and the moving-bracket approach in geometric invariant theory. Gain insights into how solitons contribute to discovering optimal geometric structures in differential geometry.

Heuristic preliminaries
Example 1: matrices
Example 3: plane curves
Shrinking CSF-solitons
Solitons in differential geometry
Soliton equation and flows
Other examples of solitons
Algebraic solitons: homogeneous case Time!!
Algebraic Ricci solitons
The moving-bracket approach (GIT)
Algebraic soliton geometric structures