One can view a flag variety in $C^n$ as an adjoint orbit inside the Lie algebra of $n \times n$ skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a flag variety from an algebraic, geometric, and dynamical perspective. Motivated by previous work on the topology of totally nonnegative flag varieties, we classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As an application, we show how the classical Toda flow fits into this framework. An important role is played by the 'twist map', an involution which preserves the totally nonnegative part. This is joint work with Anthony M. Bloch.
The talk will be via Zoom at:
https://arizona.zoom.us/j/81072911973
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