Fixed point scheme as spectrum of equivariant cohomology and Kirillov algebras

As an example of the multiplicity algebras of the Arnold school we will look at the equivariant cohomology of a Grassmannian and notice that it is inscribed in its regular fixed point scheme generalising observations of Brion-Carrell. 

In turn, we will describe it explicitely as the classical Kirillov algebra of a fundamental representation of $SL_n$, originally observed by Panyushev. These observations are motivated by mirror symmetry considerations originating in recent work with Hitchin on the mirror of very stable upward flows in the Hitchin system, which we will briefly indicate.

For more information see: https://personal.math.ubc.ca/~jbryan/Zoominar-UBC-ETH/