Fall School on Schubert Calculus at Marburg

	Fall School at Philipps Universität Marburg		Graduate Programme "Lie Theory and Complex Geometry" Schubert Calculus on Grassmannians and Related Topics abstract
		_	Schubert Calculus is the formalism governing the product structure of the cohomology (or Chow) ring of the complex Grassmannian varieties G(k, n), parameterizing k-planes in Cⁿ. The main goal of the short course is to let the audience becoming quickly familiar with Schubert Calculus. This is possible by using a certain natural Schubert derivation on a Grassmann Algebra which is a prototype of a vertex operator used to study the Boson-Fermion correspondence in the representation theory of the Heisenberg Algebra. It turns out that the fermionic representation of the latter (which will be introduced along the lectures) can be seen as a Wronskian representation of it, associated to an infinite order linear ODE with constant coefficients. Indeed, the formalism of Schubert calculus can be recovered by the natural operation of differentiating wronskians of a linear ODE (of finite order) with constant coefficients. Rephrasing Schubert Calculus for grassmannians in terms of derivatives of generalized wronskians associated to linear ODEs with constant coefficients, one obtains the “finite dimensional” version of the Bose-Fermi correspondence, which is nothing but than Poincaré duality between homology and cohomology of the Grassmannian.