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Abstract:
Loop Grassmannians appear in the geometric Langlands program as a geometrization of Hecke operators in number theory.
They are also ``the simplest'' noncommutative cohomology objects in algebraic geometry. We will reconstruct the loop
Grassmannian of a reductive group in terms of an elementary mechanism
of ``local spaces''. This is just another mathematical model of collision of particles, a version of the
Beilinson-Drinfeld notion of factorization spaces or the Feigin-Loktev fusion of representations etc. This
construction actually provides a larger class of spaces generalizing the known loop Grassmannians.
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