Doug Pickrell, The L^2 theory of root subgroup factorization for loops in SU(2)
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Abstract: Root subgroup factorization is a multiplicative analogue of Fourier series for periodic functions with values in a group (i.e. a field on a compact one dimensional space with nonlinear values). For a function having the critical degree of smoothness or better (one half a derivative in a Sobolev sense), the theory falls neatly into place. Quantum field theory forces us to study rougher fields; in fact quantum fields are generalized functions which are not ordinary functions at all. In this talk, aside from zooming out at the beginning to put things into perspective, I will describe what we cMATHan say about ordinary functions (with values in SU(2)) which do not in general have any smoothness properties at all. We are seeking a multiplicative analogue of the classical L^2 Plancherel formula. This is joint work with Estelle Basor.