A_{infinity}-structures, Brill-Noether loci and the Fourier-Mukai   transform
  We use A_{infinity}-formalism to study variation of cohomology spaces under formal deformations of coherent sheaves on projective varieties. As an application we describe formal neighborhoods of twisted Brill-Noether loci at some points. Another application is a computation of the Fourier-Mukai transform of some natural line bundles on symmetric powers of a curve. 
Alexander Polishchuk