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Monday, December 7, 2015

**Abstract:** Bosonization, namely the representation of given chiral fields (Fermi or Bose) via bosonic fields, has long been studied both in the physics and the mathematics literature, especially in connection to representation theory and integrable systems. Perhaps the best known instance is the bosonization of the charged free fermions: one of the two directions of a chiral isomorphism often referred to as "the" boson-fermion correspondence (of type A). The opposite process, fermionization, refers to the representation of given fields in terms of fermionic fields, as in the case of the representation of the Heisenberg bosonic current as a normal ordered product of the charged fermions. In this talk we discuss new instances of bosonization and fermionization, obtained by allowing multi-locality, i.e., poles in operator product expansions at roots of unity. One such new instance is the multilocal bosonization of the $\beta\gamma$ boson ghost system, and generally of the symplectic bosons (and consequently certain classes of lattice vertex algebras, of type C). Another example is the multilocal fermionization of the charged free fermions by neutral fermions, which in turn allows us to bosonize the neutral fermions, thereby completing the boson-fermion correspondence of type D.