Generalized Chern-Simons theory and skein relations in arbitrary dimensions
Gerbes and homotopy quantum field theories.
Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects
We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.