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The goal of the course is to introduce the students to the
newly-developed cohomology theory and deformation theory of
vertex algebras.But the first half of the course will be on
the Hochschild cohomology of associative algebras, the Harrison
cohomology of commutative associative algebras and Gerstenhaber¡¯s
deformation theory of associative algebras. The cohomology
theory and deformation theory of vertex algebras will be introduced
naturally as analogues of the Harrison cohomology and Gerstenhaber¡¯s
deformation theory. I will also discuss possible applications of
these theories to the representation theory of vertex operator
algebras, deformation quantization of conformal field theories,
quantum cohomology and Frobenius manifolds.
Prerequisites: Basic knowledge in algebra and complex analysis. It will be helpful (but not required) if the students know something about homological algebra or vertex operator algebras. Text: There is no single text for this course. The material will be from various research monographs and papers. Research papers will be distributed. |