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Introduction to Vertex Algebras
MATH 298

Course Information

Description

Vertex algebras provide a rigorous mathematical framework for two-dimensional conformal field theory. This course offers a comprehensive introduction to the subject, bridging its algebraic and geometric aspects. The first half focuses on local constructions, covering the foundational axioms and key examples of vertex algebras (such as Kac-Moody and Virasoro algebras). The second half transitions to the global framework, introducing conformal blocks associated with a vertex algebra and vertex algebra bundles on a curve. We will then cover the fundamentals of chiral algebras following the work of Beilinson and Drinfeld. Time permitting, we will discuss advanced topics such as representation theory, chiral differential operators, AGT Correspondence etc.

School Faculty of Arts & Sciences
Credits 4
Cross Reg

Available for Harvard Cross Registration

Department Mathematics
Course Component Lecture
Grading Basis FAS Letter Graded
General Education N/A
Quantitative Reasoning with Data N/A
Divisional Distribution Science & Engineering & Applied Science
Course Level Primarily for Graduate Students