Vertex Algebras and Special Holonomy with Torsion - Minicourse 02

Explore the intricate connections between vertex algebras and special holonomy with torsion in this second lecture of a comprehensive minicourse. Delve into advanced mathematical concepts as Mario Garcia Fernandez from ICMAT, Spain, presents sophisticated theoretical frameworks that bridge algebraic structures with geometric properties. Learn how vertex algebras, fundamental objects in mathematical physics and representation theory, relate to special holonomy groups in the presence of torsion, a topic at the forefront of modern differential geometry and string theory. Examine the mathematical foundations that underpin these relationships, including the role of torsion in modifying classical holonomy theory and how vertex algebraic structures emerge in geometric contexts. Discover applications to supersymmetric field theories, exceptional holonomy manifolds, and the geometric interpretation of conformal field theory. This lecture forms part of the 8th edition of "Geometry in Algebra, Algebra in Geometry" workshop at IMPA, designed to foster interdisciplinary research at the interface between algebraic and geometric mathematics, making it valuable for researchers and graduate students working in differential geometry, algebraic topology, mathematical physics, and related fields.