Speaker
Description
The concepts of jet scheme and arc space over an algebraic variety were introduced by John Nash in his 1968 preprint on singularities. In the last two decades, many exciting new discoveries have connected arc and jet algebras with the theory of partitions, modular forms, and algebraic geometry. Arc algebras/spaces have recently acquired increased interest within the field of vertex algebra, primarily due to their significance in the context of 4d/2d dualities in physics.
In my talk, we will focus on n-jet algebras and arc algebras that are relevant to representations of vertex algebras. We also explain how approaches rooted in vertex (super)algebras, particularly through the notion of "classical freeness" of vertex algebra and modules, offer effective solutions to the problem of determining Hilbert series of arc algebras in some cases.
Several parts of this talk are based on a joint work with H. Li.
