Conformal blocks through Mode Transition Algebras
Speaker:
Chiara Damiolini, University of Texas at Austin
Date and Time:
Friday, March 22, 2024 - 10:15am to 11:00am
Location:
Fields Institute, Room 230
Abstract:
Vertex operator algebras (VOAs) and their modules define sheaves of conformal blocks over the moduli space of stable curves. In today's talk I will describe how we can study the properties of a VOA, and their conformal blocks, through a family of associative algebras associated with it, which we call Mode Transition Algebras(MTAs). As Angela has discussed in her talk, these algebras are a valuable tool to understand the representation theory of V. In my talk I will describe how degeneration of conformal blocks to nodal curves---behavior which is not fully understood for non-rational VOAs---can be translated into intrinsic properties of the MTAs. This is based on a joint work with A. Gibney and D. Krashen.