Speaker: Swarnava Mukhopadhyay
Date: May 29, 2025
Affiliation: TIFR, Mumbai

Abstract: Given a complex vector space $V$ with a non-degenerate bilinear form and a choice of orthonormal basis $\{e_i\}$, we can try to decorate $V$ with the structure of an associative, commutative algebra. The naive approach is by assigning structure constant $\{\Phi_{i,j,k}\}$ for a multiplication $\ast$, namely $e_i\ast e_j=\sum \Phi_{i,j,k}e_k$ such that $\ast$ is commutative and associative. These impose several relations between the structure constants, which we will refer to as associativity constraints. In this talk we will discuss a recipe on how to resolve these associativity constraints using some formalisms from topology. We will focus on one particular example and discuss how the above formalism can be used to solve another question arising in a different context.