This is a traditional conference celebrating the collaboration between many institutes in USA, Latin America, Asia and Europe included in the Institute of the Mathematical Sciences of the Americas Consortium (IMSAC). The event is jointly organized by the International Centre for Mathematical Sciences (ICMS-Sofia) at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, and the Institute for the Mathematical Sciences of the Americas (IMSA) at the University of Miami.

Analysis on loop spaces, motivated by ideas from conformal field theory, leads naturally to the construction of elliptic genera—topological invariants with deep modular and representation-theoretic properties.

I will present known and new polynomials emerging from the extremal problems of geometric complex analysis.

In this lecture, I will explore some connections between elliptic genera and analysis on loop spaces. Building on classical work in cobordism and modular forms, we'll examine how the structure of the free loop space influences elliptic genus invariants.