Eveliina Peltola

I describe a method for solving Benoit & Saint-Aubin partial differential equations,
that is, PDEs which arise in conformal field theory (CFT) and in the theory of
Schramm-Loewner evolutions (SLE). An important feature of our method is
the systematic construction of solutions with boundary conditions given by
specified asymptotic behavior. This allows one to explicitly find particular solutions,
such as conformal blocks, multiple SLE pure partition functions,
and chordal SLE boundary visit (zig-zag) probability amplitudes.
Our method is a correspondence associating vectors in a tensor product representation
of a quantum group to Coulomb gas type integral functions, in which properties
of the functions are encoded in natural, representation theoretical properties of the vectors.
I discuss the core idea of the method and applications to SLE and CFT.
The talk is based on joint work with Kalle Kytölä (Aalto University, Espoo) and Steven Flores (University of Helsinki).