Abstract

In recent years, twistor theory has found novel applications within Donaldson-Thomas theory, particularly in the study of Joyce structures associated with CY3 categories. Among the most well-understood examples of Joyce structures are those linked to Painlevé equations and, more broadly, to isomonodromic deformation equations. These equations are central to the theory of nonlinear special functions, and have been a cornerstone of mathematical physics for the past century. Recent breakthroughs have sparked renewed interest in the subject. In this talk, I will introduce the fundamental concepts of isomonodromic deformations and the associated tau functions. Emphasis will be placed on the emerging perspective of isomonodromic tau functions as generating functions for the Riemann-Hilbert symplectomorphism, highlighting recent advances and their implications for the field.