Harini Desiraju

Irregular SLE Martingales and isomonodromic deformations

Schramm–Loewner Evolutions (SLE_κ) form a one-parameter family of conformally invariant random interfaces arising as scaling limits of critical statistical physics models. SLEs are deeply linked to integrability; Dubédat showed that for κ=4, certain martingales — central to the analysis of observables in dimer models — can be constructed using isomonodromic deformations in the presence of simple poles. In this talk I will first review Dubédat’s construction and then describe its extension to the setting of isomonodromic deformations with irregular singularities (higher order poles). I will conclude by motivating potential applications of the resulting “irregular” martingales.