5 papers
Chewing gums, snakes and candle cakes
Benedetta Facciotti, Marta Mazzocco, Nikita Nikolaev
The aim of these lecture notes, based on lectures given by the second author at the CIME school in Cetraro, is to illustrate a range of ideas surrounding higher Teichmuller spaces…
Decorated Local Systems and Character Varieties
Benedetta Facciotti, Marta Mazzocco, Nikita Nikolaev
The focus of this paper is the study of the moduli space of representations of fundamental groupoids of surfaces with boundaries with values in . In absenc…
Resurgence of Tritronquées Solutions of the Deformed Painlevé I Equation
Mohamad Alameddine, Olivier Marchal, Nikita Nikolaev +1
We prove that the formal -power series solution of the deformed Painlevé I equation is resurgent, which means it is generically Borel summable and its Borel transform admit…
An Exact Perturbative Existence and Uniqueness Theorem
Nikita Nikolaev
We investigate singularly perturbed nonlinear complex differential systems of the form where is a small complex perturbation paramete…
Geometry and Resurgence of WKB Solutions of Schrödinger Equations
Nikita Nikolaev
We prove that formal WKB solutions of Schrödinger equations on Riemann surfaces are resurgent. Specifically, they are Borel summable in almost all directions and their Borel trans…