16 citations · 39 across the 10 of their papers we have counts for
11 papers
The WKB Riemann-Hilbert Problem for the Painlevé I System
Mohamad Alameddine, Olivier Marchal, Nikita Nikolaev +1
In this paper, we solve the direct monodromy problem for the Borel-summed -parameter solution of Painlevé~I. Using the auxiliary time equation, we first construct formal WKB wav…
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 absence…
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 admits…
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 transf…
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…
Gevrey Asymptotic Implicit Function Theorem
Nikita Nikolaev
We prove an Asymptotic Implicit Function Theorem in the setting of Gevrey asymptotics with respect to a parameter. The unique implicitly defined solution admits a Gevrey asymptotic…
Existence and Uniqueness of Exact WKB Solutions for Second-Order Singularly Perturbed Linear ODEs
Nikita Nikolaev
We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include the one-dimension…
Exact Solutions for the Singularly Perturbed Riccati Equation and Exact WKB Analysis
Nikita Nikolaev
The singularly perturbed Riccati equation is the first-order nonlinear ODE in the complex domain where is a small complex parameter. We…
Triangularisation of Singularly Perturbed Logarithmic Differential Systems of Rank 2
Nikita Nikolaev
We study singularly perturbed linear systems of rank two of ordinary differential equations of the form , with a regul…
Abelianisation of Logarithmic -Connections
Nikita Nikolaev
We prove a functorial correspondence between a category of logarithmic -connections on a curve with fixed generic residues and a category of abelian logarithmi…