[Seminar] "Borel Summability of WKB Solutions for Higher-Order Equations" by Nikita Nikolaev

*This is not a general audience TSVP Talk*

Discussion seminar, 2pm in L5EF06

Speaker: Nikita Nikolaev

Title: Borel Summability of WKB Solutions for Higher-Order Equations

Abstract: I will explain in some detail my recent proof of Borel summability of WKB solutions of singularly perturbed higher-order linear ODEs. The proof consists of reducing the problem to a matrix Riccati differential equation in a standard form. Applying the Borel transform, we get a nonlinear PDE which we solve using the method of successive approximations. The biggest challenge is to show that this solution can be analytically continued along a ray in the Borel plane, and this involves keeping track of an interesting Stokes phenomenon.

This seminar is a part of the first TSVP Thematic Program "Exact Asymptotics: From Fluid Dynamics to Quantum Geometry" (https://groups.oist.jp/tsvp/exact-asymptotics). OIST students and researchers are welcome to participate in all scientific sessions of the program without registration.

List and profiles of program participants can be found here: https://groups.oist.jp/tsvp/23ea-program-participants