Analytic, Algebraic and Geometric Aspects of Differential Equations : Będlewo, Poland, September 2015 / edited by Galina Filipuk, Yoshishige Haraoka, Sławomir Michalik.

Format:

Book

Contributor:

Filipuk, Galina., Editor.

Haraoka, Yoshishige., Editor.

Michalik, Sławomir., Editor.

Series:

Trends in Mathematics, 2297-024X

Language:

English

Subjects (All):

Differential equations.

Geometry, Differential.

Mathematical physics.

Number theory.

Differential Equations.

Differential Geometry.

Mathematical Physics.

Number Theory.

Local Subjects:

Differential Equations.

Differential Geometry.

Mathematical Physics.

Number Theory.

Physical Description:

1 online resource (VIII, 471 p. 32 illus., 14 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.

Summary:

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.

Contents:

Preface

An introduction to Dunkl theory and its analytic aspects

Holonomic Systems

Sub-Riemannian geometry and hypoelliptic operators

Asymptotic analysis and summability of formal power series

WKB analysis and Stokes geometry of differential equations

Transcendental Meromorphic Solutions of P34 and Small Targets

Towards the convergence of generalized power series solutions of algebraic ODEs

Connection problem for regular holonomic systems in several variables

On k-summability of formal solutions for certain higher order partial differential operators with polynomial coefficients

On Stokes phenomena for the alternate discrete PI equation

Flat structures and algebraic solutions to Painlevé VI equation

Relation of Semi-classical orthogonal polynomials to General Schlesinger systems via Twistor theory

Some notes on the multi-level Gevrey solutions of singularly perturbed linear partial differential equations

Reducibility of hypergeometric equations

Parametric Borel summability of partial differential equations of irregular singular type.

ISBN:

3-319-52842-4