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Stokes Phenomenon and Isomonodromy Equations
Last Updated: 2026-02-05 15:41:20
Abstract
Ordinary differential equations with irregular singularities, Stokes phenomenon, isomonodromy deformations and appications.
Content
This seminar is about the study of ordinary differential equations with poles and its application in mathematical physics. When a system of differential equations has an irregular singularity, such as a pole of order two or higher, a solution may fail to have a well-defined asymptotic expansion at the singular locus. Instead, there is a collection of angular sectors surrounding the singular locus, in each of which an asymptotic expansion is defined. The existence of such sectorial asymptotic expansions is what is called the “Stokes phenomenon”. The Stokes phenomenon has found remarkable applications in different areas of mathematics and physics, such as in cohomological field theory, the study of stability conditions, noncommutative Hodge theory, cluster algebras, quantum groups and so on. In particular, the Stokes phenomenon is the essential ingredient in an irregular version of the Riemann-Hilbert correspondence, where the moduli space of differential equations with irregular singularities is described in terms of its associated generalized monodromy data (Stokes matrices). Moreover, the crucial role of the Stokes phenomenon in the study of representation theory and integrable systems is only beginning to emerge. The first 9 talks will include a general introduction to Stokes phenomenon and isomonodromy deformation. The last 3 talks of the seminar will focus on its applications.
Resources
Literature
Werner Balser, Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations, Chapter 1-9, Springer. P. Boalch, Stokes matrices, Poisson Lie groups and Frobenius manifolds, Invent. Math. 146 (2001), 479–506. P. Boalch, G-bundles, isomonodromy and quantum Weyl groups, Int. Math. Res. Not. (2002), no. 22, 1129–1166. B. Dubrovin, Geometry of 2d topological field theory, Lecture 1-3, https://arxiv.org/pdf/hep-th/9407018.pdf . B. Dubrovin, Painleve transcendents in two-dimensional topological field theory, The Painleve property, Springer, New York, 1999, pp. 287–412.
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- ungraded semester performance
Registration & Places
- Signup Start
- 06.01.2020
- Signup End
- 03.02.2020
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| seminar |
Stokes Phenomenon and Isomonodromy Equations
Does not take place this semester.
|
No time listed | 2 h weekly |
Offered In
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Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and afterwards choose an alternative seminar.)
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Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and afterwards choose an alternative seminar.)
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