CRM: Centro De Giorgi
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Asymptotic and computational aspects of complex differential equations

Partially supported by GNFM-INdAM and SISSA, Trieste

13 February 2017 - 17 February 2017


Differential equations appear naturally in many areas of mathematics and mathematical physics. Special functions which solve some differential equations have a long and remarkable history and they attract a lot of attention nowadays. For instance, the Painleve’ equations are the core of modern special function theory and find applications in mathematical physics, integrable system, enumerative geometry, Frobenius manifolds, evolutionary PDEs, Random Matrix theory.

The objective of the workshop is to bring together the leading experts in differential equations in the complex domain, special functions, summability theory, asymptotic analysis, isomonodromy deformations and Riemann-Hilbert problems, in order to discuss recent progresses and open questions. Some lectures will be general overviews for young researchers. Moreover, some talks will be devoted to applications, particularly the analytic theory of Frobenius manifolds and Quantum Cohomology. The participants will learn new methods in the related areas and identify new topics for future research. It is expected that the workshop will be an excellent opportunity to promote existing and start new collaborations between the participants.

Research Directions

There are a lot of open problems in the area related to the workshop program, which we plan to explore during the workshop. In particular, we are interested in concrete computational aspects of the theory of solving complex differential equations and linear systems. These problems and many others are important to the development of the theory of differential equations and will have a substantial impact. The proposed workshop is, therefore, interesting, timely and necessary for the overall progress in differential equations and special functions.

The topic will include: