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This is a two-day workshop on Integrability and Analysis of Partial Differential Equations. The meeting will take place face-to-face on 4-5 July, 2022 at the University of Essex (Colchester) and it will also broadcast through zoom for virtual participants.
In the last 50 years many interesting and deep developments have occurred in the field of Partial Differential Equations (PDEs). For example, the discovery of the Inverse Scattering Transform for the Korteweg-de Vries equation was the starting point for the modern theory of integrable systems. Many integrable PDEs were discovered since then, and their connections with other fields of mathematics (such as algebra and geometry) is an active field of research. Broadly speaking, an integrable system is a nonlinear system which admits many conserved quantities and exact solutions, which can be constructed using hidden symmetries of the equation. The graph of such an exact solution (2-soliton solution at t=0) of an integrable PDE, the KP equation, is shown in the picture. The first day of the meeting will focus on the study of such integrable PDEs.
Solvability of the Dirichlet for Laplacian is an old problem and (probably) the first work is due to G. Green (1828). Since then this problem has been studied in various type of domains including Lipschitz and non-tangentially accessible domains with Ahlfors regular boundaries and for many other PDEs. Although the Neumann problem is relatively new, it has also been extensively studied in various settings for many PDEs. The second day of the workshop will focus on different aspect of analysis of PDEs including solvability of Dirichlet and Neuman problems for certain PDEs in rough settings.
We are very excited to bring researchers in PDEs together in this two-day meeting. The aim of this event is to motivate discussions that would lead to fruitful connections between different approaches in the study of PDEs. We hope this meeting will inspire new collaborations and build bridges between the participants. This workshop is part of the activities of the Analysis and Mathematical Physics group of the Department of Mathematical Sciences at the University of Essex.
There will be limited fund for travel and accommodation to support PhD students, Postdoctoral researcher, and early career researcher to participate in the workshop. Please fill the form in the Registration tab. The deadline for funding is 31st of May, 2022.
Speakers:
Murat Akman (University of Essex)
Claire Gilson (University of Glasgow)
Rod Halburd (University College London)
Linhan Li (University of Minnesota/University of Edinburgh)
Andrew Morris (University of Birmingham)
George Papamikos (University of Essex)
Maria Carmen Reguera (University of Birmingham)
Benoit Vicedo (University of York)
Organizers: Murat Akman (murat.akman@essex.ac.uk) and George Papamikos (g.papamikos@essex.ac.uk).
This workshop is supported by the London Mathematical Society Scheme 9 Grant and by the Department of Mathematical Sciences of the University of Essex.
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